Transformed Schatten-1 Iterative Thresholding Algorithms for Low Rank Matrix Completion

We study a non-convex low-rank promoting penalty function, the transformed Schatten-1 (TS1), and its applications in matrix completion. The TS1 penalty, as a matrix quasi-norm defined on its singular values, interpolates the rank and the nuclear norm through a nonnegative parameter a. We consider the unconstrained TS1 regularized low-rank matrix recovery problem and develop a fixed point representation for its global minimizer. The TS1 thresholding functions are in closed analytical form for all parameter values. The TS1 threshold values differ in subcritical (supercritical) parameter regime where the TS1 threshold functions are continuous (discontinuous). We propose TS1 iterative thresholding algorithms and compare them with some state-of-the-art algorithms on matrix completion test problems. For problems with known rank, a fully adaptive TS1 iterative thresholding algorithm consistently performs the best under different conditions with ground truth matrix being multivariate Gaussian at varying covariance. For problems with unknown rank, TS1 algorithms with an additional rank estimation procedure approach the level of IRucL-q which is an iterative reweighted algorithm, non-convex in nature and best in performance

AutoSVD++: An Efficient Hybrid Collaborative Filtering Model via Contractive Auto-encoders

Collaborative filtering (CF) has been successfully used to provide users with personalized products and services. However, dealing with the increasing sparseness of user-item matrix still remains a challenge. To tackle such issue, hybrid CF such as combining with content based filtering and leveraging side information of users and items has been extensively studied to enhance performance. However, most of these approaches depend on hand-crafted feature engineering, which are usually noise-prone and biased by different feature extraction and selection schemes. In this paper, we propose a new hybrid model by generalizing contractive auto-encoder paradigm into matrix factorization framework with good scalability and computational efficiency, which jointly model content information as representations of effectiveness and compactness, and leverage implicit user feedback to make accurate recommendations. Extensive experiments conducted over three large scale real datasets indicate the proposed approach outperforms the compared methods for item recommendation.Comment: 4 pages, 3 figure

Porcellio scaber algorithm (PSA) for solving constrained optimization problems

In this paper, we extend a bio-inspired algorithm called the porcellio scaber algorithm (PSA) to solve constrained optimization problems, including a constrained mixed discrete-continuous nonlinear optimization problem. Our extensive experiment results based on benchmark optimization problems show that the PSA has a better performance than many existing methods or algorithms. The results indicate that the PSA is a promising algorithm for constrained optimization.Comment: 6 pages, 1 figur