Nonnegative matrix factorization method based on low-rank recovery

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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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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