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Self-paced matrix decomposition method based on Pareto optimization

A matrix decomposition and matrix technology, applied in genetic models, instruments, computing models, etc., can solve problems such as poor matrix decomposition and local minima

Inactive Publication Date: 2017-06-20
XIDIAN UNIV
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  • Application Information

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Problems solved by technology

[0010] The purpose of the present invention is to overcome the existing problems of self-paced learning in the self-paced matrix factorization method in the prior art, and effectively alleviate the problem of matrix factorization falling into a bad local minimum due to the non-convex objective function, especially when there are abnormal data and missing data in the case of

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  • Self-paced matrix decomposition method based on Pareto optimization
  • Self-paced matrix decomposition method based on Pareto optimization
  • Self-paced matrix decomposition method based on Pareto optimization

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Embodiment 1

[0039] This embodiment provides a figure 1 The self-stepping matrix factorization method based on Pareto optimization shown includes the following steps:

[0040] Step 1) Input the matrix Y∈R to be decomposed m×n , population size N p and step size information, the matrix index set of the non-missing data in the matrix Y to be decomposed is Ω, and the step size information includes the initial step size k 0 and step increment μ;

[0041] Step 2) Decompose the matrix Y to be decomposed to obtain the initial matrix U 0 ,V 0 , calculate the matrix element loss value, and then according to the weight distribution method f(w ij ; k) and random method to generate a population size of N p The initial weight population P 0 And calculate the two objective function values ​​corresponding to the population individual, at this time And set the iteration termination number G max , where U 0 ∈R m×r ,V 0 ∈R r×n ,r0 Increase μ successively to get, w ij Indicates the weight of t...

Embodiment 2

[0052] On the basis of Embodiment 1, this embodiment provides a self-step matrix decomposition method based on Pareto optimization, including the following steps:

[0053] Step 1) Input matrix Y, population size N p and step information:

[0054] Randomly generate elements Y of matrix Y ij Obey the Gaussian distribution N(0,1), and then 40% of them are selected as missing data, 20% of the data is added to the uniformly distributed noise disturbance on [-20,20] and 20% of the data is added to Gaussian noise ~ N(0,0.01) Disturbance; step size information includes initial step size k and step size increment μ;

[0055] Step 2) Decompose Y to get the initial matrix U 0 ,V 0 , calculate the loss and generate the initial weight population P 0 And set the iteration termination number G max : Population P 0 Schematic figure 2 ;

[0056] Use the traditional matrix decomposition method to get the initial matrix U 0 ,V 0 , the matrix U 0 ,V 0 Substituting the loss function ...

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Abstract

The invention provides a self-paced matrix decomposition method based on Pareto optimization, and the method comprises the steps: changing a method, which employs a monotone increasing learning step in the conventional self-paced learning to determine the weight of a sample, into a method of obtaining the weight of the sample through the technology of Pareto optimization; changing a sample weight expression range [0, 1] in the Pareto optimization process into a range [-1, 1], and enabling a difficult sample weight to exist in a reasonable distribution range, thereby guaranteeing the diversity; finally selecting a Knee point which achieves the best compromise on an optimization result PF plane as a matrix element weight, thereby speeding up the matrix decomposition process. In a word, the method is more reasonable and accords with the cognitive science in a better way.

Description

technical field [0001] The invention belongs to the technical field of machine learning, and in particular relates to a self-step matrix decomposition method based on Pareto optimization. Background technique [0002] In the field of machine learning, due to the increasingly complex problems to be solved, the optimization objective functions of many tasks are non-convex, which makes it easy to fall into a local optimum during the optimization process. Inspired by the fact that people and animals often learn simple knowledge first and then gradually learn difficult knowledge to achieve learning goals, Y.Bengio, J.Louradour, R.Collobert, and J.Weston in the literature "Curriculum learning" (ICML, 2009) proposed a learning strategy course learning (CL) based on machine learning. Its core idea is to define a "course" in which training samples gradually increase in training difficulty, and then let the model train the defined course. Experiments prove that CL is beneficial to ac...

Claims

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Application Information

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IPC IPC(8): G06N3/00G06N3/12
CPCG06N3/006G06N3/12
Inventor 公茂果武越王聪聪马晶晶李豪刘嘉王善峰张普照
Owner XIDIAN UNIV
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