Efficient bayesian hierarchical user modeling for recommendation system
SIGIR '07 Proceedings of the 30th annual international ACM SIGIR conference on Research and development in information retrieval
Knowledge and Information Systems
General Tensor Discriminant Analysis and Gabor Features for Gait Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
Factorization meets the neighborhood: a multifaceted collaborative filtering model
Proceedings of the 14th ACM SIGKDD international conference on Knowledge discovery and data mining
Collaborative filtering with temporal dynamics
Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining
Large-scale sparse logistic regression
Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining
Exact Matrix Completion via Convex Optimization
Foundations of Computational Mathematics
The power of convex relaxation: near-optimal matrix completion
IEEE Transactions on Information Theory
Matrix completion from a few entries
IEEE Transactions on Information Theory
Training and testing of recommender systems on data missing not at random
Proceedings of the 16th ACM SIGKDD international conference on Knowledge discovery and data mining
Performance of recommender algorithms on top-n recommendation tasks
Proceedings of the fourth ACM conference on Recommender systems
A Singular Value Thresholding Algorithm for Matrix Completion
SIAM Journal on Optimization
Localized factor models for multi-context recommendation
Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining
Bayesian Tensor Approach for 3-D Face Modeling
IEEE Transactions on Circuits and Systems for Video Technology
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Recovering a large matrix from a small subset of its entries is a challenging problem arising in many real world applications, such as recommender system and image in-painting. These problems can be formulated as a general matrix completion problem. The Singular Value Thresholding (SVT) algorithm is a simple and efficient first-order matrix completion method to recover the missing values when the original data matrix is of low rank. SVT has been applied successfully in many applications. However, SVT is computationally expensive when the size of the data matrix is large, which significantly limits its applicability. In this paper, we propose an Accelerated Singular Value Thresholding (ASVT) algorithm which improves the convergence rate from O(1/N) for SVT to O(1/N2), where N is the number of iterations during optimization. Specifically, the dual problem of the nuclear norm minimization problem is derived and an adaptive line search scheme is introduced to solve this dual problem. Consequently, the optimal solution of the primary problem can be readily obtained from that of the dual problem. We have conducted a series of experiments on a synthetic dataset, a distance matrix dataset and a large movie rating dataset. The experimental results have demonstrated the efficiency and effectiveness of the proposed algorithm.