GroupLens: an open architecture for collaborative filtering of netnews
CSCW '94 Proceedings of the 1994 ACM conference on Computer supported cooperative work
Social information filtering: algorithms for automating “word of mouth”
CHI '95 Proceedings of the SIGCHI Conference on Human Factors in Computing Systems
Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond
Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond
SIAM Journal on Optimization
On the Nesterov--Todd Direction in Semidefinite Programming
SIAM Journal on Optimization
The Journal of Machine Learning Research
Evaluating collaborative filtering recommender systems
ACM Transactions on Information Systems (TOIS)
Latent semantic models for collaborative filtering
ACM Transactions on Information Systems (TOIS)
Preconditioning Indefinite Systems in Interior Point Methods for Optimization
Computational Optimization and Applications
Unifying collaborative and content-based filtering
ICML '04 Proceedings of the twenty-first international conference on Machine learning
A Dual Approach to Semidefinite Least-Squares Problems
SIAM Journal on Matrix Analysis and Applications
Least-Squares Covariance Matrix Adjustment
SIAM Journal on Matrix Analysis and Applications
A Quadratically Convergent Newton Method for Computing the Nearest Correlation Matrix
SIAM Journal on Matrix Analysis and Applications
A study of mixture models for collaborative filtering
Information Retrieval
Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning)
Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning)
An inexact primal–dual path following algorithm for convex quadratic SDP
Mathematical Programming: Series A and B
The Journal of Machine Learning Research
Empirical analysis of predictive algorithms for collaborative filtering
UAI'98 Proceedings of the Fourteenth conference on Uncertainty in artificial intelligence
Solving Large-Scale Least Squares Semidefinite Programming by Alternating Direction Methods
SIAM Journal on Matrix Analysis and Applications
An inexact spectral bundle method for convex quadratic semidefinite programming
Computational Optimization and Applications
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The correlation matrix is a fundamental statistic that used in many fields. For example, GroupLens, a collaborative filtering system, uses the correlation between users for predictive purposes. Since the correlation is a natural similarity measure between users, the correlation matrix may be used as the Gram matrix in kernel methods. However, the estimated correlation matrix sometimes has a serious defect: although the correlation matrix is originally positive semidefinite, the estimated one may not be positive semidefinite when not all ratings are observed. To obtain a positive semidefinite correlation matrix, the nearest correlation matrix problem has recently been studied in the fields of numerical analysis and optimization. However, statistical properties are not explicitly used in such studies. To obtain a positive semidefinite correlation matrix, we assume an approximate model. By using the model, an estimate is obtained as the optimal point of an optimization problem formulated with information on the variances of the estimated correlation coefficients. The problem is solved by a convex quadratic semidefinite program. A penalized likelihood approach is also examined. The MovieLens data set is used to test our approach.