Non-negative matrix factorization method based on low-rank recovery

A technology of non-negative matrix decomposition and low-rank matrix, which is applied in the field of information processing and can solve problems such as non-negative decomposition noise interference

Active Publication Date: 2019-01-15
XI'AN INST OF OPTICS & FINE MECHANICS - CHINESE ACAD OF SCI
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Problems solved by technology

[0008] In order to solve the technical problem that non-negative decomposition is easily disturbed by noise, the present invention provides a non-negative matrix decomposition method based on low-rank restoration

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  • Non-negative matrix factorization method based on low-rank recovery
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  • Non-negative matrix factorization method based on low-rank recovery

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Embodiment Construction

[0047] see figure 1 , the implementation steps of a preferred embodiment of the present invention are as follows:

[0048] Step 1, perform low-rank sparse decomposition on the original data matrix.

[0049] (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;

[0050] (1b) Initialize the low-rank matrix as L 0 =X, the sparse matrix is ​​S 0 = 0, the rank of the low-rank matrix is ​​set to r, the sparsity of the sparse matrix is ​​set to k, the relative reconstruction error threshold ε, and the number of iterations t = 0.

[0051] (1c) In order to prevent the singular value of X from gradually degrading, resulting in poor approximation effect of the low-rank approximate matrix of rank r based on the original data matrix X based on bilateral projection, a power correction scheme is adopted, that is, the calculation A bilateral random projection of X instead of a b...

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Abstract

The present invention belongs to the technical field of information processing, and in particular relates to a non-negative matrix decomposition method based on low-rank restoration, comprising the following steps: 1] converting each image sample in the original database into a vector to form m×n original data Matrix X; m is the dimension of the image sample, and n is the number of image samples; 2] Perform low-rank sparse decomposition on the original data matrix X; 2.1] Set the rank of the low-rank matrix to r, and set the sparsity of the sparse matrix to k; 2.2] Use the bilateral random projection algorithm to solve the low-rank matrix L of the original data matrix X with rank r and the sparse matrix S with sparsity k; 3] perform non-negative The matrix is ​​decomposed to obtain the base matrix W and the coding matrix H. The invention obtains low-rank components and sparse components of data through low-rank sparse decomposition, and performs non-negative decomposition on the low-rank components with sparse noise removed, so that the non-negative decomposition results are free from noise interference.

Description

technical field [0001] The invention belongs to the technical field of information processing, and in particular relates to a non-negative matrix decomposition method based on low-rank restoration. Background technique [0002] With the development of informatization and the Internet, high-dimensional data continue to emerge in various fields of society. Generally speaking, these data are either semi-structured or unstructured, which makes the feature vectors for constructing these data up to tens of thousands of dimensions or even higher. The increase of data dimension brings difficulties to large-scale data processing. Non-negative matrix factorization is a research field based on unsupervised pattern recognition, which aims to obtain data-sparse, part-based low-dimensional data representation. Non-negative matrix factorization is widely used in the fields of mathematics, optimization, neural computing, pattern recognition and machine learning, data mining, image enginee...

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Application Information

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Patent Type & Authority Patents(China)
IPC IPC(8): G06F17/16G06K9/62
CPCG06F17/16G06F18/23213
Inventor 李学龙董永生崔国盛
Owner XI'AN INST OF OPTICS & FINE MECHANICS - CHINESE ACAD OF SCI
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