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Convex nonnegative matrix factorization method based on subspace clustering

A non-negative matrix decomposition and subspace technology, applied in the fields of data mining, information processing, and data analysis, can solve the problems of subspace clustering and non-negative matrix decomposition collaborative optimization framework, etc., to improve the effect of image clustering, Robustness-enhancing effects

Active Publication Date: 2018-08-17
XI'AN INST OF OPTICS & FINE MECHANICS - CHINESE ACAD OF SCI
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Problems solved by technology

The subspace reconstruction coefficients can be obtained by the subspace clustering method, however, the optimization process of the subspace clustering method is usually independent of the optimization process of the non-negative matrix factorization, and the cooperative optimization of subspace clustering and non-negative matrix factorization has not yet been seen. frame

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  • Convex nonnegative matrix factorization method based on subspace clustering
  • Convex nonnegative matrix factorization method based on subspace clustering
  • Convex nonnegative matrix factorization method based on subspace clustering

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Embodiment 1

[0063] Embodiment one (with reference to figure 1 )

[0064] Step 1, decompose the original data matrix under the proposed subspace clustering-based convex non-negative matrix factorization framework.

[0065] (1a) Pull each image in the image sample set into a vector to form an m×n original data matrix X, m is the dimension of each sample, and n is the number of samples;

[0066] (1b) Initialize the matrix G of n×l 0 , l×n encoding matrix V 0 It is a non-negative random matrix, l=n s ×n c is the dimension of the learned low-dimensional non-negative subspace, n c is the total number of classes in the database, n s For the number of centers of each cluster, generally set n s =10, the number of iterations t=0.

[0067] (1c) Use the K nearest neighbor algorithm to construct the initial neighbor graph, the number of neighbors K is set to 5, and the initial graph Laplacian matrix L is calculated 0 , where L 0 =D 0 -W 0 , W 0 Represents a symmetric weight matrix, D 0 i...

Embodiment 2

[0095] Embodiment two (with reference to figure 2 )

[0096] Step 1, decompose the original data matrix under the proposed subspace clustering-based convex non-negative matrix factorization framework.

[0097] (1a) Pull each image in the image sample set into a vector to form an m×n original data matrix X, m is the dimension of each sample, and n is the number of samples;

[0098] (1b) Initialize the matrix G of n×l 0 , l×n encoding matrix V 0 It is a non-negative random matrix, l=n s ×n c is the dimension of the learned low-dimensional non-negative subspace, n c is the total number of classes in the database, n s For the number of centers of each cluster, generally set n s =10, the number of iterations t=0.

[0099] (1c) Use the K nearest neighbor algorithm to construct the initial neighbor graph, the number of neighbors K is set to 5, and the initial graph Laplacian matrix L is calculated 0 , where L 0 =D 0 -W 0 , W 0 Represents a symmetric weight matrix, D 0 is...

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Abstract

The invention discloses a convex nonnegative matrix factorization method based on subspace clustering. The method comprises the implementation steps of (1) stretching an image in an original databaseinto vectors to compose an original data matrix; (2) performing convex nonnegative matrix factorization based on spectral clustering on the original data matrix, solving by use of two optimization methods to obtain a basis matrix and an encoding matrix; and (3) performing a clustering test of a k-means clustering algorithm on the encoding matrix, counting experimental results, calculating two measure criteria of clustering precision and normalized mutual information. According to the convex nonnegative matrix factorization method based on subspace clustering, compared with an existing method,subspace structural information inside data is explored and utilized, meanwhile the local subspace constraints exerted to the algorithm enhances robustness of the algorithm and improves the clusteringeffect of the image; and the method can be widely applied to the field of data mining and data analysis.

Description

technical field [0001] The invention belongs to the technical field of information processing, and in particular relates to a non-negative low-dimensional data processing method, which can be used in data mining, data analysis and other fields. Background technique [0002] Non-negative matrix factorization as a feature extraction technique, since Lee and Seung's seminal work "Learning the Parts of Objects by Non-Negative Matrix Factorization, Nature, vol.401, no.6755, pp.788-791,1999" , the non-negative matrix factorization algorithm is becoming more and more popular in the field of computer vision and pattern recognition. In their work, it is pointed out that the non-negative constraints on the factor matrix can automatically learn the part-based representation of the data, which is closely related to the brain's perception mechanism. In addition to this discovery, another contribution of his work is to propose a simple but very effective solution algorithm. Thanks to th...

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Application Information

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IPC IPC(8): G06F17/16G06K9/62
CPCG06F17/16G06F18/23213
Inventor 李学龙崔国盛董永生
Owner XI'AN INST OF OPTICS & FINE MECHANICS - CHINESE ACAD OF SCI
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