Matrix computations (3rd ed.)
Probabilistic latent semantic indexing
Proceedings of the 22nd annual international ACM SIGIR conference on Research and development in information retrieval
Clustering Algorithms
Parallel Optimization: Theory, Algorithms and Applications
Parallel Optimization: Theory, Algorithms and Applications
Relative Expected Instantaneous Loss Bounds
COLT '00 Proceedings of the Thirteenth Annual Conference on Computational Learning Theory
Approximate solutions to markov decision processes
Approximate solutions to markov decision processes
The Journal of Machine Learning Research
Convex Optimization
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 1 - Volume 01
Multi-label informed latent semantic indexing
Proceedings of the 28th annual international ACM SIGIR conference on Research and development in information retrieval
Fast maximum margin matrix factorization for collaborative prediction
ICML '05 Proceedings of the 22nd international conference on Machine learning
Spectral clustering for multi-type relational data
ICML '06 Proceedings of the 23rd international conference on Machine learning
The support vector decomposition machine
ICML '06 Proceedings of the 23rd international conference on Machine learning
Unsupervised learning on k-partite graphs
Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining
Supervised probabilistic principal component analysis
Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining
Clustering with Bregman Divergences
The Journal of Machine Learning Research
Relational clustering by symmetric convex coding
Proceedings of the 24th international conference on Machine learning
Combining content and link for classification using matrix factorization
SIGIR '07 Proceedings of the 30th annual international ACM SIGIR conference on Research and development in information retrieval
A probabilistic framework for relational clustering
Proceedings of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining
Extracting information from informal communication
Extracting information from informal communication
Closed-form supervised dimensionality reduction with generalized linear models
Proceedings of the 25th international conference on Machine learning
Relational learning via collective matrix factorization
Proceedings of the 14th ACM SIGKDD international conference on Knowledge discovery and data mining
Fast Optimization Methods for L1 Regularization: A Comparative Study and Two New Approaches
ECML '07 Proceedings of the 18th European conference on Machine Learning
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
Nonnegative Lagrangian relaxation of k-means and spectral clustering
ECML'05 Proceedings of the 16th European conference on Machine Learning
SLSFS'05 Proceedings of the 2005 international conference on Subspace, Latent Structure and Feature Selection
Probabilistic Factorization of Non-negative Data with Entropic Co-occurrence Constraints
ICA '09 Proceedings of the 8th International Conference on Independent Component Analysis and Signal Separation
On smoothing and inference for topic models
UAI '09 Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence
UAI '09 Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence
Probabilistic latent tensor factorization
LVA/ICA'10 Proceedings of the 9th international conference on Latent variable analysis and signal separation
Collaborative competitive filtering: learning recommender using context of user choice
Proceedings of the 34th international ACM SIGIR conference on Research and development in Information Retrieval
Regularized latent semantic indexing
Proceedings of the 34th international ACM SIGIR conference on Research and development in Information Retrieval
Large-scale matrix factorization with distributed stochastic gradient descent
Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining
Pattern change discovery between high dimensional data sets
Proceedings of the 20th ACM international conference on Information and knowledge management
Multi-relational matrix factorization using bayesian personalized ranking for social network data
Proceedings of the fifth ACM international conference on Web search and data mining
Algorithms for probabilistic latent tensor factorization
Signal Processing
Detecting communities in K-partite K-uniform (hyper)networks
Journal of Computer Science and Technology - Special issue on Community Analysis and Information Recommendation
Fast bregman divergence NMF using taylor expansion and coordinate descent
Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining
Learning to rank social update streams
SIGIR '12 Proceedings of the 35th international ACM SIGIR conference on Research and development in information retrieval
Mining from protein–protein interactions
Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery
Regularized Latent Semantic Indexing: A New Approach to Large-Scale Topic Modeling
ACM Transactions on Information Systems (TOIS)
On the equivalence of PLSI and projected clustering
ACM SIGMOD Record
Sparkler: supporting large-scale matrix factorization
Proceedings of the 16th International Conference on Extending Database Technology
Document Re-ranking Using Partial Social Tagging
WI-IAT '12 Proceedings of the The 2012 IEEE/WIC/ACM International Joint Conferences on Web Intelligence and Intelligent Agent Technology - Volume 01
Latent outlier detection and the low precision problem
Proceedings of the ACM SIGKDD Workshop on Outlier Detection and Description
Retargeted matrix factorization for collaborative filtering
Proceedings of the 7th ACM conference on Recommender systems
Learning descriptive visual representation by semantic regularized matrix factorization
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
CoBaFi: collaborative bayesian filtering
Proceedings of the 23rd international conference on World wide web
Poisson Noise Reduction with Non-local PCA
Journal of Mathematical Imaging and Vision
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We present a unified view of matrix factorization that frames the differences among popular methods, such as NMF, Weighted SVD, E-PCA, MMMF, pLSI, pLSI-pHITS, Bregman co-clustering, and many others, in terms of a small number of modeling choices. Many of these approaches can be viewed as minimizing a generalized Bregman divergence, and we show that (i) a straightforward alternating projection algorithm can be applied to almost any model in our unified view; (ii) the Hessian for each projection has special structure that makes a Newton projection feasible, even when there are equality constraints on the factors, which allows for matrix co-clustering; and (iii) alternating projections can be generalized to simultaneously factor a set of matrices that share dimensions. These observations immediately yield new optimization algorithms for the above factorization methods, and suggest novel generalizations of these methods such as incorporating row and column biases, and adding or relaxing clustering constraints.