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Matrix completion method based on self-adaptive neighbors

A matrix completion and self-adaptive technology, applied in the field of matrix completion, can solve the problem of ignoring data prior information and achieve high precision

Pending Publication Date: 2019-07-09
NANJING UNIV OF SCI & TECH
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Problems solved by technology

However, the existing matrix completion methods often ignore some prior information of the data, such as category information, local structure information, etc.

Method used

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  • Matrix completion method based on self-adaptive neighbors
  • Matrix completion method based on self-adaptive neighbors
  • Matrix completion method based on self-adaptive neighbors

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Embodiment Construction

[0033] Such as Figure 1 ~ Figure 3 As shown, a matrix completion method based on adaptive nearest neighbor, the specific steps are:

[0034] Step 1. Construct a reconstruction objective function based on neighbor learning;

[0035] The original matrix is ​​X, and the purpose of this invention is to restore the original matrix X from the obtained data matrix D, where X∈R n ×N . For partially missing data, the similarity matrix W can be obtained by the following function:

[0036]

[0037] s.t.P π (D)=P π (X),

[0038]

[0039]

[0040] In the formula, X is the original data matrix, D is the matrix to be completed, W is the similarity matrix, L w is the Laplacian matrix of W, c is the number of categories, 1 means a column vector whose element values ​​are all 1, W j is the vector of column j in W, W i,j is the element of row i and column j in W, π is the subscript set of the obtained data, P π To represent the projection to π, the parameter β is obtained by ...

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Abstract

The invention discloses a matrix completion method based on self-adaptive neighbors, which comprises the following steps: applying rank constraint to a Laplace matrix of a similar matrix, enabling neighbors and missing samples to belong to the same category, and constructing an objective function based on neighbor reconstruction; and solving the objective function through an iterative optimizationmethod to obtain a matrix after completion. According to the method, complete data can be recovered from a large number of missing data samples, and high precision is achieved.

Description

technical field [0001] The invention relates to matrix completion technology, in particular to a matrix completion method based on self-adaptive neighbors. Background technique [0002] With the rapid development of information technology and the continuous increase of data sampling methods, the acquisition of large-scale high-dimensional data has become easier. However, due to various external factors, most of the data we obtain is damaged or noisy. For example, due to sensor sensitivity, the data we collect often differs from the original data. Secondly, errors or omissions often occur during the data entry process due to human factors. How to obtain accurate data is an urgent problem that researchers must solve. Therefore, matrix completion has attracted extensive attention as a method for data restoration. [0003] Matrix completion is used in many areas of engineering and applied science, such as recommender systems, image processing, signal processing, etc. In the...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F17/16G06T5/00
CPCG06F17/16G06T5/77
Inventor 刘丝雨严慧
Owner NANJING UNIV OF SCI & TECH
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