Ultralow rank tensor data filling method

A filling method and rank tensor technology, which can be used in image data processing, complex mathematical operations, instruments, etc., and can solve problems such as low precision

Inactive Publication Date: 2017-10-24
NORTHWESTERN POLYTECHNICAL UNIV
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Problems solved by technology

[0004] In order to overcome the deficiency of low accuracy of existing tensor data processing methods, the present invention provides an ultra-low rank tensor data filling method

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Embodiment Construction

[0068] The specific steps of the ultra-low rank tensor data filling method of the present invention are as follows:

[0069] Step 1. Build a tensor filling model.

[0070] For an implicit tensor of rank K (The tensor data to be filled are collectively referred to as hidden tensors), under the influence of noise, part of the observations Y can be obtained Ω , Ω represents the index of the observation, then the observation model is expressed as:

[0071] Y Ω =L Ω +M Ω (1)

[0072] where Y Ω ={y i} i∈Ω is the observed quantity, y i means Y Ω Atom with index i in M Ω for noise data. To describe both low-rank and non-low-rank structures, the hidden tensor L can be decomposed into a low-rank structure X (the truly low-rank part of L) and a non-low-rank structure (residual component) E, where E is approximately full rank.

[0073] L=X+E (2)

[0074] According to the observation model of formula (1), the present invention assumes that Y Ω Each atom in is independent ...

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Abstract

The invention discloses an ultralow rank tensor data filling method, used to solve a technical problem that an existing tensor data processing method is low in precision. The technical scheme comprises: decomposing a tensor to a low-rank structure and a non-low-rank structure, using a Gaussian Mixture Model (MOG) to perform priori description on the non-low-rank structure, using a Gibbs to sample to obtain sample average of the non-low-rank structure E and the low-rank structure X which is decomposed based on CP, and using an average approximate band to obtain implicit tensor. On one hand, the method fully excavates sparsity of CANDECOMP/PARAFAC(CP) decomposed weight, and a low-rank model based on sparsity is established, on the other hand, the Gaussian Mixture Model (MOG) is used to simulate the complex non-low-rank structure. The two points ensure that even though under the condition of lower than 10% observation rate, the method can adaptively fill tensor. Through tests, relative reconstruction error is reduced, and reconstruction precision is improved.

Description

technical field [0001] The invention relates to a tensor data processing method, in particular to an ultra-low rank tensor data filling method. Background technique [0002] Tensor data has been widely used in the fields of computer vision, neuroscience, and chemistry. However, in practical applications, due to the influence of factors such as collection and transmission, tensors have data missing problems, such as incomplete social relationship networks, Corrupted video data, etc. Therefore, the research on tensor filling method has gradually attracted extensive attention of scholars at home and abroad. Extensive experiments show that tensor filling method based on low-rank representation is an effective way. [0003] The document "Q. Zhao, L. Zhang, and A. Cichocki. Bayesian CP factorization of incomplete tensors with automatic rank determination. IEEE Transactions on Pattern Analysis and Machine Intelligence, 37(9): 1751–1763, 2015." discloses a Zhang methods of data p...

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06K9/62G06T5/00G06F17/16
CPCG06F17/16G06T5/002G06T2207/10016G06F18/2136G06F18/24155
Inventor 魏巍张艳宁张磊王聪
Owner NORTHWESTERN POLYTECHNICAL UNIV
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