Bayesian tensor completion algorithm based on complex noise

Abstract

The invention provides a Bayesian tensor complementation algorithm based on complex noise, which aims at target data with missing values and complex noise, expresses the target data as a tensor which is the sum of a tensor estimated value and noise, and extracts low-rank information of the tensor by adopting CP decomposition, so that the target data with missing values and complex noise can be complemented. Gibbs sampling is carried out by combining CP decomposition and a Bayesian method framework, a tensor estimation value is obtained through iteration, and target data are complemented and denoised simultaneously based on the tensor estimation value. The low-rank information of the tensor is fully mined by adopting CP decomposition, the observed tensor information is fully utilized, and iterative sampling is carried out, so that the completion algorithm can realize good completion and denoising on abnormal values and complex noise, is a robust and effective tensor completion algorithm, and compared with a completion method in the prior art, the tensor completion algorithm has the advantages that the complexity is low, and the efficiency is high. According to the complementation algorithm provided by the invention, a more accurate tensor estimation value can be obtained, so that more accurate target data complementation and denoising are realized.

Description

technical field [0001] The invention belongs to the technical field of tensor completion for data with noise, and in particular relates to a Bayesian tensor completion algorithm based on complex noise. Background technique [0002] In the era of big data, the data generated by the operation of human society is becoming more and more complex, and the dimensions are also higher and higher. At the same time, many data in the real world often have data missing and noise. How to deal with such data has also become one of the important issues in machine learning, data mining, computer vision and other fields. Tensors are high-dimensional arrays that, as a generalization of vectors and matrices, can be used to express multidimensional data with complex intrinsic structures. Tensors are a natural representation of real-world high-dimensional data. Therefore, the analysis of tensors has become an important tool in multidimensional data analysis and has applications in many fields. ...

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Problems solved by technology

[0004] Chen et al. (2016) proposed an EM algorithm model to solve the problem of mixed Gaussian noise in the absence of tensors, but it may cause overfitting problems

Luo et al. (2017) proposed a Bayesian framework to solve the mixed Gaussian noise problem of tensors, but Luo et al. (2017) did not consider the problem of missing data

Zhao et al. (2015c) assume that the observed value of the tensor is a low-rank tensor, the sum of outliers and Gaussian noise, which only has better performance when the tensor data is mixed with outliers and smaller Gaussian noise, but cannot Dealing with Complex Noise Problems

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