Image feature dimension reduction method, device and equipment based on unsupervised feature selection

Abstract

The application relates to an image feature dimension reduction method, device and equipment based on unsupervised feature selection. The method comprises the following steps: obtaining corresponding sample vectors by expanding sample images based on pixels, arranging the sample vectors to form a data matrix, constructing an SPCA unsupervised feature selection convex model based on the data matrix and a semi-positive constraint, iteratively solving the SPCA unsupervised feature selection convex model by alternately using derivatives and semi-positive projections until convergence, obtaining an optimal reconstruction matrix, and performing feature dimension reduction on the data matrix according to the optimal reconstruction matrix. The method can simultaneously consider the performance, algorithm stability and operation efficiency of image feature dimension reduction.

Description

Technical Field

[0001] This application relates to the fields of image recognition and classification, and pattern recognition technology, and in particular to an image feature dimensionality reduction method, apparatus and device based on unsupervised feature selection. Background Technology

[0002] With advancements in information technologies such as storage, the dimensionality of data encountered in image recognition and classification is increasing daily. This high-dimensional data brings a large amount of redundant or noisy features, leading not only to a sharp increase in processing time but also negatively impacting clustering results. How to remove these useless features has become one of the current research hotspots in the field of machine learning.

[0003] In general, there are two approaches to solving this problem. One is to abandon traditional clustering algorithms such as K-means and research clustering algorithms based on new mechanisms, such as subspace clustering algorithms. The other approach is to start from the source and study data dimensionality reduction methods. Current research on data dimensionality reduction mainly falls into two categories: feature extraction and feature selection. Feature extraction refers to the linear or nonlinear combination of features to project the original features into a lower-dimensional space. The most typical feature extraction algorithm is Principal Component Analysis (PCA). Although feature extraction algorithms have been widely used in the past, they still have certain limitations. Because all original features are assigned weights during the dimensionality reduction process of feature extraction, redundant or noisy features still participate in the construction of the new feature space. In the past, some scholars have attempted to reduce the influence of useless features by making their weights approach zero through sparse constraints, such as SPCA (H. Zou, T. Hastie, and R. Tibshirani, “Sparse principal component analysis,”[J]. Comput. Graph. Statist, vol. 15, no. 2, pp. 265–186, 2006.). However, when faced with high-dimensional experimental data, the weights of useless features are difficult to approach zero and are still difficult to ignore. Therefore, feature selection algorithms have received widespread attention in recent years. Feature selection algorithms score each feature according to certain rules, select the highest-scoring features, and then directly concatenate them into a new feature vector without any processing. In this way, both dimensionality reduction is achieved, and low-scoring features are directly avoided from participating in subsequent clustering, thus isolating their influence. Feature selection algorithms are divided into filter, wrapper, and embedded types. Embedded systems are currently the mainstream research direction because they can embed the feature selection process into the machine learning model, completing learning and feature selection simultaneously in an optimization problem, saving computation time. This is a very important characteristic for processing high-dimensional data. In recent years, there have been two main branches in the research of unsupervised feature selection algorithms: one is the spectral analysis-based algorithm, which uses the idea of ​​spectral clustering to perform machine learning and capture important features by constructing an undirected graph of the data matrix; the other is the SPCA-based algorithm, which uses the SPCA optimization problem to learn the direction of the largest feature of the data and combines certain feature scoring rules to transform the traditional feature extraction algorithm SPCA into a feature selection algorithm. Compared with the spectral analysis-based algorithm, the SPCA-based algorithm has the following advantages: (1) it does not depend on the construction of a noise-sensitive undirected graph; (2) the computational complexity of each iteration is generally independent of the number of samples, so the processing time will not increase dramatically with the increase of the number of samples. This is an important attribute in the context of big data.The latest research result of the feature selection algorithm based on SPCA in the academic community is the SPCA model proposed by Z. Li et al. based on the l. 2,p norm (Z. Li, F. Nie, J. Bian, D. Wu, and X. Li, “Sparse pca via l2,pnormregularization for unsupervised feature selection,” IEEE TransactionsonPattern Analysis and Machine Intelligence, pp. 1–1, 2021.). In this model, the l 2,p norm (0 < p < 1) is introduced into the optimization problem of PCA to form a sparse constraint on the projection matrix. After iterative convergence, the norm of each row vector of the obtained projection matrix is calculated as the score of the corresponding feature, so as to achieve feature selection. The advantages of this algorithm are that it is lightweight and simple, has short computing time, and its performance is better than that of the algorithm based on spectral analysis. However, as a non-convex model, its solution is not stable enough: when the coefficient of the l 2,p term takes certain values, there may be invalid solutions such as complex solutions, and the selection of the p value in the l 2,p norm has no obvious rule on the performance, making it difficult to be applied in practice. Summary of the Invention

[0004] Based on this, in view of the above technical problems, it is necessary to provide an image feature dimensionality reduction method, device and equipment based on unsupervised feature selection that can quickly perform feature selection for feature dimensionality reduction.

[0005] An image feature dimensionality reduction method based on unsupervised feature selection, the method includes:

[0006] Obtain multiple sample images, expand each sample image based on pixels to obtain corresponding sample vectors, and arrange each of the sample vectors to form a data matrix;

[0007] Based on the data matrix and the positive semi-definite constraint, construct a convex model for SPCA unsupervised feature selection: where X represents the data matrix, Ω represents the reconstruction matrix, <y represents the d-dimensional positive semi-definite cone space, ||Ω|| 2，1 represents the l 2，1 norm of Ω, ||Ω|| * represents the nuclear norm of Ω, and λ and η are both greater than 0 as its regularization coefficients;

[0008] Iteratively solve the convex model for SPCA unsupervised feature selection by alternately using derivatives and positive semi-definite projection until convergence to obtain the optimal reconstruction matrix;

[0009] Based on the column vector magnitude of the optimal reconstruction matrix, each feature in the sample vector is sorted in descending order, and the first preset number of feature numbers are selected from them.

[0010] Based on the feature index, the corresponding pixels are selected from the data matrix to construct a new data matrix after feature dimensionality reduction, thereby achieving image feature dimensionality reduction.

[0011] In one embodiment, each of the sample images contains the same number of pixels.

[0012] In one embodiment, before iteratively solving the SPCA-based unsupervised feature selection convex model using derivatives and positive semi-definite projections alternately, the data matrix is ​​decentered and its covariance matrix is ​​calculated. This covariance matrix is ​​then substituted into the SPCA unsupervised feature selection convex model, expanded to obtain the trace function form, and used as the objective function for solving. The optimization problem is then expressed as:

[0013] min Tr(ΩSΩ T )-2Tr(SΩ)+λTr(ΩWΩ T )+ηTr(Ω)

[0014]

[0015] In the above formula, S represents the covariance matrix of the decentralized data matrix, and W represents a diagonal matrix whose j-th diagonal element is... ω j Let represent the j-th column vector of Ω, ε represent a positive number, and Tr(·) represent finding the trace of the matrix.

[0016] In one embodiment, when iteratively solving the objective function by alternately using derivatives and positive semi-definite projections:

[0017] The diagonal matrix and the reconstruction matrix are initialized;

[0018] By fixing the values ​​of the diagonal matrix, taking the derivative of the objective function, and setting the derivative to zero, an unconstrained solution for the reconstructed matrix is ​​obtained.

[0019] By fixing the value of the diagonal matrix, the unconstrained solution of the reconstruction matrix is ​​projected onto the positive semi-definite cone space using a positive semi-definite projection operator to obtain the updated reconstruction matrix.

[0020] The diagonal matrix is ​​updated based on the updated reconstruction matrix to obtain the updated diagonal matrix;

[0021] The objective function is calculated based on the updated reconstruction matrix and the updated diagonal matrix, and the objective function is judged to converge based on the calculation result. If it converges, the updated reconstruction matrix obtained at this time is the optimal reconstruction matrix.

[0022] If convergence is not achieved, the updated reconstruction matrix and the updated diagonal matrix will continue to undergo derivative and positive semi-definite projection calculations until the objective function converges.

[0023] In one embodiment, the values ​​of the diagonal matrix are fixed, the objective function is differentiated, and the derivative is set to zero to obtain an unconstrained solution, which is the unconstrained solution of the reconstructed matrix, using the following formula:

[0024]

[0025] In the above formula, Ω′ represents the unconstrained solution of the reconstructed matrix, ε is a very small positive number, and I d Denotes the identity matrix, εI d This indicates a method used to enhance the robustness of matrix inversion.

[0026] In one embodiment, the values ​​of the diagonal matrix are fixed, and the unconstrained solution of the reconstruction matrix is ​​projected onto the positive semi-definite cone space using a positive semi-definite projection operator to obtain an updated reconstruction matrix, using the following formula:

[0027]

[0028]

[0029] In the above two formulas, Ω″ represents the reconstruction matrix after projection onto the symmetric space, and S d Describes a d-dimensional symmetric matrix space. express The projection operator, This represents the eigenvalue decomposition of the reconstructed matrix after projection onto a symmetric space, (σ i ) + This indicates the eigenvalues ​​that are positive in sign.

[0030] In one embodiment, after obtaining the new data matrix after feature dimensionality reduction, the contents of the multiple sample images are further classified, clustered, or identified based on the new data matrix.

[0031] An image feature dimensionality reduction device based on unsupervised feature selection, the device comprising:

[0032] The data matrix acquisition module is used to acquire multiple sample images, expand each sample image based on pixels to obtain the corresponding sample vector, and arrange the sample vectors to form a data matrix.

[0033] The convex model construction module is used to construct an SPCA unsupervised feature selection convex model based on the data matrix and positive semidefinite constraints. Where X represents the data matrix, and Ω represents the reconstruction matrix. Let ||Ω|| represent a d-dimensional positive semi-definite cone space. 2，1 l represents Ω 2，1 Norm, ||Ω|| * Let λ represent the nuclear norm of Ω, where λ and η are both greater than 0 and are the coefficients of its regularization term;

[0034] The convex model solving module is used to iteratively solve the SPCA unsupervised feature selection convex model by alternately using derivatives and positive semidefinite projections until convergence, and to obtain the optimal reconstruction matrix.

[0035] The feature selection matrix construction module is used to sort each feature in the sample vector in descending order according to the column vector magnitude of the optimal reconstruction matrix, and select the first preset number of feature indices from them.

[0036] The image feature dimensionality reduction module is used to select the corresponding pixels in the data matrix according to the feature index to construct a new data matrix after feature dimensionality reduction, so as to realize image feature dimensionality reduction.

[0037] A computer device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program performing the following steps:

[0038] Multiple sample images are acquired, each sample image is expanded based on pixels to obtain corresponding sample vectors, and the sample vectors are arranged to form a data matrix.

[0039] Based on the aforementioned data matrix and positive semidefinite constraints, a SPCA unsupervised feature selection convex model is constructed: Where X represents the data matrix, and Ω represents the reconstruction matrix. Let ||Ω|| represent a d-dimensional positive semi-definite cone space. 2，1 l represents Ω 2，1 Norm, ||Ω|| * Let λ represent the nuclear norm of Ω, where λ and η are both greater than 0 and are the coefficients of its regularization term;

[0040] The SPCA unsupervised feature selection convex model is iteratively solved by alternating between derivatives and positive semidefinite projections until convergence, and the optimal reconstruction matrix is ​​obtained.

[0041] Based on the column vector magnitude of the optimal reconstruction matrix, each feature in the sample vector is sorted in descending order, and the first preset number of feature numbers are selected from them.

[0042] Based on the feature index, the corresponding pixels are selected from the data matrix to construct a new data matrix after feature dimensionality reduction, thereby achieving image feature dimensionality reduction.

[0043] A computer-readable storage medium having a computer program stored thereon, the computer program performing the following steps when executed by a processor:

[0044] Multiple sample images are acquired, each sample image is expanded based on pixels to obtain corresponding sample vectors, and the sample vectors are arranged to form a data matrix.

[0045] Based on the aforementioned data matrix and positive semidefinite constraints, a SPCA unsupervised feature selection convex model is constructed: Where X represents the data matrix, and Ω represents the reconstruction matrix. Let ||Ω|| represent a d-dimensional positive semi-definite cone space. 2，1 l represents Ω 2，1 Norm, ||Ω|| * Let λ represent the nuclear norm of Ω, where λ and η are both greater than 0 and are the coefficients of its regularization term;

[0046] The SPCA unsupervised feature selection convex model is iteratively solved by alternating between derivatives and positive semidefinite projections until convergence, and the optimal reconstruction matrix is ​​obtained.

[0047] Based on the column vector magnitude of the optimal reconstruction matrix, each feature in the sample vector is sorted in descending order, and the first preset number of feature numbers are selected from them.

[0048] Based on the feature index, the corresponding pixels are selected from the data matrix to construct a new data matrix after feature dimensionality reduction, thereby achieving image feature dimensionality reduction.

[0049] The aforementioned image feature dimensionality reduction method, apparatus, and device based on unsupervised feature selection involves expanding sample images pixel-wise to obtain corresponding sample vectors, arranging these vectors to form a data matrix, and then constructing a SPCA unsupervised feature selection convex model based on the data matrix and positive semi-definite constraints. The SPCA unsupervised feature selection convex model is iteratively solved using derivatives and positive semi-definite projections until convergence, yielding the optimal reconstruction matrix. Feature dimensionality reduction is then performed on the data matrix based on the optimal reconstruction matrix. This method exhibits computational complexity independent of the number of samples during the optimization iteration process, resulting in high image data processing efficiency and making it more suitable for practical applications. The method constructs a convex model and mathematically provides the solution space of the optimal solution—a positive semi-definite cone space. The optimization algorithm based on gradient and positive semi-definite projection operators significantly reduces the number of iterations, saving computation time. Furthermore, based on the convex model derived from SPCA, this method can automatically find the largest feature direction in the data matrix, effectively selecting highly separable features. Attached Figure Description

[0050] Figure 1 This is a flowchart illustrating an image feature dimensionality reduction method based on unsupervised feature selection in one embodiment.

[0051] Figure 2 This is a flowchart of an image clustering method based on image feature dimensionality reduction in one embodiment;

[0052] Figure 3 This is a schematic diagram comparing the clustering accuracy (ACC) and mutual information (NMI) of this method with other algorithms on the PIE and Imm40 face image datasets in a simulation experiment.

[0053] Figure 4 This is a diagram showing a comparison of the feature selection results of this method and other algorithms on a face dataset in a simulation experiment.

[0054] Figure 5 This is a schematic diagram comparing the computation time of this method with other algorithms on the PIE and Imm40 face image datasets in a simulation experiment.

[0055] Figure 6 This is a structural block diagram of an image feature dimensionality reduction device based on unsupervised feature selection in one embodiment;

[0056] Figure 7 This is an internal structural diagram of a computer device in one embodiment. Detailed Implementation

[0057] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0058] Image recognition is one of the most important applications of image processing. Image recognition technology has developed rapidly and is widely used in the recognition of faces, numbers, and other objects. It also has broad applications in agriculture, commerce, security, finance, and daily life, possessing practical research significance and a wide range of application scenarios. Image feature matching is a crucial step in achieving image recognition and currently has extensive applications in many fields, such as security alarm systems, financial identity verification, and urban population management. With the development of image recognition technology and the advancement of smart city construction, the size of image databases is increasing daily. Dimensionality reduction of image features, while ensuring recognition accuracy, is of great significance for improving the efficiency of image feature matching.

[0059] like Figure 1As shown, an image feature dimensionality reduction method based on unsupervised feature selection is provided, including the following steps:

[0060] Step S100: Obtain multiple sample images, expand each sample image based on pixels to obtain the corresponding sample vector, and arrange the sample vectors to form a data matrix.

[0061] Step S110: Based on the data matrix and the positive semidefinite constraints, construct the SPCA unsupervised feature selection convex model: Where X represents the data matrix, and Ω represents the reconstruction matrix. Let ||Ω|| represent a d-dimensional positive semi-definite cone space. 2，1 l represents Ω 2，1 Norm, ||Ω|| * Let λ represent the nuclear norm of Ω, where λ and η are both greater than 0 and are the coefficients of its regularization term;

[0062] Step S120: Iteratively solve the SPCA unsupervised feature selection convex model by alternately using derivatives and positive semidefinite projections until convergence, and obtain the optimal reconstruction matrix.

[0063] Step S130: Sort each feature in the sample vector in descending order according to the column vector magnitude of the optimal reconstruction matrix, and select the first preset number of feature numbers from them.

[0064] Step S140: Select the corresponding pixels in the data matrix according to the feature index to construct a new data matrix after feature dimensionality reduction, so as to realize image feature dimensionality reduction.

[0065] In this embodiment, a convex model under positive semidefinite constraints is derived from SPCA. Then, an optimization algorithm combining gradient and positive semidefinite projection operators is designed to enable the iterative process to converge quickly in the solution space. The obtained reconstruction matrix is ​​then used for feature selection, and finally, the selected features are input into a clusterer for clustering.

[0066] In step S100, sample images can be selected according to the scenario in which the image recognition will be applied. For example, in a face recognition scenario, sample images such as occluded faces, faces seen through car windows, and faces seen at large angles can be used. In a scenario where images of a class of objects are classified, each sample image includes different sample images belonging to the same class of objects.

[0067] In this embodiment, each sample image contains the same number of pixels.

[0068] Specifically, n sample images containing d pixels are each generated into a d x 1 sample vector and arranged into a data matrix. Where, x i Let represent the i-th sample vector.

[0069] Furthermore, each row of the data matrix represents a corresponding sample image, while each column represents the pixels at the same location on each sample image, which are the features.

[0070] In step S110, an unsupervised feature selection convex model of SPCA is constructed based on the positive definite constraint, which is expressed as:

[0071]

[0072] In formula (1), X represents the data matrix, and Ω represents the reconstruction matrix, which is the variable that needs to be solved for the convex model. Let ||Ω|| represent a d-dimensional positive semi-definite cone space. 2，1 l represents Ω 2，1 Norm, ||Ω|| * Let represent the nuclear norm of Ω, be the sum of its singular values, and have λ and η, both greater than 0, as coefficients of its regularization term. ω ij This represents the element in the i-th row and j-th column of Ω.

[0073] In this embodiment, the data matrix is ​​decentered and its covariance matrix is ​​calculated. Then, the covariance matrix is ​​substituted into the SPCA-based unsupervised feature selection convex model and expanded to obtain the trace function form, which is then used as the objective function for subsequent differentiation operations.

[0074] Specifically, the covariance matrix of the decentralized data matrix is ​​represented as:

[0075] S = XHX T (2)

[0076] In formula (2), H = I n -1 / n11 T , Represents the identity matrix. Let represent a vector of all 1s. Considering the positive semi-definite constraint, the convex model of the optimization is expanded into a trace function form, and the optimization problem is expressed as:

[0077]

[0078] In formula (3), S represents the covariance matrix of the decentralized data matrix, and W represents a diagonal matrix whose j-th diagonal element is... ω j Let represent the j-th column vector of Ω, ε represent a very small positive number to prevent the denominator from being zero, and Tr(·) represents the trace of the matrix.

[0079] In step S120, when iteratively solving the objective function using derivatives and positive semi-definite projection alternately: First, the diagonal matrix and the reconstruction matrix are initialized, that is, given initial values. When differentiating the objective function, the value of the diagonal matrix is ​​fixed, and the derivative is set to zero, resulting in an unconstrained solution, which is the intermediate reconstruction matrix. Then, the positive semi-definite projection operator is used to project the intermediate reconstruction matrix onto the positive semi-definite cone space, obtaining an updated reconstruction matrix. During this process, the diagonal matrix remains unchanged with its initial value. After obtaining the updated reconstruction matrix, the diagonal matrix is ​​updated again based on this matrix, resulting in the updated diagonal matrix. This completes one iterative calculation.

[0080] After completing one iteration, the objective function is calculated based on the updated reconstruction matrix and the updated diagonal matrix. The convergence of the objective function is then determined based on the calculation results. If convergence occurs, the updated reconstruction matrix obtained at this point is the optimal reconstruction matrix. If convergence does not occur, the derivative and positive semi-definite projection calculations are performed on the updated reconstruction matrix and the updated diagonal matrix until the objective function converges.

[0081] Specifically, by taking the derivative of the objective function and setting it to zero, we obtain the unconstrained solution, which is the unconstrained solution for reconstructing the matrix, using the following formula:

[0082]

[0083] In formula (4), Ω′ represents the unconstrained solution of the reconstruction matrix, ε is a very small positive number, and I d Denotes the identity matrix, εI d This indicates a method used to enhance the robustness of matrix inversion.

[0084] Specifically, the unconstrained solution of the reconstruction matrix is ​​projected onto the positive semi-definite cone space using the positive semi-definite projection operator to obtain the updated reconstruction matrix, using the following formula:

[0085]

[0086]

[0087] In formulas (5) and (6), Ω″ represents the reconstruction matrix after projection onto the symmetric space, and S d Describes a d-dimensional symmetric matrix space. express The projection operator, This represents the eigenvalue decomposition of the reconstructed matrix after projection onto a symmetric space, (σ i ) + This indicates the eigenvalues ​​that are positive in sign.

[0088] Specifically, each diagonal element in the diagonal matrix is ​​calculated based on the updated reconstruction matrix. This is to achieve the update of the diagonal matrix.

[0089] In step S130, the obtained optimal solution Ω * The column vector magnitude is used to sort each feature in the sample vector in descending order, and the top preset number of feature indices are selected. Since the magnitude of the column vector can be used to characterize the importance of the corresponding feature, the larger the magnitude value, the more important the characterization. Therefore, by sorting the features in descending order of magnitude, unimportant features can be discarded, leaving more important features. For image data, this means removing unimportant pixels from each image and retaining the important ones.

[0090] Finally, in step S140, corresponding elements are selected from the data matrix according to the feature selection matrix to form a new data matrix. The new data matrix has fewer rows than the original data matrix, meaning that unimportant pixel features in each sample image are removed while important pixel features are retained, thus achieving dimensionality reduction of image features.

[0091] In this embodiment, based on the image feature dimensionality reduction method described above, after obtaining the new data matrix after feature dimensionality reduction, the content in multiple sample images can be classified, clustered, or identified according to the new data matrix.

[0092] In this embodiment, as Figure 2 As shown, a method for image clustering based on the above method is also provided. After obtaining a new data matrix after feature dimensionality reduction according to the above image feature dimensionality reduction method, the data matrix is ​​input into the K-means clusterer to obtain the clustering result.

[0093] In this embodiment, a method for image clustering based on the above method is also provided. After obtaining a new data matrix after feature dimensionality reduction according to the above image feature dimensionality reduction method, the data matrix is ​​input into a trained deep neural network to obtain the classification result.

[0094] In this paper, experimental simulations are also conducted based on an image feature dimensionality reduction method based on unsupervised feature selection (hereinafter referred to as this method), such as... Figure 3 The image shows a comparison of the clustering accuracy (ACC) and mutual information (NMI) of our method with other algorithms on the PIE and Imm40 face image datasets. Each sample in the PIE dataset has 1024 features, 1166 samples, and 53 classes; each sample in the Imm40 dataset has 1024 features, 240 samples, and 40 classes.

[0095] The experiment inputs the feature selection results of each algorithm into a K-means clusterer for clustering (the clustering process is repeated 20 times to eliminate differences in the starting points of K-means). Then, the Hungarian algorithm is used to map the pseudo-labels to the real labels to calculate the accuracy (ACC) and mutual information (NMI) respectively. The experiment sets different numbers of features, and at each number, a grid search is used to traverse {10...} -8 10 -7 10 -6 , ..., 1, 10, ... 10 7 10 8 The regularization coefficients within the range are used to record the highest ACC and NMI for each algorithm. It can be seen that this method maintains a high level of ACC and NMI, outperforming the method based on l. 2,p The SPCA feature selection algorithm based on norms also outperforms other spectral analysis-based algorithms. While the CSPCA algorithm is similar to our method in ACC and NMI on the PIE dataset, it is superior due to… Figure 5 It can be seen that its average calculation time is greater than that of this method. Therefore, this method has a greater computational advantage in practical applications.

[0096] Figure 4 A visualization comparing the feature selection results of this method with other algorithms on a face dataset is provided. The experiment used the PIE face dataset, which contains 1166 images, each with a resolution of 32*32 pixels. In the algorithm, each image is unfolded into a 1024-dimensional vector for computation. Figure 4 The image shows the positions of the selected features (i.e., pixels) in the original image, with the number of selected features increasing sequentially from left to right, starting with an initial value of 50 and a step size of 50. When the number of features is small, at 100 (the area within the red box in the image), only this method, CSPCA, and SPCAFS (p=0.5) can effectively select facial features (eyes, nose, mouth, etc.). The performance of SPCAFS is significantly affected by the value; for example, with 100 features, the nose feature is not selected. Therefore, in practical applications, SPCAFS has certain limitations due to the need for value adjustment. While CSPCA selects similar features to this method, its performance is significantly affected by the value. Figure 5 It can be seen that its computation time is longer than that of this method. Therefore, this method has a greater computational advantage in practical applications. Figure 5 This chart compares the computation time of our method with other algorithms on the PIE and Imm40 face image datasets. It can be seen that our method consumes relatively less computation time.

[0097] In summary, this invention can effectively reduce the dimensionality of image features while maintaining high computational efficiency, and has high engineering application value.

[0098] The aforementioned image feature dimensionality reduction method based on unsupervised feature selection expands the sample image pixel by pixel to obtain corresponding sample vectors, arranges these vectors to form a data matrix, and then constructs a SPCA unsupervised feature selection convex model based on the data matrix and positive semi-definite constraints. The SPCA unsupervised feature selection convex model is iteratively solved using derivatives and positive semi-definite projections alternately until convergence, yielding the optimal reconstruction matrix. Dimensionality reduction is then performed on the data matrix based on this optimal reconstruction matrix. The computational complexity of this method during the optimization iteration process is independent of the number of samples, resulting in high efficiency in image data processing and making it more suitable for practical applications. This method constructs a convex model and mathematically provides the solution space of the optimal solution—a positive semi-definite cone space. The optimization algorithm based on gradient and positive semi-definite projection operators significantly reduces the number of iterations, saving computation time. Furthermore, based on the convex model derived from SPCA, this method can automatically find the largest feature direction in the data matrix, effectively selecting highly separable features.

[0099] It should be understood that, although Figure 1 The steps in the flowchart are shown sequentially as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order in which these steps are executed, and they can be performed in other orders. Figure 1 At least some of the steps in the process may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least some of the sub-steps or stages of other steps.

[0100] In one embodiment, such as Figure 6 As shown, an image feature dimensionality reduction device based on unsupervised feature selection is provided, comprising: a data matrix acquisition module 200, a convex model construction module 210, a convex model solving module 220, a feature selection matrix construction module 230, and an image feature dimensionality reduction module 240, wherein:

[0101] The data matrix acquisition module 200 is used to acquire multiple sample images, expand each sample image based on pixels to obtain corresponding sample vectors, and arrange the sample vectors to form a data matrix.

[0102] Convex model construction module 210 is used to construct an SPCA unsupervised feature selection convex model based on the data matrix and the positive semidefinite constraints. Where X represents the data matrix, and Ω represents the reconstruction matrix. Let ||Ω|| represent a d-dimensional positive semi-definite cone space.2，1 l represents Ω 2，1 Norm, ||Ω|| * Let λ represent the nuclear norm of Ω, where λ and η are both greater than 0 and are the coefficients of its regularization term;

[0103] The convex model solving module 220 is used to iteratively solve the SPCA unsupervised feature selection convex model by alternately using derivatives and positive semidefinite projections until convergence, and to obtain the optimal reconstruction matrix.

[0104] The feature selection matrix construction module 230 is used to sort each feature in the sample vector in descending order according to the column vector magnitude of the optimal reconstruction matrix, and select the first preset number of feature numbers from them.

[0105] The image feature dimensionality reduction module 240 is used to select the corresponding pixels in the data matrix according to the feature index to construct a new data matrix after feature dimensionality reduction, so as to realize image feature dimensionality reduction.

[0106] Specific limitations regarding the image feature dimensionality reduction device based on unsupervised feature selection can be found in the limitations of the image feature dimensionality reduction method based on unsupervised feature selection mentioned above, and will not be repeated here. Each module in the aforementioned image feature dimensionality reduction device based on unsupervised feature selection can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device in hardware form, or stored in the memory of a computer device in software form, so that the processor can call and execute the operations corresponding to each module.

[0107] In one embodiment, a computer device is provided, which may be a terminal, and its internal structure diagram may be as follows: Figure 7 As shown, the computer device includes a processor, memory, network interface, display screen, and input devices connected via a system bus. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The network interface is used to communicate with external terminals via a network connection. When executed by the processor, the computer program implements an image feature dimensionality reduction method based on unsupervised feature selection. The display screen can be a liquid crystal display (LCD) or an e-ink display. The input devices can be a touch layer covering the display screen, buttons, a trackball, or a touchpad mounted on the computer device casing, or an external keyboard, touchpad, or mouse.

[0108] Those skilled in the art will understand that Figure 7The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0109] In one embodiment, a computer device is provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to perform the following steps:

[0110] Multiple sample images are acquired, each sample image is expanded based on pixels to obtain corresponding sample vectors, and the sample vectors are arranged to form a data matrix.

[0111] Based on the aforementioned data matrix and positive semidefinite constraints, a SPCA unsupervised feature selection convex model is constructed: Where X represents the data matrix, and Ω represents the reconstruction matrix. Let ||Ω|| represent a d-dimensional positive semi-definite cone space. 2，1 l represents Ω 2，1 Norm, ||Ω|| * Let λ represent the nuclear norm of Ω, where λ and η are both greater than 0 and are the coefficients of its regularization term;

[0112] The SPCA unsupervised feature selection convex model is iteratively solved by alternating between derivatives and positive semidefinite projections until convergence, and the optimal reconstruction matrix is ​​obtained.

[0113] Based on the column vector magnitude of the optimal reconstruction matrix, each feature in the sample vector is sorted in descending order, and the first preset number of feature numbers are selected from them.

[0114] Based on the feature index, the corresponding pixels are selected from the data matrix to construct a new data matrix after feature dimensionality reduction, thereby achieving image feature dimensionality reduction.

[0115] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, the computer program performing the following steps when executed by a processor:

[0116] Multiple sample images are acquired, each sample image is expanded based on pixels to obtain corresponding sample vectors, and the sample vectors are arranged to form a data matrix.

[0117] Based on the aforementioned data matrix and positive semidefinite constraints, a SPCA unsupervised feature selection convex model is constructed: Where X represents the data matrix, and Ω represents the reconstruction matrix. Let ||Ω|| represent a d-dimensional positive semi-definite cone space. 2，1 l represents Ω2，1 Norm, ||Ω|| * Let λ represent the nuclear norm of Ω, where λ and η are both greater than 0 and are the coefficients of its regularization term;

[0118] The SPCA unsupervised feature selection convex model is iteratively solved by alternating between derivatives and positive semidefinite projections until convergence, and the optimal reconstruction matrix is ​​obtained.

[0119] Based on the column vector magnitude of the optimal reconstruction matrix, each feature in the sample vector is sorted in descending order, and the first preset number of feature numbers are selected from them.

[0120] Based on the feature index, the corresponding pixels are selected from the data matrix to construct a new data matrix after feature dimensionality reduction, thereby achieving image feature dimensionality reduction.

[0121] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0122] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0123] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. An image feature dimension reduction method based on unsupervised feature selection, characterized in that, The method comprises: acquiring multiple sample images, expanding each sample image based on pixels to obtain a corresponding sample vector, and arranging each sample vector to form a data matrix; Based on the data matrix and the semi-positive constraint, a convex model of SPCA unsupervised feature selection is constructed: Wherein, X represents the data matrix, Ω represents the reconstruction matrix, represents the semi-positive cone space of d dimension, ||Ω|| 2,1 represents the l 2,1 norm of Ω, ||Ω|| * represents the kernel norm of Ω, λ and η are greater than 0 as the regularization term coefficients; iteratively solving the SPCA unsupervised feature selection convex model by alternately using derivatives and semi-positive projections until convergence, to obtain an optimal reconstruction matrix; arranging each feature in the sample vector in descending order according to the column vector length of the optimal reconstruction matrix, and selecting a preset number of feature serial numbers therefrom; selecting corresponding pixels in the data matrix according to the feature serial numbers to construct a new data matrix after feature dimension reduction, so as to realize image feature dimension reduction.

2. The image feature dimension reduction method of claim 1, wherein, Each sample image comprises the same number of pixels.

3. The image feature dimension reduction method of claim 1, wherein, Before iteratively solving the SPCA unsupervised feature selection convex model by alternately using derivatives and semi-positive projections, the data matrix is decentered to obtain a covariance matrix, the covariance matrix is brought into the SPCA unsupervised feature selection convex model, the trace function form is obtained by expanding the SPCA unsupervised feature selection convex model, and the trace function form is solved as an objective function, so that the optimization problem is represented as: min Tr(ΩSΩ T )-2Tr(SΩ)+λTr(ΩWΩ T )+ηTr(Ω) In the above equation, S denotes the covariance matrix of the decentralized data matrix, W denotes a diagonal matrix whose jth diagonal element is ω j denotes the jth column vector of Ω, ε denotes a positive number, and Tr(·) denotes the trace of a matrix.

4. The image feature dimension reduction method of claim 3, wherein, When the objective function is iteratively solved by alternately using derivatives and semi-positive projections: the diagonal matrix and the reconstruction matrix are initialized; the derivative of the objective function is solved by fixing the value of the diagonal matrix, and the unconstrained solution of the reconstruction matrix is obtained by setting the derivative to zero; the unconstrained solution of the reconstruction matrix is projected into the semi-positive cone space by using the semi-positive projection operator to obtain an updated reconstruction matrix by fixing the value of the diagonal matrix; the diagonal matrix is updated according to the updated reconstruction matrix to obtain an updated diagonal matrix; the objective function is calculated according to the updated reconstruction matrix and the updated diagonal matrix, and it is judged whether the objective function converges according to the calculation result; if the objective function converges, the updated reconstruction matrix obtained at this time is the optimal reconstruction matrix; if the objective function does not converge, the derivative and the semi-positive projection calculation of the updated reconstruction matrix and the updated diagonal matrix are continued until the objective function converges.

5. The image feature dimension reduction method of claim 4, wherein, The derivative of the objective function is solved by fixing the value of the diagonal matrix, and the unconstrained solution, that is, the unconstrained solution of the reconstruction matrix, is obtained by setting the derivative to zero, using the following formula: In the above equation, Ω' represents the unconstrained solution of the reconstruction matrix, ε is a small positive number, I d represents the identity matrix, and εI d represents a term used to enhance the robustness of the matrix inversion.

6. The image feature dimension reduction method of claim 5, wherein, The unconstrained solution of the reconstruction matrix is projected into the semi-positive cone space by using the semi-positive projection operator to obtain an updated reconstruction matrix by fixing the value of the diagonal matrix, using the following formula: In the above two formulas, Ω″ represents the reconstruction matrix after projection onto the symmetric space, and S d Describes a d-dimensional symmetric matrix space. express The projection operator, This represents the eigenvalue decomposition of the reconstructed matrix after projection onto a symmetric space, (σ i ) + This indicates the eigenvalues ​​that are positive in sign.

7. The image feature dimensionality reduction method according to any one of claims 1-6, characterized in that, After obtaining the new data matrix after feature dimension reduction, the contents in the multiple sample images are classified, clustered or recognized according to the new data matrix.

8. An apparatus for image feature dimension reduction based on unsupervised feature selection, characterized in that, The device comprises: a data matrix acquisition module, configured to acquire multiple sample images, expand each sample image based on pixels to obtain a corresponding sample vector, and arrange each sample vector to form a data matrix; A convex model constructing module is configured to construct a SPCA unsupervised feature selection convex model based on the data matrix and a semi-positive constraint. Wherein, X represents the data matrix, Ω represents a reconstruction matrix, represents a semi-positive cone space of d dimensions, and ||Ω|| represents an l 2,1 norm of Ω, ||Ω|| represents an l 2,1 norm of Ω, and ||Ω|| represents a kernel norm of Ω. * norm of Ω, and λ and η are greater than 0 as regular term coefficients. a convex model solving module, configured to iteratively solve the SPCA unsupervised feature selection convex model by alternately using derivatives and semi-positive projections until convergence, to obtain an optimal reconstruction matrix; The feature selection matrix construction module is configured to arrange each feature in the sample vector in descending order according to the column vector module length of the optimal reconstruction matrix, and select the first preset number of feature serial numbers therefrom; The image feature dimension reduction module is configured to select corresponding pixels from the data matrix according to the feature serial numbers to construct a new data matrix after feature dimension reduction, so as to realize image feature dimension reduction. 9.A computer device, comprising a memory and a processor, wherein the memory stores a computer program, and the computer device is configured to perform the method according to any one of claims 1-8 when the computer program is executed by the processor. The processor implements the steps of the method of claim 7 when executing the computer program.

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