Multi-view data clustering method and device, equipment and storage medium

Abstract

The embodiment of the invention provides a clustering method and device of multiple view data, equipment and a storage medium, and relates to the technical field of data processing. The method comprises the following steps: acquiring view data corresponding to a plurality of views, projecting the corresponding view data to a low-dimensional space based on a projection matrix of the view for each view to obtain a subspace representation matrix and an error matrix, and calculating to obtain local total information according to the subspace representation matrix and a weight matrix, and constructing an optimization target item according to the nuclear norm of the subspace representation matrix, the preset norm of the error matrix and the local total information, solving an optimization target function to obtain a representation optimization matrix corresponding to each view, and performing data clustering according to all the representation optimization matrixes to obtain at least one clustering result. In the dimension reduction process, subspace representation is synchronously carried out, in the process of optimizing the target function, mutual promotion and co-evolution of the projection matrix and the subspace representation matrix are achieved, the accuracy of subspace representation is improved, and the clustering quality is improved.

Description

Technical Field

[0001] The present application relates to the field of data processing technology, and in particular to a method, apparatus, device, and storage medium for clustering multiple view data. Background Art

[0002] In the customer to factory (C2F) manufacturing model, it is often necessary to use the multi-view clustering (MVC) method to integrate data from multiple different views and obtain multimodal data to meet the processing needs of flexible manufacturing systems.

[0003] In related technologies, the MVC method usually adopts the strategy of first reducing the dimensionality of the data and then learning the corresponding subspace representation to reduce the interference of noise and redundant information in high-dimensional data on the clustering results. Although this method can reduce redundant information through dimensionality reduction, it will lose subtle structural information, resulting in a decrease in the final clustering performance. In addition, there is also a method of directly conducting a representation learning process based on the original data, and then using low-rank constraints to reduce redundancy and retain global structural information. However, this method ignores the local information contained in the data and cannot fully capture the complex correlations between different data, which in turn causes the clustering results to deviate from the actual data distribution. Summary of the Invention

[0004] The main purpose of the embodiments of the present application is to provide a method, apparatus, device, and storage medium for clustering multiple view data, thereby improving the accuracy of clustering results of the multiple view data.

[0005] To achieve the above-mentioned objective, a first aspect of an embodiment of the present application proposes a clustering method for multiple view data, comprising: Get the view data corresponding to multiple views; For each of the views, based on a projection matrix of the view, project the corresponding view data into a low-dimensional space to obtain a subspace representation matrix and an error matrix, obtain a weight matrix based on a product of a transposed matrix of the view data and the view data, and calculate local structure information based on the subspace representation matrix and the weight matrix; Accumulating each piece of the local structural information to obtain local total information, constructing an optimization objective term for each of the views based on the nuclear norm of the subspace representation matrix, the preset norm of the error matrix, and the local total information, and obtaining a constraint condition for the optimization objective term based on the view data, the projection matrix, the subspace representation matrix, and the error matrix; Obtaining an optimization objective function according to the constraint conditions and the corresponding optimization objective items, and solving the optimization objective function to obtain a representation optimization matrix corresponding to each of the views; Data clustering is performed according to all the representation optimization matrices to obtain at least one clustering result.

[0006] In some embodiments, constructing an optimization objective term based on the nuclear norm of the subspace representation matrix, the preset norm of the error matrix, and the local total information includes: Obtaining a reference subspace representation matrix corresponding to each of the subspace representation matrices, wherein a view of the reference subspace representation matrix is ​​different from that of the subspace representation matrix; Calculating a diversity matrix according to the reference subspace representation matrix corresponding to the subspace representation matrix, and accumulating all the diversity matrices to obtain the diversity constraint information; An optimization objective item is constructed according to the nuclear norm of the subspace representation matrix, the preset norm of the error matrix, the local total information and the diversity constraint information.

[0007] In some embodiments, obtaining the constraint condition of the optimization objective term according to the view data, the projection matrix, the subspace representation matrix, and the error matrix includes: taking the product of the transposed matrix of the projection matrix and the view data as a first data item, multiplying the first data item by the subspace representation matrix, and then adding the error matrix to obtain a second data item, setting the first data item and the second data item to be equal to obtain a first constraint condition; Setting the subspace representation matrix to be not less than zero, thereby obtaining a second constraint condition; Taking the product of the transposed matrix of the view data and the projection matrix as a third data item, setting the product of the first data item and the third data item as an identity matrix, and obtaining a third constraint condition; The constraint condition is obtained according to the first constraint condition, the second constraint condition and the third constraint condition.

[0008] In some embodiments, solving the optimization objective function to obtain a representation optimization matrix corresponding to each view includes: The subspace representation matrix is ​​replaced by the auxiliary matrix corresponding to each of the views to obtain an updated nuclear norm, and a fourth constraint condition is added to the constraint condition, setting the corresponding auxiliary matrix equal to the subspace representation matrix; The optimization objective function is adjusted according to the updated nuclear norm and the updated constraint condition to obtain an optimization objective update function, the constraint condition is added to the optimization objective update function to obtain an augmented Lagrangian function, and the augmented Lagrangian function is solved to obtain a representation optimization matrix corresponding to each of the views.

[0009] In some embodiments, adding the constraint condition to the optimization objective update function to obtain an augmented Lagrangian function includes: Obtaining a diagonal matrix of the weight matrix, obtaining a difference matrix between the diagonal matrix and the weight matrix, obtaining a first matrix trace according to the diagonal matrix, the difference matrix, and the weight matrix, and obtaining the local structure information according to the first matrix trace; Obtaining a second matrix trace according to the subspace representation matrix and the corresponding reference subspace representation matrix, and obtaining the diversity matrix according to the second matrix trace; For each of the views, the augmented Lagrangian function corresponding to the optimization objective update function is obtained at least based on the updated nuclear norm, the preset norm, the first matrix trace, the diversity matrix, the subspace representation matrix, the error matrix, the projection matrix, the auxiliary matrix, the first Lagrangian multiplier and the second Lagrangian multiplier, and the constraint condition of the augmented Lagrangian function is the third constraint condition.

[0010] In some embodiments, solving the augmented Lagrangian function to obtain a representation optimization matrix corresponding to each view includes: For each of the views, obtaining update functions corresponding to solution parameters according to the augmented Lagrangian function, and alternately updating the solution parameters according to the update functions, where the solution parameters include at least the projection matrix, the subspace representation matrix, the auxiliary matrix, the error matrix, the first Lagrangian multiplier, and the second Lagrangian multiplier; The updating process is performed at least once until a preset convergence condition is satisfied, and the subspace representation matrix updated last is used as the representation optimization matrix.

[0011] In some embodiments, when the solution parameter is the projection matrix, obtaining update functions corresponding to the solution parameters according to the augmented Lagrangian function, and alternately updating the solution parameters according to the update functions, includes: Obtaining projection data items related to the projection matrix from the augmented Lagrangian function; Obtaining the update function of the projection matrix according to the projection data item, and calculating the gradient of the update function with respect to the projection matrix to obtain a gradient function; A manifold optimization solution is performed according to the update function and the gradient function to obtain an updated projection matrix.

[0012] In some embodiments, when the solution parameter is the subspace representation matrix, obtaining update functions corresponding to the solution parameters according to the augmented Lagrangian function, and alternately updating the solution parameters according to the update functions, includes: Obtaining at least one representation matrix data item related to the subspace representation matrix from the augmented Lagrangian function; Obtaining a first partial derivative of the representation matrix data item with respect to the subspace representation matrix, accumulating the first partial derivative to obtain an accumulated data item, setting the accumulated data item equal to zero, and obtaining the update function corresponding to the subspace representation matrix; A matrix solution is performed on the update function to obtain an updated subspace representation matrix.

[0013] In some embodiments, when the solution parameter is the auxiliary matrix, obtaining update functions corresponding to the solution parameters according to the augmented Lagrangian function, and alternately updating the solution parameters according to the update functions, includes: Obtaining auxiliary data items related to the auxiliary matrix from the augmented Lagrangian function; Obtaining a second partial derivative of the auxiliary data item with respect to the auxiliary matrix, setting the second partial derivative equal to zero, and obtaining the update function corresponding to the auxiliary matrix; The update function is solved using a singular value threshold to obtain the updated auxiliary matrix.

[0014] In some embodiments, when the solution parameter is the error matrix, obtaining update functions corresponding to the solution parameters according to the augmented Lagrangian function, and alternately updating the solution parameters according to the update functions, includes: Obtaining error data items related to the error matrix from the augmented Lagrangian function; Obtaining a third partial derivative of the error data item with respect to the error matrix, setting the third partial derivative equal to zero, and combining with a shrinkage operator to obtain the update function corresponding to the error matrix; The update function is solved to obtain the updated error matrix.

[0015] In some embodiments, when the solution parameter is the first Lagrangian multiplier or the second Lagrangian multiplier, obtaining update functions corresponding to the solution parameters according to the augmented Lagrangian function, and alternately updating the solution parameters according to the update functions, includes: acquiring, from the augmented Lagrangian function, a first multiplier data item associated with the first Lagrangian multiplier or a second multiplier data item associated with the second Lagrangian multiplier; Obtaining a fourth partial derivative of the first multiplier data item with respect to the first Lagrange multiplier, or a fifth partial derivative of the second multiplier data item with respect to the second Lagrange multiplier; Setting the fourth partial derivative equal to zero to obtain the update function corresponding to the first Lagrange multiplier, or setting the fifth partial derivative equal to zero to obtain the update function corresponding to the second Lagrange multiplier; The update function is solved to obtain the updated first Lagrangian multiplier or the second Lagrangian multiplier.

[0016] In some embodiments, clustering data according to all the representation optimization matrices to obtain at least one clustering result includes: Calculating an average representation matrix corresponding to all the representation optimization matrices; Perform spectral clustering on the average representation matrix to obtain at least one clustering result.

[0017] To achieve the above-mentioned purpose, a second aspect of an embodiment of the present application provides a device for clustering multiple view data, including: Data acquisition module: used to obtain view data corresponding to multiple views; a projection calculation module configured to project the corresponding view data into a low-dimensional space based on the projection matrix of each view to obtain a subspace representation matrix and an error matrix, obtain a weight matrix based on the product of the transposed matrix of the view data and the view data, and obtain local structure information based on the subspace representation matrix and the weight matrix; an optimization target construction module configured to accumulate each piece of the local structural information to obtain local total information, construct an optimization target item for each view based on the nuclear norm of the subspace representation matrix, the preset norm of the error matrix, and the local total information, and obtain constraints for the optimization target item based on the view data, the projection matrix, the subspace representation matrix, and the error matrix; Optimization solution module: used for obtaining an optimization objective function according to the constraint conditions and the corresponding optimization objective items, and solving the optimization objective function to obtain a representation optimization matrix corresponding to each view; Clustering module: used for performing data clustering according to all the representation optimization matrices to obtain at least one clustering result.

[0018] To achieve the above-mentioned purpose, the third aspect of an embodiment of the present application proposes an electronic device, which includes a memory and a processor, wherein the memory stores a computer program, and the processor implements the method described in the first aspect when executing the computer program.

[0019] To achieve the above-mentioned purpose, the fourth aspect of the embodiment of the present application proposes a storage medium, which is a storage medium. The storage medium stores a computer program, and when the computer program is executed by a processor, the method described in the first aspect is implemented.

[0020] The present invention proposes a method, apparatus, device, and storage medium for clustering multiple view data. The method obtains view data corresponding to multiple views and, for each view, projects the corresponding view data into a low-dimensional space based on the view's projection matrix to obtain a subspace representation matrix and an error matrix. A weight matrix is ​​then obtained by multiplying the view data's transpose matrix and the view data. Local structure information is then calculated based on the subspace representation matrix and the weight matrix. Local total information is then accumulated based on each piece of local structure information. For each view, an optimization objective is constructed based on the nuclear norm of the subspace representation matrix, a preset norm of the error matrix, and the local total information. Constraints for the optimization objective are obtained based on the view data, the projection matrix, the subspace representation matrix, and the error matrix. An optimization objective function is obtained based on the constraints and the corresponding optimization objective. The optimization objective function is solved to obtain a representation optimization matrix corresponding to each view. Finally, data is clustered based on all the representation optimization matrices to obtain at least one clustering result. The present invention utilizes a projection matrix to perform dimensionality reduction on the view data and simultaneously performs subspace representation during the dimensionality reduction process. Given that different projection methods will cause data to present different spatial representations in low-dimensional space, the embodiments of the present application combine the two. In the process of optimizing the objective function, the projection matrix and the subspace representation matrix promote each other and evolve together, thereby finding the best projection that best matches the original feature space for each view data, maximizing the retention of key information related to tasks such as clustering in each view, preventing excessive information loss, and ensuring that the representation of data in low-dimensional space can accurately reflect its essential characteristics in the original high-dimensional space, thereby improving the accuracy of subspace representation and ultimately improving clustering quality. In addition, adding local total information during the optimization process aims to preserve the data structure of the data itself, which can effectively enhance the clustering performance of high-dimensional data. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 This is a flowchart of a method for clustering multiple view data provided by an embodiment of the present application.

[0022] Figure 2It is a flowchart provided by an embodiment of the present application for constructing an optimization target item based on the nuclear norm of the subspace representation matrix, the preset norm of the error matrix and the local total information.

[0023] Figure 3 This is a flowchart of an embodiment of the present application for obtaining the constraint conditions of the optimization target item based on view data, projection matrix, subspace representation matrix and error matrix.

[0024] Figure 4 This is a flowchart of solving the optimization objective function to obtain the corresponding optimization matrix for each view provided by an embodiment of the present application.

[0025] Figure 5 This is a flowchart of an embodiment of the present application for adding constraints to an optimization objective update function to obtain an augmented Lagrangian function.

[0026] Figure 6 A flowchart of solving the augmented Lagrangian function to obtain the representation optimization matrix corresponding to each view provided in an embodiment of the present application.

[0027] Figure 7 A flowchart of an embodiment of the present application for obtaining update functions corresponding to solution parameters according to an augmented Lagrangian function, and alternately updating the solution parameters according to the update functions.

[0028] Figure 8 Another flowchart provided in an embodiment of the present application is for obtaining update functions corresponding to solution parameters according to the augmented Lagrangian function, and alternately updating the solution parameters according to the update functions.

[0029] Figure 9 Another flowchart provided in an embodiment of the present application is for obtaining update functions corresponding to solution parameters according to the augmented Lagrangian function, and alternately updating the solution parameters according to the update functions.

[0030] Figure 10 Another flowchart provided in an embodiment of the present application is for obtaining update functions corresponding to solution parameters according to the augmented Lagrangian function, and alternately updating the solution parameters according to the update functions.

[0031] Figure 11 Another flowchart provided in an embodiment of the present application is for obtaining update functions corresponding to solution parameters according to the augmented Lagrangian function, and alternately updating the solution parameters according to the update functions.

[0032] Figure 12 This is a schematic diagram of the overall process of the clustering method for multiple view data provided in an embodiment of the present application.

[0033] Figure 13This is a structural block diagram of a device for clustering multiple view data provided by another embodiment of the present application.

[0034] Figure 14 This is a schematic diagram of the hardware structure of the electronic device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0035] In order to make the purpose, technical solutions and advantages of this application more clearly understood, the following further describes this application in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain this application and are not intended to limit this application.

[0036] It should be noted that although the functional modules are divided in the device schematic and the logical order is shown in the flowchart, in some cases, the steps shown or described can be performed in a different order than the module division in the device or the order in the flowchart.

[0037] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the art to which this application pertains. The terms used herein are for the purpose of describing the embodiments of this application only and are not intended to limit this application.

[0038] Industrial data has the characteristics of diverse sources, high dimensionality, heterogeneity and noise. Reasonable integration and classification of industrial data can provide strong support for the intelligent optimization of manufacturing processes.

[0039] In the customer-to-factory (C2F) manufacturing model, data often originates from multiple different views. Given that each view provides specific information, multi-view clustering (MVC) methods are often employed to integrate data from these multiple views. This effectively leverages the complementary and integrated information from these multiple views to improve clustering performance. This approach enables real-time analysis of the similarities between multimodal data during the production process, enabling intelligent scheduling and decision-making for production plans to meet the processing requirements of flexible manufacturing systems.

[0040] In related technologies, the MVC method usually adopts the strategy of first reducing the dimensionality of the data and then learning the corresponding subspace representation to reduce the interference of noise and redundant information in high-dimensional data on the clustering results. Although this method can reduce redundant information through dimensionality reduction, it will lose subtle structural information, resulting in a decrease in the final clustering performance. In addition, there is also a method of directly conducting a representation learning process based on the original data, and then using low-rank constraints to reduce redundancy and retain global structural information. However, this method ignores the local information contained in the data and cannot fully capture the complex correlations between different data, which in turn causes the clustering results to deviate from the actual data distribution.

[0041] Based on this, the embodiment of the present application provides a clustering method, device, equipment and storage medium for multiple view data, which uses a projection matrix to perform dimensionality reduction operations on the view data, and simultaneously performs subspace representation during the dimensionality reduction process. In view of the fact that different projection methods will cause the data to present different spatial representations in the low-dimensional space, the embodiment of the present application combines the two. In the process of optimizing the objective function, the projection matrix and the subspace representation matrix promote each other and co-evolve, thereby finding the best projection that best matches the original feature space for each view data, maximally retaining the key information related to tasks such as clustering in each view, preventing excessive information loss, and ensuring that the representation of the data in the low-dimensional space can accurately reflect its essential characteristics in the original high-dimensional space, thereby improving the accuracy of the subspace representation and ultimately improving the clustering quality. In addition, the addition of local total information during the optimization process is intended to retain the data structure of the data itself, so that the clustering performance of high-dimensional data can be effectively enhanced.

[0042] The embodiments of the present application provide a method, apparatus, device, and storage medium for clustering multiple view data, which are specifically described through the following embodiments. First, the method for clustering multiple view data in the embodiments of the present application is described.

[0043] The clustering method for multiple view data provided in the embodiment of the present application relates to the field of data processing technology. The clustering method for multiple view data provided in the embodiment of the present application can be applied in a terminal, can also be applied in a server, and can also be a computer program running in a terminal or a server. For example, the computer program can be a native program or software module in the operating system; it can be a native application (APP), that is, a program that needs to be installed in the operating system to run, such as a client that supports clustering of multiple view data, that is, a program that only needs to be downloaded to a browser environment to run; it can also be a small program that can be embedded in any APP. In short, the above-mentioned computer program can be an application, module or plug-in in any form. Among them, the terminal communicates with the server through a network. The clustering method for multiple view data can be executed by the terminal or the server, or by the terminal and the server in collaboration.

[0044] In some embodiments, the terminal may be a smartphone, tablet computer, laptop computer, desktop computer, or smartwatch. The server may be a standalone server or a cloud server providing basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communications, middleware services, domain name services, security services, content delivery networks (CDNs), and big data and artificial intelligence platforms. Alternatively, the server may be a service node in a blockchain system, where each service node in the blockchain system forms a peer-to-peer (P2P) network. The P2P protocol is an application layer protocol that runs on top of the Transmission Control Protocol (TCP). The terminal and server may be connected via Bluetooth, a Universal Serial Bus (USB), or a network connection, but this embodiment does not impose any limitations thereto.

[0045] The present application can be used in many general or special computer system environments or configurations. For example: personal computers, server computers, handheld or portable devices, tablet devices, multiprocessor systems, microprocessor-based systems, set-top boxes, programmable consumer electronics, network PCs, minicomputers, mainframe computers, distributed computing environments including any of the above systems or devices, and the like. The present application can be described in the general context of computer-executable instructions executed by a computer, such as program modules. Generally, program modules include routines, programs, objects, components, data structures, and the like that perform specific tasks or implement specific abstract data types. The present application can also be practiced in distributed computing environments in which tasks are performed by remote processing devices connected via a communication network. In a distributed computing environment, program modules can be located in local and remote computer storage media, including storage devices.

[0046] The following describes a method for clustering multiple view data in an embodiment of the present application.

[0047] Figure 1 This is an optional flowchart of a method for clustering multiple view data provided in an embodiment of the present application. Figure 1 The method may include but is not limited to steps 110 to 150. It is also understood that this embodiment is Figure 1 The order of steps 110 to 150 is not specifically limited, and the order of steps can be adjusted or some steps can be reduced or added according to actual needs.

[0048] Step 110: Obtain view data corresponding to multiple views.

[0049] In one embodiment, each view data element corresponds to the data captured by the view in which it resides. A matrix structure is used to store the data elements for the corresponding view, with the rows and columns of the matrix representing information of different dimensions. View data herein encompasses various types, including sensor data from different devices, product image features, inventory data, and production parameters. Multiple different view data elements often utilize distinct features to describe the same instance. For example, in industrial manufacturing, sensor data from different devices can constitute corresponding view data. Similarly, for product image features, by organizing the data corresponding to multiple extracted image feature dimensions (such as color and texture), corresponding view data can also be formed.

[0050] Step 120: For each view, based on the projection matrix of the view, the corresponding view data is projected into a low-dimensional space to obtain a subspace representation matrix and an error matrix, and a weight matrix is ​​obtained based on the product of the transposed matrix of the view data and the view data. Local structure information is calculated based on the subspace representation matrix and the weight matrix.

[0051] In one embodiment, assuming the number of views is , at this time, the view data corresponding to each view is projected. The following takes the vth view as an example to illustrate, where, .

[0052] First, get the low-dimensional projection matrix corresponding to the v-th view , then use the projection matrix The view data corresponding to the vth view Projecting to a low-dimensional space to achieve the purpose of dimensionality reduction, the projection process is expressed in the form of a dictionary, then the dictionary at this time is: , and then use the dictionary to learn the subspace representation matrix , thereby automatically reducing the noise and redundancy in the view data.

[0053] At this point, the relationship between the projection matrix, view data, and subspace learning matrix can be expressed as:

[0054] in, represents the error matrix.

[0055] In one embodiment, given that the spatial relationships between different measurement data points play a crucial role in overall analysis when dealing with a large amount of view data, a weight matrix is ​​introduced to characterize the spatial closeness of the measurement data points in the view data. The weight matrix can quantitatively reflect the closeness of the spatial distribution of the measurement data points. For example, when analyzing infrared view data at different locations on the surface of a three-dimensional object, the temperature values ​​of the measurement data points may not be completely consistent with each other. Temperature trends of measurement data points that are closer together are often more similar, and accordingly, their spatial closeness is stronger. Specifically, the weight matrix in this embodiment is obtained by multiplying the view data's transposed matrix by the view data.

[0056] Therefore, the weight matrix Expressed as:

[0057] In one embodiment, since the subspace representation matrix retains the local structure of the view data, the local structure information can be calculated using the subspace representation matrix and the weight matrix. The specific process can be described as follows: First, the index of each element in the subspace representation matrix is ​​represented as {i, j}. This index acts like a coordinate, allowing you to precisely locate a specific element in the matrix. Furthermore, i is set as the first index and j as the second index, achieving ordered identification.

[0058] Next, obtain the subspace representation matrix The first index vector corresponding to the first index i in , and the second index vector corresponding to the second index j When the subspace representation matrix is ​​a two-dimensional matrix, the first index vector It can be regarded as a set of vector values ​​along the row direction of the matrix, and the second index vector It can be viewed as a set of vector values ​​along the column direction.

[0059] Then, we consider that if a pair of measurement data points are close in the view data space, then they should also be close in the subspace representation matrix, i.e. , so the embodiment of the present application calculates the first index vector and the second index vector Vector difference , and further find the vector difference The corresponding vector difference norm value , this vector difference norm value is intended to measure the degree of difference between the two vectors.

[0060] After that, get the first index i and the second index j in the weight matrix The weight coefficient in , after accumulating all weight coefficients, we get the total coefficient , where the weight matrix is ​​calculated from the original feature space and is used to directly describe the local structural relationship between samples. The total coefficient is fixed after calculation. Then the vector difference norm value and the total coefficient Multiply, thereby obtaining the local structural information that characterizes the local structural relationship between the elements in the subspace representation matrix Because the objective function is minimized, the larger the total coefficient is, the smaller the corresponding vector difference is. The smaller it is, the better the measurement data point is. and The closer they are to each other, the higher the probability that they belong to the same category.

[0061] Step 130: Accumulate each local structural information to obtain local total information. For each view, construct an optimization target item based on the nuclear norm of the subspace representation matrix, the preset norm of the error matrix, and the local total information, and obtain the constraint conditions of the optimization target item based on the view data, projection matrix, subspace representation matrix, and error matrix.

[0062] In one embodiment, during the multi-view data clustering process, an optimization objective function is constructed to solve for optimal parameters. Given that the subspace representation matrix can display the distribution of data in different subspaces from a multidimensional perspective, thereby reflecting the inherent structural characteristics of the data; the error matrix is ​​primarily used to measure the degree of deviation between actual data and expected data or model calculation results; and the local structure information reflects information related to the local structure of each view. Therefore, in this embodiment of the application, optimization objective terms are constructed based on at least the subspace representation matrix, the error matrix, and the local total information, and then the optimization objective function is generated by combining the optimization objective terms.

[0063] In one embodiment, during the optimization process, for the subspace representation matrix, it is necessary to calculate the subspace representation matrix of each view. A low-rank constraint is imposed to capture the global structural information of each view data. Therefore, this embodiment uses the subspace representation matrix The low rank constraint is achieved by using the nuclear norm of , where the nuclear norm is defined as the sum of the singular values ​​of the matrix. During the optimization process, the low rank constraint can be achieved by minimizing the nuclear norm.

[0064] Among them, the nuclear norm of the subspace representation matrix is ​​expressed as:

[0065] In one embodiment, during the optimization process, it is also necessary to eliminate noise based on the error matrix, so it is necessary to obtain the error matrix The preset norm of is expressed as:

[0066] in, Indicates the calculation method of the preset norm, which makes the columns of the error matrix sparse, making some columns The norm approaches 0, which can better handle the noise in the column vector. Represents an optimization parameter whose value range is , this parameter is a discrete value, within the range of As an interval to take value, for example { }.

[0067] In one embodiment, each view has its own unique local structural information. Only by integrating this local structural information can the overall data characteristics be more comprehensively presented. For example, when analyzing product images taken from multiple angles, each view contains local structural information regarding the product structure, texture, and other aspects. By accumulating this local structural information from each view, local aggregate information can be obtained that covers the local characteristics of all views. This embodiment of the present application utilizes local aggregate information to grasp the overall data characteristics.

[0068] At this time, the local total information is expressed as:

[0069] In one embodiment, during the optimization process, the local total information is used as a smoothing regularization term in the subsequent optimization objective function. At this time, an adjustment parameter can be introduced: The degree of participation of local total information is adjusted during the optimization process, so the update of local total information is expressed as:

[0070] Among them, the adjustment parameters The value range and optimization parameters consistent.

[0071] According to the above process, the optimization target item corresponding to view v is expressed as:

[0072] In one embodiment, considering that the view data of each view has its own unique information, it is hoped that the similarity matrix of each view can retain as much information of the view as possible. Therefore, a sparsity constraint between views is added to the optimization objective item to make the representation matrices of each subspace as sparse as possible. Figure 2 , Figure 2This is a flowchart of constructing an optimization target item based on the nuclear norm of the subspace representation matrix, the preset norm of the error matrix, and the local total information provided by an embodiment of the present application, specifically including the following steps: Step 210: Obtain a reference subspace representation matrix corresponding to each subspace representation matrix.

[0073] In one embodiment, the view of the reference subspace representation matrix is ​​different from the subspace representation matrix. That is, for the subspace representation matrix corresponding to each view, a cross-view strategy is adopted to select the subspace representation matrix of another view as the reference subspace representation matrix for that view. For example, assume there are three views with images taken from three different perspectives, corresponding to three subspace representation matrices A, B, and C, respectively. Then, for the subspace representation matrix corresponding to A, the subspace representation matrix corresponding to B may be selected as its reference subspace representation matrix, and so on.

[0074] In one embodiment, for the subspace representation matrix For example, its reference subspace representation matrix can be , where v and h are different.

[0075] The purpose of this approach is to use the subspace representation matrices from other views as references to compare and analyze the data structure characteristics of the current view from different perspectives. Because different views often focus on different data features, these differences provide a more comprehensive understanding of the relationships between the subspace representation matrices, providing a richer and more diverse reference basis for subsequent clustering operations, thereby improving the quality of multi-view data processing.

[0076] Step 220: Calculate a diversity matrix based on the reference subspace representation matrix corresponding to the subspace representation matrix, and accumulate all diversity matrices to obtain diversity constraint information.

[0077] In one embodiment, the Hadamard product of the subspace representation matrix and the corresponding reference subspace representation matrix is ​​calculated, and the zero norm of the Hadamard product is calculated to obtain the diversity matrix. Next, all diversity matrices are accumulated to obtain the diversity constraint information.

[0078] Therefore, the diversity matrix is ​​expressed as:

[0079] in, represents the Hadamard product operation, Represents the zero norm.

[0080] The diversity constraint information is expressed as:

[0081] Step 230: Construct an optimization target item according to the nuclear norm of the subspace representation matrix, the preset norm of the error matrix, the local total information and the diversity constraint information.

[0082] In one embodiment, the diversity constraint information obtained according to the above process can be used to update the optimization target item. The updated optimization target item is expressed as:

[0083] Next, describe the constraints corresponding to the optimization objective. Figure 3 , Figure 3 This is a flowchart of obtaining the constraint conditions of the optimization target item based on view data, projection matrix, subspace representation matrix and error matrix provided by an embodiment of the present application, which specifically includes the following steps: Step 310: Take the product of the transposed matrix of the projection matrix and the view data as the first data item, multiply the first data item by the subspace representation matrix, add the error matrix to obtain the second data item, set the first data item and the second data item equal to obtain the first constraint condition.

[0084] In one embodiment, the first constraint is expressed as:

[0085] in, represents the transposed matrix of the projection matrix, represents the first data item, Represents the second data item.

[0086] Step 320: Set the subspace representation matrix to be not less than zero to obtain the second constraint condition.

[0087] In one embodiment, the second constraint is expressed as:

[0088] Step 330: The product of the transposed matrix of the view data and the projection matrix is ​​used as the third data item, and the product of the first data item and the third data item is set to the identity matrix to obtain the third constraint condition.

[0089] In one embodiment, the third constraint is expressed as:

[0090] in, Represents the third data item, Represents the identity matrix of dimension d, where the dimension is set according to the actual situation.

[0091] Step 340: Obtain constraint conditions according to the first constraint condition, the second constraint condition and the third constraint condition.

[0092] In one embodiment, the constraint is expressed as:

[0093] Step 140: Obtain an optimization objective function according to the constraint conditions and the corresponding optimization target items, and solve the optimization objective function to obtain a representation optimization matrix corresponding to each view.

[0094] In one embodiment, under the premise of satisfying the constraints, all optimization objective items are minimized to obtain the optimization objective function. Therefore, the optimization objective function is expressed as:

[0095] It can be seen that the purpose of optimizing the objective function is to minimize the optimization objective item corresponding to each view by adjusting data such as the subspace representation matrix, error matrix, and weight matrix within the constraints of the constraints. In the process of optimizing the objective function in the embodiment of the present application, the redundancy of data and the impact of noise can be effectively reduced, and the data dimensionality reduction and the learning of the coefficient matrix can be integrated into an organic whole, which serves as a basic framework. By using a variable low-dimensional projection matrix, the best projection that best matches the original feature space is explored for each view, thereby promoting the learning process of the subspace representation. Subsequently, the learned subspace representation matrix will in turn serve as feedback information to guide the learning of the projection matrix. During the iterative process, the projection matrix and the subspace representation promote each other and co-evolve, achieving a good situation of mutual promotion and co-evolution between the two, and then finding the best projection that best matches the original feature space for each view data, maximizing the retention of key information related to tasks such as clustering in each view, avoiding excessive information loss, and ensuring that the representation of the data in the low-dimensional space can accurately reflect its essential characteristics in the original high-dimensional space, thereby improving the accuracy of the subspace representation and ultimately improving the clustering quality.

[0096] Next, we describe how to solve the above optimization objective function.

[0097] In one embodiment, referring to Figure 4 , Figure 4 This is a flowchart of solving the optimization objective function to obtain the representation optimization matrix corresponding to each view provided by an embodiment of the present application, which specifically includes the following steps: Step 410: Use the auxiliary matrix corresponding to each view to replace the subspace representation matrix to obtain the updated nuclear norm, and add a fourth constraint condition to the constraint condition to set the corresponding auxiliary matrix equal to the subspace representation matrix.

[0098] In one embodiment, considering that the optimization objective function includes the nuclear norm This will make the optimization objective function non-smooth, causing the optimization problem in the embodiment of this application to become non-convex and difficult to solve directly. The gradient-based optimization method usually used in the optimization process cannot be directly applied. This is because the nuclear norm is not differentiable at certain points, and the gradient of the optimization objective function containing the nuclear norm cannot be directly calculated. Therefore, in the embodiment of this application, for each subspace representation matrix Set an auxiliary matrix To separate the variables, so as to achieve the solution of the alternating iterative process.

[0099] Therefore, the updated nuclear norm is expressed as:

[0100] The fourth constraint is expressed as:

[0101] Step 420: Adjust the optimization objective function according to the updated nuclear norm and the updated constraints to obtain an optimization objective update function, add the constraints to the optimization objective update function to obtain an augmented Lagrangian function, and solve the augmented Lagrangian function to obtain the representation optimization matrix corresponding to each view.

[0102] In one embodiment, the optimization objective update function is expressed as:

[0103] The updated constraints are expressed as:

[0104] In one embodiment, the constraints need to be added to the optimization objective update function to obtain the augmented Lagrangian function. Figure 5 , Figure 5 This is a flowchart of adding constraints to the optimization objective update function to obtain an augmented Lagrangian function, provided by an embodiment of the present application, which specifically includes the following steps: Step 510: Obtain a diagonal matrix of the weight matrix, obtain a difference matrix between the diagonal matrix and the weight matrix, obtain a first matrix trace based on the diagonal matrix, the difference matrix and the weight matrix, and obtain local structure information based on the first matrix trace.

[0105] In one embodiment, in order to facilitate calculation during iteration, local structural information needs to be reconstructed.

[0106] First get the diagonal matrix of the weight matrix , and the diagonal matrix The diagonal elements of Expressed as:

[0107] Get the diagonal matrix and the weight matrix The difference matrix , expressed as:

[0108] Then according to the diagonal matrix , difference matrix and the weight matrix Get the first matrix trace, expressed as:

[0109] Next, the first matrix trace is used to replace the local structure information, and the adjustment parameters are introduced, so the local structure information is expressed as:

[0110] Step 520: Obtain a second matrix trace according to the subspace representation matrix and the corresponding reference subspace representation matrix, and obtain a diversity matrix according to the second matrix trace.

[0111] In one embodiment, to facilitate iterative calculations, it is necessary to rewrite the diversity matrix. The specific operation is as follows: first, obtain the product of the subspace representation matrix and the corresponding reference subspace representation matrix, then calculate the trace of the product result to obtain the second matrix trace. Therefore, the second matrix trace can be expressed as:

[0112] Next, the diversity matrix is ​​replaced by the second matrix trace, so the diversity matrix is ​​expressed as:

[0113] Step 530: For each view, obtain an augmented Lagrangian function corresponding to the optimization objective update function based on at least the updated nuclear norm, the preset norm, the first matrix trace, the diversity matrix, the subspace representation matrix, the error matrix, the projection matrix, the auxiliary matrix, the first Lagrangian multiplier, and the second Lagrangian multiplier.

[0114] In one embodiment, the augmented Lagrangian function is generally used to solve optimization problems with constraints by adding constraints to the objective function and introducing Lagrangian multipliers to handle the constraints. Therefore, the constraints are applied to the optimization objective update function to obtain the augmented Lagrangian function.

[0115] Among them, the augmented Lagrangian function contains at least the projection matrix , subspace representation matrix , auxiliary matrix , error matrix , the first Lagrange multiplier and the second Lagrange multiplier , expressed as .in, is the penalty parameter.

[0116] Specifically, the third constraint condition is used as the constraint condition of the augmented Lagrangian function, and the obtained augmented Lagrangian function is expressed as:

[0117]

[0118] in, is an intermediate parameter, Indicates calculating the Frobenius norm of the correlation matrix.

[0119] In one embodiment, after obtaining the augmented Lagrangian function, a solution calculation is required. Figure 6 , Figure 6 The flowchart provided in the embodiment of the present application for solving the augmented Lagrangian function to obtain the representation optimization matrix corresponding to each view specifically includes the following steps: Step 610: For each view, obtain update functions corresponding to the solution parameters according to the augmented Lagrangian function, and alternately update the solution parameters according to the update functions.

[0120] In one embodiment, the solution parameters in the augmented Lagrangian function include at least the projection matrix , subspace representation matrix , auxiliary matrix , error matrix , the first Lagrange multiplier and the second Lagrange multiplier The specific update process refers to solving each solution parameter. During the solution process, each solution parameter is updated in the order of the solution parameters. When updating a solution parameter, other solution parameters are kept fixed.

[0121] In one embodiment, when the parameter to be solved is the projection matrix, refer to Figure 7 , Figure 7 A flowchart for obtaining update functions corresponding to solution parameters according to the augmented Lagrangian function and alternately updating the solution parameters according to the update functions provided in an embodiment of the present application specifically includes the following steps: Step 710: Obtain projection data items related to the projection matrix from the augmented Lagrangian function.

[0122] In one embodiment, the augmented Lagrangian function is related to the projection matrix The relevant projection data items are:

[0123]

[0124] Step 720: Obtain an update function of the projection matrix according to the projection data item, and calculate the gradient of the update function with respect to the projection matrix to obtain a gradient function.

[0125] In one embodiment, assuming , , based on the constraint terms, the projection data terms are expanded as follows:

[0126] Then, update the function Expressed as:

[0127] Calculate the gradient function of the update function with respect to the projection matrix Expressed as:

[0128] Step 730: Perform manifold optimization solution based on the update function and the gradient function to obtain an updated projection matrix.

[0129] In one embodiment, manifold optimization is an optimization method performed on a nonlinear constraint space (manifold). Its goal is to find the minimum value of an objective function while satisfying specific constraints. Therefore, in this embodiment, the intermediate update function serves as the objective function of manifold optimization, combined with the gradient function for optimization.

[0130] In the manifold optimization process, first select the appropriate initial value of the projection matrix while satisfying the constraints. Then the iterative process is carried out. In each iteration, the gradient function is used to update the value of the projection matrix. The update formula is:

[0131] in, represents the step size of the kth iteration, The operation is an operation that maps the vector in the tangent space back to the manifold. The specific operation process depends on the specific structure of the manifold selected in practice. For example, The operation can be an exponential mapping of a matrix, etc. The step size here can be determined using a line search method so that the objective function can be sufficiently reduced in each iteration.

[0132] In addition, during the iteration process, the convergence condition is used to determine whether to end the iteration. If the convergence condition is met, the iteration is stopped and the current value is the approximate optimal solution of the updated projection matrix. The convergence condition can be that the norm of the gradient is less than a preset threshold. , the convergence condition is expressed as: It can also be that the change in the objective function value is less than a certain threshold , the convergence condition is expressed as: The threshold here can be adjusted according to actual needs.

[0133] In one embodiment, when the solution parameter is a subspace representation matrix, refer to Figure 8 , Figure 8 Another flowchart for obtaining update functions corresponding to solution parameters according to the augmented Lagrangian function and alternately updating the solution parameters according to the update functions provided in an embodiment of the present application specifically includes the following steps: Step 810: Obtain at least one representation matrix data item related to the subspace representation matrix from the augmented Lagrangian function.

[0134] In one embodiment, there are three representation matrix data items related to the subspace representation matrix in the augmented Lagrangian function, namely:

[0135]

[0136]

[0137] Step 820: Obtain the first partial derivative of the representation matrix data item with respect to the subspace representation matrix, accumulate the first partial derivative to obtain an accumulated data item, set the accumulated data item equal to zero, and obtain the update function corresponding to the subspace representation matrix.

[0138] In one embodiment, the three matrix data items obtained above are calculated with respect to the subspace representation matrix The partial derivative of , which is called the first partial derivative.

[0139] Among them, for the first matrix data item, according to the matrix derivative formula , the calculated first partial derivative is expressed as: .

[0140] For the second matrix data item, according to the matrix derivative formula , the calculated first partial derivative is expressed as: .

[0141] The calculation of the partial derivative of the third matrix data item is more complicated. The specific process is: Add assumptions based on previous A and B , the first partial derivative is expressed as: .

[0142] Next, the three first partial derivatives are added together to obtain a cumulative data term. Setting the cumulative data term to zero gives the update function corresponding to the following subspace representation matrix, which is expressed as:

[0143] Step 830: Perform matrix solution on the update function to obtain an updated subspace representation matrix.

[0144] In one embodiment, the update function is solved by the Bartels-Stewart algorithm, which solves matrix equations through eigenvalue decomposition and intermediate matrix construction.

[0145] The specific solution process is described as: First, organize the update function into The standard matrix equation form of , where A, B, and C are given by the update function 、 、 、 The matrix is ​​obtained by the corresponding operation. Next, the matrices A and B obtained by the above process are decomposed by eigenvalues, where 、 , 、 denotes a diagonal matrix containing the eigenvalues ​​of A or B, respectively. 、 is the corresponding eigenvector matrix.

[0146] Then construct the intermediate matrix , such that: ,Will Substitute the standard matrix equation ,get: . Simplifying it, we get: .

[0147] remember , then the equation becomes: .because 、 is a diagonal matrix, Each element in Can be achieved through To solve, where 、 They are 、 The diagonal elements of are the diagonal elements of D. Finally, by get The solution of , and the updated subspace representation matrix is ​​obtained.

[0148] In one embodiment, when the solution parameter is an auxiliary matrix, refer to Figure 9 , Figure 9 Another flowchart for obtaining update functions corresponding to solution parameters according to the augmented Lagrangian function and alternately updating the solution parameters according to the update functions provided in an embodiment of the present application specifically includes the following steps: Step 910: Obtain auxiliary data items related to the auxiliary matrix from the augmented Lagrangian function.

[0149] In one embodiment, the auxiliary data term associated with the auxiliary matrix in the augmented Lagrangian function is expressed as:

[0150] Step 920: Obtain the second partial derivative of the auxiliary data item with respect to the auxiliary matrix, set the second partial derivative equal to zero, and obtain the update function corresponding to the auxiliary matrix.

[0151] In one embodiment, the auxiliary data items obtained above are calculated with respect to the auxiliary matrix The partial derivative of is called the second partial derivative. At the same time, since the nuclear norm is not differentiable at some points, the subgradient property of the nuclear norm is combined in the process of calculating the second partial derivative.

[0152] Among them, the nuclear norm The subgradient of is:

[0153] in, The operator representing the singular value threshold SVT, the optimization parameter Indicates the threshold value.

[0154] Setting the second partial derivative to zero gives:

[0155] in, It can be for , next, let , sorting out the above formula, the update function is expressed as:

[0156] Step 930: Solve the update function using the singular value threshold to obtain an updated auxiliary matrix.

[0157] In one embodiment, a singular value threshold operation is used to perform the matrix Perform singular value decomposition and set the value less than the threshold The singular values ​​of are set to zero, and those greater than the threshold The singular value of minus the threshold , perform low-rank approximation and obtain the updated auxiliary matrix.

[0158] In one embodiment, when the solution parameter is an error matrix, refer to Figure 10 , Figure 10 Another flowchart for obtaining update functions corresponding to solution parameters according to the augmented Lagrangian function and alternately updating the solution parameters according to the update functions provided in an embodiment of the present application specifically includes the following steps: Step 1010: Obtain error data items related to the error matrix from the augmented Lagrangian function.

[0159] In one embodiment, the error data term associated with the error matrix in the augmented Lagrangian function is as follows:

[0160] Step 1020: Obtain the third partial derivative of the error data item with respect to the error matrix, set the third partial derivative equal to zero, and combine it with the shrinkage operator to obtain the update function corresponding to the error matrix.

[0161] In one embodiment, the error data items obtained above are calculated with respect to the error matrix The partial derivative of is called the third partial derivative, where the third partial derivative is expressed as:

[0162] Setting the third partial derivative to zero gives:

[0163] in, Represents an optimization parameter whose value range is , this parameter is a discrete value, within the range of Take values ​​as intervals.

[0164] Next, let , sorting out the above formula, the update function is expressed as:

[0165] Step 1030: Solve the update function to obtain an updated error matrix.

[0166] In one embodiment, the solution is performed based on a solution method of a contraction operator.

[0167] First of all, The matrix is ​​subjected to singular value decomposition to obtain the corresponding diagonal matrix . Then calculate , whose diagonal elements are ,in, is a diagonal matrix Elements on the upper diagonal. Reuse Get the updated error matrix.

[0168] In one embodiment, when the solution parameter is the first Lagrangian multiplier or the second Lagrangian multiplier, refer to Figure 11 , Figure 11 Another flowchart for obtaining update functions corresponding to solution parameters according to the augmented Lagrangian function and alternately updating the solution parameters according to the update functions provided in an embodiment of the present application specifically includes the following steps: Step 1110: Obtain a first multiplier data item related to the first Lagrangian multiplier or a second multiplier data item related to the second Lagrangian multiplier from the augmented Lagrangian function.

[0169] In one embodiment, the first multiplier data item associated with the first Lagrangian multiplier in the augmented Lagrangian function is expressed as:

[0170] The second multiplier data term associated with the second Lagrange multiplier is expressed as:

[0171] Step 1120: Obtain the fourth partial derivative of the first multiplier data item with respect to the first Lagrange multiplier, or the fifth partial derivative of the second multiplier data item with respect to the second Lagrange multiplier.

[0172] In one embodiment, the first Lagrange multiplier is obtained for the first multiplier data item obtained above. The partial derivative of is called the fourth partial derivative, where the fourth partial derivative is expressed as:

[0173] In one embodiment, the second Lagrange multiplier is obtained for the second multiplier data item obtained above. The partial derivative of is called the fifth partial derivative, where the fifth partial derivative is expressed as:

[0174] Step 1130: Set the fourth partial derivative equal to zero to obtain the update function corresponding to the first Lagrange multiplier, or set the fifth partial derivative equal to zero to obtain the update function corresponding to the second Lagrange multiplier.

[0175] In one embodiment, the fourth partial derivative is set to zero, and the update function corresponding to the first Lagrange multiplier is expressed as:

[0176]

[0177] Among them, the penalty parameter here is The value range of 、 These two constants are related according to actual needs.

[0178] Next, let the fifth partial derivative be equal to zero, and the update function corresponding to the second Lagrange multiplier is expressed as:

[0179] Step 1140: Solve the update function to obtain an updated first Lagrange multiplier or a second Lagrange multiplier.

[0180] In one embodiment, for the update function corresponding to the first Lagrange multiplier, according to the updated projection matrix calculated above , subspace representation matrix , auxiliary matrix , error matrix and the first Lagrange multiplier For the update function corresponding to the second Lagrange multiplier, the updated subspace representation matrix calculated above is , auxiliary matrix Calculate the second Lagrange multiplier The updated value of .

[0181] Through the above process, the projection matrix is ​​updated in sequence , subspace representation matrix , auxiliary matrix , error matrix , the first Lagrange multiplier and the second Lagrange multiplier .

[0182] Step 620: Execute at least one update process until a preset convergence condition is met, and use the last updated subspace representation matrix as the representation optimization matrix.

[0183] In one embodiment, the above-mentioned update operation is performed once in each iteration. After each update is completed, it is necessary to determine whether the preset convergence condition is met. The convergence condition here can be set as the difference between the two updated values ​​is less than the preset judgment value, or other convergence conditions defined according to actual needs. If the preset convergence condition is met, then the subspace representation matrix obtained by the last update is selected As the representation optimization matrix. It should be clear that the calculation process of the representation optimization matrix belongs to a comprehensive optimization process, during which both the projection matrix and the error matrix have achieved the optimal solution.

[0184] Step 150: Perform data clustering based on all representation optimization matrices to obtain at least one clustering result.

[0185] In one embodiment, the optimized representation matrix for each view is obtained by comprehensively considering multiple factors, such as the subspace representation matrix, the error matrix, and local total information, by constructing an optimization objective function and performing a series of solver operations while satisfying constraints. Therefore, as an optimized representation of data features for each view, the optimized representation matrix can more accurately reflect the data structure and internal relationships of that view.

[0186] After obtaining the representation optimization matrix corresponding to each view, the embodiment of the present application next calculates the average representation matrix corresponding to all the representation optimization matrices. With the help of the average representation matrix, the optimized data features of each view are integrated and averaged to obtain a data matrix that can comprehensively reflect the commonalities and average states of all views, thereby grasping the overall characteristics of multiple view data from a holistic perspective. Finally, spectral clustering is performed on the average representation matrix. Spectral clustering is a clustering method based on graph theory and matrix eigendecomposition. It analyzes the similarity graph structure constructed by the average representation matrix and uses relevant information such as the matrix's eigenvalues ​​and eigenvectors to divide the data into different categories, thereby obtaining at least one clustering result.

[0187] As can be seen from the above overall process, in the optimization process of the embodiment of the present application, low-rank constraints are used to capture the global structure, and smooth regularization terms are used to retain the local structure of the data, thereby effectively retaining the global and local geometric structures of multiple view data. In view of the complementary information between different views, by using diversity constraint information to ensure the information consistency between multiple views, the representation optimization matrix of each view is enabled to retain more information unique to the view. In addition, the embodiment of the present application integrates the reduction of redundant information and the learning of the representation matrix into the same optimization framework, and automatically reduces the influence of redundant and noise information while learning the representation matrix, achieving efficient interaction of information between multiple views. With the help of this integration method, information is made to flow, the loss of structural information is avoided, and the overall effect of multi-view clustering is effectively improved. It reduces the impact of problems such as the disconnection between redundant dimensionality reduction and subspace representation learning, the difficulty in eliminating noise information, and insufficient information transmission between views in the multi-view clustering method in the related art on the clustering results.

[0188] In one embodiment, referring to Figure 12 , Figure 12 This is a schematic diagram of the overall process of the clustering method for multiple view data provided in an embodiment of the present application. Figure 12The diagram shows the view data corresponding to multiple views, and then uses the view projection matrix to project the corresponding view data into a low-dimensional space to obtain the subspace representation matrix. Next, the local total information and diversity constraint information are introduced into the optimization process. In the overall optimization process, at least the optimal solution projection matrix is ​​obtained. and the subspace representation matrix Then select the subspace representation matrix obtained by the last update The optimized matrix is ​​used as a representation matrix, and data clustering is performed on the optimized matrix to obtain at least one clustering result.

[0189] The technical solution provided by the embodiments of the present application obtains view data corresponding to multiple views. For each view, based on the view's projection matrix, the corresponding view data is projected into a low-dimensional space to obtain a subspace representation matrix and an error matrix. A weight matrix is ​​obtained by multiplying the view data's transpose matrix and the view data. Local structural information is calculated based on the subspace representation matrix and the weight matrix. Next, each piece of local structural information is accumulated to obtain local total information. For each view, an optimization objective term is constructed based on the nuclear norm of the subspace representation matrix, the preset norm of the error matrix, and the local total information. Constraints for the optimization objective term are obtained based on the view data, the projection matrix, the subspace representation matrix, and the error matrix. An optimization objective function is obtained based on the constraints and the corresponding optimization objective term. The optimization objective function is solved to obtain a representation optimization matrix corresponding to each view. Finally, data is clustered based on all the representation optimization matrices to obtain at least one clustering result. The embodiments of the present application perform dimensionality reduction operations on the view data using the projection matrix, and subspace representation is performed simultaneously during the dimensionality reduction process. Given that different projection methods will cause data to present different spatial representations in low-dimensional space, the embodiments of the present application combine the two. In the process of optimizing the objective function, the projection matrix and the subspace representation matrix are dynamically adjusted together to achieve mutual promotion and co-evolution of the optimization results. This allows for finding the best projection that best matches the original feature space for each view data, maximizing the retention of key information related to tasks such as clustering in each view, preventing excessive information loss, and ensuring that the representation of data in low-dimensional space accurately reflects its essential characteristics in the original high-dimensional space. This improves the accuracy of the subspace representation and ultimately enhances the clustering quality. Furthermore, by adding local total information during the optimization process, the aim is to preserve the data structure of the data itself, which effectively enhances the clustering performance of high-dimensional data.

[0190] The embodiment of the present application also provides a device for clustering multiple view data, which can implement the above-mentioned method for clustering multiple view data. Figure 13 , the device comprises: The data acquisition module 1310 is configured to acquire view data corresponding to multiple views.

[0191] Projection calculation module 1320: for each view, based on the projection matrix of the view, projecting the corresponding view data into a low-dimensional space to obtain a subspace representation matrix and an error matrix, and obtaining a weight matrix based on the product of the transposed matrix of the view data and the view data, and calculating the local structure information based on the subspace representation matrix and the weight matrix.

[0192] Optimization target construction module 1330: used to accumulate each local structural information to obtain local total information. For each view, the optimization target item is constructed according to the nuclear norm of the subspace representation matrix, the preset norm of the error matrix and the local total information, and the constraint conditions of the optimization target item are obtained according to the view data, projection matrix, subspace representation matrix and error matrix.

[0193] Optimization solution module 1340: used to obtain an optimization objective function according to the constraint conditions and the corresponding optimization target items, and solve the optimization objective function to obtain the representation optimization matrix corresponding to each view.

[0194] Clustering module 1350: used to perform data clustering according to all representation optimization matrices to obtain at least one clustering result.

[0195] The specific implementation of the apparatus for clustering multiple view data in this embodiment is substantially the same as the specific implementation of the method for clustering multiple view data described above, and will not be described in detail herein.

[0196] An embodiment of the present application further provides an electronic device, including: at least one memory; at least one processor; at least one program; The program is stored in the memory, and the processor executes the at least one program to implement the above-mentioned method for clustering multiple view data in the present application. The electronic device can be any smart terminal including a mobile phone, a tablet computer, a personal digital assistant (PDA), an in-vehicle computer, etc.

[0197] See also Figure 14 , Figure 14 The hardware structure of an electronic device according to another embodiment is shown. The electronic device includes: The processor 1401 can be implemented by a general-purpose central processing unit (CPU), a microprocessor, an application-specific integrated circuit (ASIC), or one or more integrated circuits, and is used to execute relevant programs to implement the technical solutions provided in the embodiments of the present application; the memory 1402 can be implemented in the form of a read-only memory (ROM), a static storage device, a dynamic storage device, or a random access memory (RAM). The memory 1402 can store an operating system and other application programs. When the technical solutions provided in the embodiments of this specification are implemented through software or firmware, the relevant program code is stored in the memory 1402, and the processor 1401 calls and executes the clustering method of multiple view data in the embodiments of the present application; the input / output interface 1403 is used to implement information input and output; the communication interface 1404 is used to implement communication interaction between this device and other devices, and communication can be achieved through wired means (such as USB, network cable, etc.) or wireless means (such as mobile network, WIFI, Bluetooth, etc.); and the bus 1405 transmits information between the various components of the device (such as the processor 1401, memory 1402, input / output interface 1403 and communication interface 1404); wherein the processor 1401, memory 1402, input / output interface 1403 and communication interface 1404 are connected to each other within the device through the bus 1405.

[0198] An embodiment of the present application further provides a storage medium, which is a storage medium storing a computer program. When the computer program is executed by a processor, the above-mentioned method for clustering multiple view data is implemented.

[0199] The memory, as a non-transient storage medium, can be used to store non-transient software programs and non-transient computer executable programs. In addition, the memory may include a high-speed random access memory and may also include a non-transient memory, such as at least one disk storage device, a flash memory device, or other non-transient solid-state storage device. In some embodiments, the memory may optionally include a memory remotely arranged relative to the processor, and these remote memories may be connected to the processor via a network. Examples of the above-mentioned network include, but are not limited to, the Internet, an intranet, a local area network, a mobile communication network, and combinations thereof.

[0200] The clustering method, apparatus, device and storage medium for multiple view data proposed in the embodiments of the present application obtain view data corresponding to multiple views respectively. For each view, based on the projection matrix of the view, the corresponding view data is projected into a low-dimensional space to obtain a subspace representation matrix and an error matrix, and a weight matrix is ​​obtained according to the product of the transpose matrix of the view data and the view data. Local structural information is calculated based on the subspace representation matrix and the weight matrix. Next, each local structural information is accumulated to obtain local total information. For each view, an optimization target item is constructed according to the nuclear norm of the subspace representation matrix, the preset norm of the error matrix and the local total information, and the constraints of the optimization target item are obtained according to the view data, the projection matrix, the subspace representation matrix and the error matrix. The optimization objective function is obtained according to the constraints and the corresponding optimization target item. The optimization objective function is solved to obtain the representation optimization matrix corresponding to each view. Finally, data clustering is performed according to all representation optimization matrices to obtain at least one clustering result.

[0201] The embodiment of the present application uses a projection matrix to perform a dimensionality reduction operation on the view data, and simultaneously performs subspace representation during the dimensionality reduction process. In view of the fact that different projection methods will cause the data to present different spatial representations in the low-dimensional space, the embodiment of the present application combines the two. In the process of optimizing the objective function, the projection matrix and the subspace representation matrix promote each other and co-evolve, thereby finding the best projection that best matches the original feature space for each view data, maximally retaining the key information related to tasks such as clustering in each view, preventing excessive information loss, and ensuring that the representation of the data in the low-dimensional space can accurately reflect its essential characteristics in the original high-dimensional space, thereby improving the accuracy of the subspace representation and ultimately improving the clustering quality. In addition, the addition of local total information during the optimization process is intended to retain the data structure of the data itself, so that the clustering performance of high-dimensional data can be effectively enhanced.

[0202] The embodiments described in the embodiments of this application are intended to more clearly illustrate the technical solutions of the embodiments of this application and do not constitute a limitation on the technical solutions provided by the embodiments of this application. Those skilled in the art will appreciate that with the evolution of technology and the emergence of new application scenarios, the technical solutions provided in the embodiments of this application are also applicable to similar technical problems.

[0203] It will be understood by those skilled in the art that the technical solutions shown in the figures do not constitute a limitation on the embodiments of the present application, and may include more or fewer steps than shown in the figures, or a combination of certain steps, or different steps. The device embodiments described above are merely schematic, in which the units described as separate components may or may not be physically separated, that is, they may be located in one place, or they may be distributed over multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the scheme of this embodiment. It will be understood by those of ordinary skill in the art that all or some of the steps, systems, and functional modules / units in the devices disclosed above may be implemented as software, firmware, hardware, and appropriate combinations thereof.

[0204] The terms "first," "second," "third," "fourth," and the like (if any) in the specification of the present application and the accompanying drawings are used to distinguish similar objects and are not necessarily used to describe a particular order or precedence. It should be understood that the terms used in this manner are interchangeable where appropriate, so that the embodiments of the present application described herein can be implemented in orders other than those illustrated or described herein. In addition, the terms "including" and "having," and any variations thereof, are intended to cover non-exclusive inclusions. For example, a process, method, system, product, or apparatus comprising a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such process, method, product, or apparatus.

[0205] It should be understood that in this application, "at least one (item)" means one or more, and "more" means two or more. "And / or" is used to describe the association relationship of associated objects, indicating that three relationships can exist. For example, "A and / or B" can mean: only A exists, only B exists, and A and B exist at the same time, where A and B can be singular or plural. The character " / " generally indicates that the previous and next associated objects are in an "or" relationship. "At least one of the following items" or similar expressions refers to any combination of these items, including any combination of single or plural items. For example, at least one of a, b, or c can mean: a, b, c, "a and b", "a and c", "b and c", or "a and b and c", where a, b, c can be single or plural.

[0206] In the several embodiments provided in this application, it should be understood that the disclosed devices and methods can be implemented in other ways. For example, the device embodiments described above are merely schematic. For example, the division of the above-mentioned units is only a logical function division. In actual implementation, there may be other division methods, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of devices or units, which can be electrical, mechanical or other forms.

[0207] The units described above as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed across multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment. In addition, the functional units in the various embodiments of the present application may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit. The above-mentioned integrated units may be implemented in the form of hardware or in the form of software functional units.

[0208] If the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present application, or the part that contributes to the prior art, or all or part of the technical solution can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes multiple instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of various embodiments of the present application. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM), random access memory (RAM), disk or optical disk, and other media that can store programs.

[0209] The preferred embodiments of the present invention are described above with reference to the accompanying drawings, but are not intended to limit the scope of the present invention. Any modifications, equivalent substitutions, and improvements made by those skilled in the art without departing from the scope and essence of the present invention should be within the scope of the present invention.

Claims

1. A clustering method for multiple view data, characterized in that: include: Get the view data corresponding to multiple views respectively; For each of the views, based on a projection matrix of the view, the corresponding view data is projected into a low-dimensional space to obtain a subspace representation matrix and an error matrix, a weight matrix is ​​obtained according to a product of a transposed matrix of the view data and the view data, and local structure information is calculated according to the subspace representation matrix and the weight matrix; Accumulating each of the local structural information to obtain local total information, for each of the views, constructing an optimization target item according to the nuclear norm of the subspace representation matrix, the preset norm of the error matrix and the local total information, and obtaining a constraint condition of the optimization target item according to the view data, the projection matrix, the subspace representation matrix and the error matrix; Obtaining an optimization objective function according to the constraint conditions and the corresponding optimization objective items, and solving the optimization objective function to obtain a representation optimization matrix corresponding to each of the views; Data clustering is performed according to all the representation optimization matrices to obtain at least one clustering result.

2. A clustering method for multiple view data according to claim 1, characterized in that: The constructing the optimization target item according to the nuclear norm of the subspace representation matrix, the preset norm of the error matrix and the local total information includes: Obtaining a reference subspace representation matrix corresponding to each of the subspace representation matrices, wherein a view of the reference subspace representation matrix is ​​different from that of the subspace representation matrix; Calculating a diversity matrix according to the reference subspace representation matrix corresponding to the subspace representation matrix, and accumulating all the diversity matrices to obtain the diversity constraint information; An optimization target item is constructed according to the nuclear norm of the subspace representation matrix, the preset norm of the error matrix, the local total information and the diversity constraint information.

3. The clustering method of multiple view data according to claim 2, characterized in that: The obtaining of the constraint condition of the optimization target item according to the view data, the projection matrix, the subspace representation matrix and the error matrix comprises: Taking the product of the transposed matrix of the projection matrix and the view data as a first data item, multiplying the first data item by the subspace representation matrix, and then adding the error matrix to obtain a second data item, setting the first data item equal to the second data item, and obtaining a first constraint condition; The subspace representation matrix is ​​set to be not less than zero, thereby obtaining a second constraint condition; Taking the product of the transposed matrix of the view data and the projection matrix as a third data item, setting the product of the first data item and the third data item as a unit matrix, and obtaining a third constraint condition; The constraint condition is obtained according to the first constraint condition, the second constraint condition and the third constraint condition.

4. The clustering method of multiple view data according to claim 3, characterized in that: The step of solving the optimization objective function to obtain a representation optimization matrix corresponding to each of the views includes: The subspace representation matrix is ​​replaced by the auxiliary matrix corresponding to each of the views to obtain an updated nuclear norm, and a fourth constraint condition is added to the constraint condition, which sets the corresponding auxiliary matrix equal to the subspace representation matrix; The optimization objective function is adjusted according to the updated nuclear norm and the updated constraint condition to obtain an optimization objective update function, the constraint condition is added to the optimization objective update function to obtain an augmented Lagrangian function, and the augmented Lagrangian function is solved to obtain a representation optimization matrix corresponding to each of the views.

5. The clustering method of multiple view data according to claim 4, characterized in that: The step of adding the constraint condition to the optimization objective update function to obtain an augmented Lagrangian function includes: Obtaining a diagonal matrix of the weight matrix, obtaining a difference matrix between the diagonal matrix and the weight matrix, obtaining a first matrix trace according to the diagonal matrix, the difference matrix and the weight matrix, and obtaining the local structure information according to the first matrix trace; Obtain a second matrix trace according to the subspace representation matrix and the corresponding reference subspace representation matrix, and obtain the diversity matrix according to the second matrix trace; For each of the views, the augmented Lagrangian function corresponding to the optimization objective update function is obtained at least based on the updated nuclear norm, the preset norm, the first matrix trace, the diversity matrix, the subspace representation matrix, the error matrix, the projection matrix, the auxiliary matrix, the first Lagrangian multiplier and the second Lagrangian multiplier, and the constraint condition of the augmented Lagrangian function is the third constraint condition.

6. The method for clustering multiple view data according to claim 5, characterized in that: The step of solving the augmented Lagrangian function to obtain a representation optimization matrix corresponding to each of the views includes: For each of the views, obtaining update functions corresponding to solution parameters respectively according to the augmented Lagrangian function, and alternately updating the solution parameters according to the update functions, wherein the solution parameters at least include the projection matrix, the subspace representation matrix, the auxiliary matrix, the error matrix, the first Lagrangian multiplier, and the second Lagrangian multiplier; At least one updating process is performed until a preset convergence condition is met, and the subspace representation matrix updated last is used as the representation optimization matrix.

7. The clustering method of multiple view data according to claim 6, characterized in that: When the solution parameter is the projection matrix, obtaining update functions corresponding to the solution parameters respectively according to the augmented Lagrangian function, and alternately updating the solution parameters according to the update function, comprises: Acquire projection data items related to the projection matrix from the augmented Lagrangian function; Obtaining the update function of the projection matrix according to the projection data item, and calculating the gradient of the update function with respect to the projection matrix to obtain a gradient function; A manifold optimization solution is performed according to the update function and the gradient function to obtain an updated projection matrix.

8. The method for clustering multiple view data according to claim 6, characterized in that: When the solution parameter is the subspace representation matrix, obtaining update functions corresponding to the solution parameters respectively according to the augmented Lagrangian function, and alternately updating the solution parameters according to the update function, comprises: Acquire at least one representation matrix data item related to the subspace representation matrix from the augmented Lagrangian function; Obtaining a first partial derivative of the representation matrix data item with respect to the subspace representation matrix, accumulating the first partial derivative to obtain an accumulated data item, setting the accumulated data item equal to zero, and obtaining the update function corresponding to the subspace representation matrix; A matrix solution is performed on the update function to obtain an updated subspace representation matrix.

9. The method for clustering multiple view data according to claim 6, characterized in that: When the solution parameter is the auxiliary matrix, obtaining update functions corresponding to the solution parameters respectively according to the augmented Lagrangian function, and alternately updating the solution parameters according to the update function, comprises: Acquire auxiliary data items related to the auxiliary matrix from the augmented Lagrangian function; Obtaining a second partial derivative of the auxiliary data item with respect to the auxiliary matrix, setting the second partial derivative equal to zero, and obtaining the update function corresponding to the auxiliary matrix; The update function is solved using a singular value threshold to obtain the updated auxiliary matrix.

10. The method for clustering multiple view data according to claim 6, characterized in that: When the solution parameter is the error matrix, obtaining update functions corresponding to the solution parameters respectively according to the augmented Lagrangian function, and alternately updating the solution parameters according to the update function, comprises: Obtaining error data items related to the error matrix from the augmented Lagrangian function; Obtaining the third partial derivative of the error data item with respect to the error matrix, setting the third partial derivative equal to zero, and combining with a shrinkage operator to obtain the update function corresponding to the error matrix; The update function is solved to obtain the updated error matrix.

11. The method for clustering multiple view data according to claim 6, characterized in that: When the solution parameter is the first Lagrangian multiplier or the second Lagrangian multiplier, acquiring update functions corresponding to the solution parameters according to the augmented Lagrangian function, and alternately updating the solution parameters according to the update functions, comprises: Acquire a first multiplier data item related to the first Lagrangian multiplier or a second multiplier data item related to the second Lagrangian multiplier from the augmented Lagrangian function; Obtaining a fourth partial derivative of the first multiplier data item with respect to the first Lagrangian multiplier, or a fifth partial derivative of the second multiplier data item with respect to the second Lagrangian multiplier; Setting the fourth partial derivative equal to zero to obtain the update function corresponding to the first Lagrangian multiplier, or setting the fifth partial derivative equal to zero to obtain the update function corresponding to the second Lagrangian multiplier; The update function is solved to obtain the updated first Lagrangian multiplier or the second Lagrangian multiplier.

12. The method for clustering multiple view data according to any one of claims 1 to 11, characterized in that: The step of clustering data according to all the representation optimization matrices to obtain at least one clustering result includes: Calculate the average representation matrix corresponding to all the representation optimization matrices; Perform spectral clustering on the average representation matrix to obtain at least one clustering result.

13. A device for clustering multiple view data, characterized in that: include: Data acquisition module: used to acquire view data corresponding to multiple views; A projection calculation module: configured to project the corresponding view data to a low-dimensional space based on the projection matrix of the view for each view, obtain a subspace representation matrix and an error matrix, obtain a weight matrix according to the product of the transposed matrix of the view data and the view data, and obtain local structure information according to the subspace representation matrix and the weight matrix; An optimization target construction module: used for accumulating each of the local structural information to obtain local total information, for each of the views, constructing an optimization target item according to the nuclear norm of the subspace representation matrix, the preset norm of the error matrix and the local total information, and obtaining the constraint conditions of the optimization target item according to the view data, the projection matrix, the subspace representation matrix and the error matrix; Optimization solution module: used for obtaining an optimization objective function according to the constraint conditions and the corresponding optimization objective items, and solving the optimization objective function to obtain a representation optimization matrix corresponding to each of the views; Clustering module: used to perform data clustering according to all the representation optimization matrices to obtain at least one clustering result.

14. An electronic device, characterized in that: The electronic device comprises a memory and a processor, wherein the memory stores a computer program, and the processor implements the clustering method for multiple view data according to any one of claims 1 to 12 when executing the computer program.

15. A storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the computer program implements the method for clustering a plurality of view data according to any one of claims 1 to 12.

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