Fuzzy Double Trace Norm Minimization for Recommendation Systems

Recovering low-rank matrices from incomplete observations is a fundamental problem with many applications, especially in recommender systems. In theory, under certain conditions, this problem can be solved by convex or nonconvex relaxation. However, most existing provable algorithms suffer from supe...

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Vydané v:IEEE transactions on fuzzy systems Ročník 26; číslo 4; s. 2039 - 2049
Hlavní autori: Shang, Fanhua, Liu, Yuanyuan, Cheng, James, Yan, Da
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York IEEE 01.08.2018
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Predmet:
Algorithm design and analysis
Algorithms
Collaborative filtering
contextual information
Convergence
double trace norm
Fuzzy systems
fuzzy weighting
Iterative methods
matrix completion
Matrix converters
Matrix decomposition
Minimization
Optimization
Recommender systems
Recoverability
ISSN:1063-6706, 1941-0034
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Popis
Shrnutí:Recovering low-rank matrices from incomplete observations is a fundamental problem with many applications, especially in recommender systems. In theory, under certain conditions, this problem can be solved by convex or nonconvex relaxation. However, most existing provable algorithms suffer from superlinear per-iteration cost, which severely limits their applicability to large-scale problems. In this paper, we propose a novel fuzzy double trace norm minimization (DTNM) method for recommender systems. We first present a tractable DTNM model, in which we can integrate both the user social relationship and the user reputation information using a fuzzy weighting way and coupling fuzzy matrix factorization. In essence, our model is a Schatten-<inline-formula><tex-math notation="LaTeX">{1/2}</tex-math> </inline-formula> quasi-norm minimization problem. Moreover, we develop two efficient augmented Lagrangian algorithms to solve the proposed problems, and prove the convergence of our algorithms. Finally, we investigate the empirical recoverability properties of our model and its advantage over classical trace norm. Extensive experimental results on both synthetic and real-world data sets verified both the efficiency and effectiveness of our method compared with the state-of-the-art algorithms.
Bibliografia:ObjectType-Article-1
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ISSN:1063-6706
1941-0034
DOI:10.1109/TFUZZ.2017.2760287