A direct and fast image clustering method based on bipartite graph co-clustering

Abstract

The present application relates to a kind of direct fast image clustering method based on two-part graph collaborative clustering, the collaborative clustering method based on spectral clustering can cause high time complexity due to the construction of graph laplacian matrix, carries out eigenvalue decomposition or singular value decomposition, and the clustering result needs further processing to obtain clear class distribution problem, the present application proposes a kind of direct fast image clustering method based on two-part graph collaborative clustering, by introducing anchor point, the dependence of the method based on spectral clustering for graph laplacian matrix is eliminated, and the calculation complexity and space complexity of algorithm are reduced. Two-step alternating optimization is used in solving optimization process, directly solve the original regularized cut problem by the idea of coordinate descent, iteratively solve binary data point label matrix and binary anchor point label matrix, eigenvalue decomposition or singular value decomposition is not needed, greatly improve the optimization speed, can directly obtain final clustering result, can directly and quickly realize collaborative clustering.

Description

Technical Field

[0001] The present invention belongs to the field of image processing and machine learning clustering, and relates to a direct and fast image clustering method based on bipartite graph collaborative clustering. Background Art

[0002] Clustering technology is a hot topic of research in fields such as machine learning, pattern recognition, and computer vision. Clustering is an unsupervised learning method that can uncover the underlying structural information in given data and partition it into disjoint subsets. Spectral clustering, based on spectral graph theory, is a key branch of clustering technology and an algorithm derived from graph theory. The main idea of ​​spectral clustering is to treat all data as points in space, connected by edges to form a graph. This graph is then sliced ​​to ensure that the edge weights within a subgraph are as high as possible and the edge weights between subgraphs are as low as possible. Traditional spectral clustering techniques are easily transferable and adaptable to diverse and geometrically complex datasets. They are widely used in fields such as data mining, face recognition, and image segmentation. However, they still have several drawbacks. For example, the construction of the graph Laplacian matrix and the eigenvalue decomposition lead to high computational complexity. The clustering results require post-processing to obtain a clear class distribution. In addition, clustering can only be performed on rows (generally representing samples) or columns (generally representing features) of the input data matrix.

[0003] Recently, collaborative clustering techniques have attracted widespread attention from scholars. They can simultaneously cluster input data samples and features. Graph-based collaborative clustering methods represent the binary information between samples and features as a bipartite graph. Zhang Jiwen et al. ("Joint Clustering of Words and Documents Based on Spectral Clustering," Journal of Guizhou University (Natural Science Edition), 2014, 31(5): 53-57) performed spectral clustering on a bipartite graph to achieve collaborative clustering of words and documents. This approach provides a good global solution in practice. However, this method also requires post-processing to obtain clear clustering results. Nie et al. (Learning a structured optimal bipartite graph for co-clustering. In Proceedings of the 31st International Conference on Neural Information Processing Systems (NIPS'17). Curran Associates Inc., Red Hook, NY, USA, 4132–4141.) proposed a novel co-clustering method for learning structured optimal bipartite graphs (Structured Optimal Bipartite Graph, SOBG). This method iteratively performs spectral clustering based on the bipartite graph and a low-rank approximation of the original bipartite graph, directly obtaining clustering results without the need for post-processing. However, this method still has high computational complexity. The reason is that the aforementioned methods are all co-clustering improvements based on spectral clustering, and therefore cannot completely avoid the problems of low computational efficiency and the need for post-processing. Summary of the Invention

[0004] Technical problems to be solved

[0005] In order to avoid the shortcomings of the prior art, the present invention proposes a direct and fast image clustering method based on bipartite graph collaborative clustering

[0006] Technical Solution

[0007] A direct and fast image clustering method based on bipartite graph collaborative clustering is characterized by the following steps:

[0008] Step 1: Stretch the dataset containing n a×b pixel-scale images into an image data matrix Each row is a sample, n is the number of images, d = a × b is the total number of pixels in a single image, that is, the characteristic dimension of the image;

[0009] Use Kmeans clustering method to generate m representative anchor points and obtain the anchor matrix Where m is the number of selected anchor points;

[0010] Step 2: According to the image data matrix And the obtained anchor matrix An, the adaptive neighborhood assignment method is used to construct the bipartite graph affinity matrix b obtained by adaptive neighborhood assignment method ij as follows:

[0011]

[0012] where μ j Represents the sample point x i The jth nearest anchor point, Represents the sample point x i With anchor point μ j The square of the Euclidean distance between them, k is an artificially selected parameter;

[0013] Step 3: Based on the constructed bipartite graph affinity matrix B, a clustering model based on bipartite graph collaborative clustering is constructed. The objective function is expressed as follows:

[0014]

[0015]

[0016] in, is the graph Laplacian matrix, is the degree matrix, is the soft label matrix; Y∈Ind represents is a binary label matrix; N = n + m is the sum of the number of sample points and anchor points, and c is the final number of clusters;

[0017] Replace the Laplace matrix with the following regularized Laplace matrix:

[0018]

[0019] in, is the graph similarity matrix; is a diagonal matrix whose j-th diagonal element is the identity matrix;

[0020] The binary label matrix is ​​written as follows:

[0021]

[0022] in, are binary sample label matrix and anchor label matrix respectively, They are the sample soft label matrix and the anchor soft label matrix respectively;

[0023] Substitute the regularized Laplacian matrix, the rewritten binary label matrix, and the soft label matrix into the original problem for transformation. The detailed process is as follows:

[0024]

[0025] The original problem is equivalent to a maximization problem:

[0026]

[0027]

[0028] A two-step alternating optimization algorithm is used to solve the above problem;

[0029] Step 4: Fix the anchor soft label V and update the sample soft label U to optimize the objective function

[0030] When V is fixed, the optimization problem is equivalent to:

[0031]

[0032]

[0033] in,

[0034] Expanding the above problem of finding the maximum trace of a matrix, we can get:

[0035]

[0036] in,(·) ·j represents the jth column of the matrix, (·) ij represents the element in the i-th row and j-th column of the matrix; the sample label matrix Y u The solution of each row is an independent process, and the optimal solution of each row is solved in turn according to the following formula:

[0037]

[0038] in, Represents Y u The increment of the objective function when the element in row i and column j changes from 0 to 1;

[0039] The obtained Y u The update strategy for row i is as follows:

[0040]

[0041] Step 5: Fix the sample soft label U and update the anchor soft label V to optimize the objective function

[0042] When U is fixed, the optimization problem is equivalent to:

[0043]

[0044]

[0045] in, Expanding the above problem of finding the maximum trace of a matrix, we can get:

[0046]

[0047] in,(·) ij Represents the element in the i-th row and j-th column of the matrix;

[0048] In this problem, the anchor label matrix Y v The solution of each row is an independent process, and the optimal solution of each row is solved in turn according to the following formula:

[0049]

[0050] in, Represents Y v The increment of the objective function when the element in row i and column j changes from 0 to 1, (·) i· represents the i-th row of the matrix, (·) ·j Represents the jth column of the matrix; get Y v The update strategy for row i is as follows:

[0051]

[0052] Step 6: Alternately optimize the sample label U and anchor label V through steps 4 and 5 to obtain the binary sample label matrix Y after the direct objective function converges u and anchor label matrix Y v , the only "1" element in each row directly reflects the cluster category to which the sample point or anchor point corresponds to the image.

[0053] Beneficial effects

[0054] The present invention proposes a direct and fast image clustering method based on bipartite graph collaborative clustering. This method addresses the problems of existing collaborative clustering methods based on spectral clustering, such as high time complexity due to the construction of graph Laplacian matrices and eigenvalue decomposition or singular value decomposition, and the need for further processing of clustering results to obtain a clear category distribution. By introducing anchor points, the method eliminates the reliance of spectral clustering methods on graph Laplacian matrices, reducing the computational and spatial complexity of the algorithm. A two-step alternating optimization solution is used in the optimization process. The original regularized graph cutting problem is directly solved with the help of the idea of ​​coordinate descent. The binary data point label matrix and the binary anchor point label matrix are iteratively solved without the need for eigenvalue decomposition or singular value decomposition, greatly improving the optimization speed. The final clustering result can be directly obtained, allowing for direct and rapid collaborative clustering.

[0055] The beneficial effects of the method of the present invention mainly include:

[0056] (1) By introducing anchor points, the collaborative clustering method eliminates its dependence on the graph Laplacian matrix, and can directly perform regularized graph cutting on the bipartite graph affinity matrix. This avoids the high computational complexity of the collaborative clustering method based on spectral clustering due to the construction of the graph Laplacian matrix, eigenvalue decomposition, or singular value decomposition, thereby improving the efficiency of the collaborative clustering method of the present invention and its adaptability to large-scale data.

[0057] (2) The two-step alternating optimization algorithm used in the present invention transforms the problem of solving the soft label matrix into the problem of directly solving the discrete label matrix with the help of the coordinate descent idea. The binary data point label matrix and the binary anchor point label matrix are iteratively solved to directly obtain the clustering results, thus avoiding the defect of the collaborative clustering algorithm based on spectral clustering that requires post-processing.

[0058] (3) The anchor point labels obtained in this invention can be used as prior knowledge when performing downstream tasks based on the currently obtained classification results. The anchor point cluster distribution preliminarily indicates the potential cluster information of the currently processed data set. Moreover, since the number of anchor point data is generally much smaller than the number of sample points, the rational application of anchor points for downstream tasks can effectively improve the efficiency of the algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 It is a method flow chart

[0060] Figure 2 This is a specific implementation flowchart on the Coil20 object dataset DETAILED DESCRIPTION

[0061] The present invention will now be further described with reference to the embodiments and accompanying drawings:

[0062] This paper proposes a direct and rapid image clustering method based on bipartite graph co-clustering. The specific steps for clustering images using the object image dataset Coil20 are explained, but the technical content of this invention is not limited to this description. The Coil20 object image dataset contains 1440 object images, each with a length and width of 128 pixels. There are 20 categories, each with 72 sample points.

[0063] The present invention proposes a direct and fast image clustering method based on bipartite graph collaborative clustering, which includes the following steps:

[0064] Step 1: Downsample the Coil20 dataset image to an image with a length and width of 32 pixels. Use the grayscale feature of the image as the data feature of the image. Straighten the pixel grayscale value of each image into a vector. The dimension of the vector is 1024, and the feature matrix corresponding to the image is Each row of the matrix is ​​a sample, n = 1440 is the number of image samples, and d = 1024 is the dimension of the feature. The Kmeans clustering method is used to generate m representative anchor points, and m anchor points are generated to obtain the anchor matrix Where m is the number of manually selected anchor points.

[0065] Step 2: Image data matrix based on the previous step And the obtained anchor matrix An, construct the bipartite graph affinity matrix

[0066]

[0067] Initialize the following parameters before iterative solution:

[0068] (1) Calculation matrix is a diagonal matrix whose j-th diagonal element

[0069] (2) Calculating the graph similarity matrix Sum degree matrix

[0070] (3) Matrix Make it satisfy Y u ,Y v ∈Ind;

[0071] (4) Matrix

[0072] (5) Matrix

[0073] (6) Matrix

[0074] Step 3: Update the sample point binary label matrix Y u , define t as the number of iterations

[0075]

[0076] in

[0077] Step 4: Update the anchor binary label matrix Y v :

[0078]

[0079] in

[0080] Step 5: Repeat steps 3 and 4 until the algorithm converges and output the sample label matrix and anchor label matrix The only "1" element in each row indicates the cluster category to which the sample point or anchor point belongs, and no post-processing steps are required. So far, the method proposed in this invention has completed the image clustering task on the object image dataset Coil20, and the obtained sample label matrix Y u Each row directly indicates the cluster category to which the corresponding image belongs.

[0081] In order to verify the effectiveness and efficiency of the image clustering method of the present invention in clustering when m=100 on the object image dataset Coil20, the label matrix corresponding to the lowest objective function value in ten repeated experiments was selected as the final clustering result. In the present invention, the introduction of the anchor graph eliminates the dependence of the collaborative clustering on the graph Laplacian matrix, reducing the computational complexity and space complexity of the algorithm; and a two-step alternating optimization solution is used in the optimization process, and the original regularized cut graph problem is directly solved with the help of the idea of ​​coordinate descent. There is no need to perform eigenvalue decomposition or singular value decomposition, which greatly improves the optimization speed and can directly obtain the final clustering result. By comparing the calculated label matrix with the true label of the sample, it can be obtained that the clustering accuracy of the present invention is 55.45%, which is 15.40% higher than the SOBG method in accuracy and 66.597s less time than SOBG. It not only improves the image clustering accuracy, but also greatly reduces the algorithm running time, which effectively verifies the effectiveness and efficiency of the present invention in image clustering tasks.

[0082] The above description is only a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with this technical field can easily think of various equivalent modifications or replacements within the technical scope disclosed in the present invention, and these modifications or replacements should all be included in the scope of protection of the present invention.

Claims

1. A direct and fast image clustering method based on bipartite graph collaborative clustering, characterized by Here are the steps: Step 1: Stretch the dataset containing n a×b pixel-scale images into an image data matrix Each row is a sample, n is the number of images, d = a × b is the total number of pixels in a single image, that is, the characteristic dimension of the image; Use Kmeans clustering method to generate m representative anchor points and obtain the anchor matrix Where m is the number of selected anchor points; Step 2: According to the image data matrix And the obtained anchor matrix An, the adaptive neighborhood assignment method is used to construct the bipartite graph affinity matrix b obtained by adaptive neighborhood assignment method ij as follows: where μ j Represents the sample point x i The jth nearest anchor point, Represents the sample point x i With anchor point μ j The square of the Euclidean distance between them, k is an artificially selected parameter; Step 3: Based on the constructed bipartite graph affinity matrix B, a clustering model based on bipartite graph collaborative clustering is constructed. The objective function is expressed as follows: in, is the graph Laplacian matrix, is the degree matrix, is the soft label matrix; Y∈Ind represents is a binary label matrix; N = n + m is the sum of the number of sample points and anchor points, and c is the final number of clusters; Replace the Laplace matrix with the following regularized Laplace matrix: in, is the graph similarity matrix; is a diagonal matrix whose j-th diagonal element is the identity matrix; The binary label matrix is ​​written as follows: in, are binary sample label matrix and anchor label matrix respectively, They are the sample soft label matrix and the anchor soft label matrix respectively; Substitute the regularized Laplacian matrix, the rewritten binary label matrix, and the soft label matrix into the original problem for transformation. The detailed process is as follows: The original problem is equivalent to a maximization problem: A two-step alternating optimization algorithm is used to solve the above problem; Step 4: Fix the anchor soft label V and update the sample soft label U to optimize the objective function When V is fixed, the optimization problem is equivalent to: in, Expanding the above problem of finding the maximum trace of a matrix, we can get: in,(·) ·j represents the jth column of the matrix, (·) ij represents the element in the i-th row and j-th column of the matrix; the sample label matrix Y u The solution of each row is an independent process, and the optimal solution of each row is solved in turn according to the following formula: in, Indicates Y u The increment of the objective function when the element in row i and column j changes from 0 to 1; The obtained Y u The update strategy for row i is as follows: Step 5: Fix the sample soft label U and update the anchor soft label V to optimize the objective function When U is fixed, the optimization problem is equivalent to: in, Expanding the above problem of finding the maximum trace of a matrix, we can get: in,(·) ij Represents the element in the i-th row and j-th column of the matrix; In this problem, the anchor label matrix Y v The solution of each row is an independent process, and the optimal solution of each row is solved in turn according to the following formula: in, Indicates Y v The increment of the objective function when the element in row i and column j changes from 0 to 1, (·) i· represents the i-th row of the matrix, (·) ·j Represents the jth column of the matrix; get Y v The update strategy for row i is as follows: Step 6: Alternately optimize the sample label U and anchor label V through steps 4 and 5 to obtain the binary sample label matrix Y after the direct objective function converges u and anchor label matrix Y v , the only "1" element in each row directly reflects the cluster category to which the sample point or anchor point corresponds to the image.

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