Fast and efficient algorithm for matrix completion via closed-form 2/3-thresholding operator

Matrix completion is arguably one of the most studied problems in machine learning and data analysis. Inspired by the closed-form formulas for L2/3 regularization, we employ the Schatten 2/3 quasi-norm to approximate the rank of a matrix, which can provide a better approximation than traditional way...

Celý popis

Uloženo v:
Podrobná bibliografie
Vydáno v:Neurocomputing (Amsterdam) Ročník 330; s. 212 - 222
Hlavní autoři: Wang, Zhi, Wang, Wendong, Wang, Jianjun, Chen, Siqi
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 22.02.2019
Témata:
2/3-thresholding operator
Closed-form formulas of L2/3 regularization
Fixed point iterative thresholding algorithm
Matrix completion
Fixed point iterative thresholding algorithm
Closed-form formulas of L2/3 regularization
2/3-thresholding operator
Matrix completion
ISSN:0925-2312, 1872-8286
On-line přístup:Získat plný text
Tagy: Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
Popis
Shrnutí:Matrix completion is arguably one of the most studied problems in machine learning and data analysis. Inspired by the closed-form formulas for L2/3 regularization, we employ the Schatten 2/3 quasi-norm to approximate the rank of a matrix, which can provide a better approximation than traditional ways. We also establish a necessary optimal condition and propose a fixed point iterative scheme for solving L2/3 regularization problem. Through analysing the monotonicity and the accumulation point of L2/3 regularization problem, the convergence of this iteration is analysed. By discussing the optimal selection of the regularization parameter together with a fast Monte Carlo algorithm and an approximate singular value decomposition (SVD) procedure, we build a fast and efficient algorithm that solves the induced optimization problem well. Extensive experiments have been conducted and the results show that the proposed algorithm is fast, efficient and robust. Specifically, we compare the proposed algorithm with state-of-the-art matrix completion algorithms on many synthetic data and large recommendation datasets. Our proposed algorithm is able to achieve similar or better prediction performance, while being faster and more efficient than alternatives. Furthermore, we demonstrate the effectiveness of our proposed algorithm by solving image inpainting problems.
ISSN:0925-2312
1872-8286
DOI:10.1016/j.neucom.2018.10.065