13,021 research outputs found
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
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