Data recovery method based on schatten capped p-norm

Abstract

The invention discloses a matrix completion method based on the Schatten Capped p-norm, comprising the following steps: S1, obtaining the corresponding orthogonal mapping operator representation of the input incomplete data matrix The set of positions where the corresponding item of the data matrix D is not empty; represents the restored matrix; S2, defines the Schatten Capped p norm of the matrix where it represents the truncation parameter, θ i Represents the i-th singular value of the matrix, p represents the power exponent, p∈(0,1]; S3, solve the optimization problem of the following formula until it converges, and output the completed data matrix s.t.E Ω =X Ω -D Ω ,X=W, where W is an equivalent variable, and γ is a penalty parameter. The method of the present invention performs matrix completion, so that the data matrix is ​​of low rank, and can ensure that main information is not lost, and the data recovery accuracy is high, that is, the present invention has a good recovery effect on incomplete matrices with low rank properties.

Description

technical field [0001] The invention relates to a data recovery method based on Schatten Capped p norm, belonging to the technical field of data recovery. 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 data accordin...

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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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