Nonnegative matrix factorization method based on low-rank recovery

A non-negative matrix decomposition, low-rank matrix technology, applied in the field of information processing, can solve the problem of non-negative decomposition noise interference and so on

Active Publication Date: 2016-09-07
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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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 invention belongs to the technical field of information processing and particularly relates to a nonnegative matrix factorization method based on low-rank recovery. The method comprises following steps: 1. each image sample in a raw database is converted into a vector to form an m*n original data matrix X, wherein m is the dimension of the image sample, n is the number of image samples; 2. low-rank sparse factorization is performed on the original data matrix X; 2.1 the rank of the low-rank matrix is set as r, and the sparseness of the sparse matrix is set as k; 2.2 a low-rank matrix L with the rank of r and a sparse matrix S with the rank of k of the original data matrix X is solved by means of the bilateral random projection algorithm; 3. nonnegative matrix factorization is performed on the low-rank matrix L obtained in step 2. to obtain a basis matrix W and an encoding matrix H. According to the nonnegative matrix factorization method based on low-rank recovery, data low-rank components and sparse components are obtained through low-rank sparse factorization and nonnegative matrix factorization is performed on the low-rank components removed of sparse noise parts to make the nonnegative matrix factorization results 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 recovery. 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 engineerin...

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Application Information

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Patent Type & Authority Applications(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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