Matrix completion method based on Schatten Capped p norm

Abstract

The invention discloses a matrix completion method based on a Schatten Capped p norm. The matrix completion method comprises the following steps: S1, solving an orthogonal mapping operator corresponding to an input incomplete data matrix, wherein the orthogonal mapping operator represents a set of positions where corresponding items of a data matrix D are not empty; representing the recovered matrix; S2, defining a Schatten Capped p norm of the matrix to represent a truncation parameter, wherein Theta i represents an ith singular value of the matrix, p represents a power index, and p belongs to (0, 1]; S3, solving an optimization problem of the following formula until convergence, and outputting a complemented data matrix s.t.E Omega= X Omega-D Omega with X equal to W, wherein W is an equivalent variable and gamma is a penalty parameter. Matrix completion is conducted through the method, so that the data matrix is low in rank. Main information is not lost. Data recovery precision is high. The method has a good recovery effect on an incomplete matrix with the low-rank property.

Description

technical field [0001] The invention relates to a matrix completion method based on Schatten Capped p norm, which belongs to the technical field of data restoration. Background technique [0002] In machine learning and data mining, such as computer vision, collaborative filtering, signal processing, recommendation systems, etc., engineers often recover high-dimensional information (original data) with high probability based on low-dimensional features (partial information). The reason why the work can be done is that the data abstracted from the original information has the characteristics of sparse or low rank, and the sparseness of the vector corresponds to the low rank of the matrix. Matrix filling is one of the most classical applications of low-rank properties. [0003] The problem of matrix filling processing is to assume that the data matrix is ​​of low rank and there is correlation between matrix elements, then the missing data can be recovered from the observed da...

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Problems solved by technology

However, Schatten p norm takes every singular value into account, which does not conform to the characteristics of low rank (for small singular values, there is often noise, which should be removed, and if retained, the recovery effect will be worse), while Capped norm only considers If the size of the rank is increased, some information may be lost (the essence of Capped norm is to set the smaller singular value to 0, and subtract a small part from the larger singular value, which reduces the rank, but also loses some main information), resulting in less effective data recovery

In addition, the existing TNNR-APGL algorithm, Logarithm-ADMM algorithm and Logarithm-IRNN algorithm are usually used for matrix completion and data recovery, but overall, their data recovery quality is still not ideal

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