Journal of Algorithms
Rank, decomposition, and uniqueness for 3-way and n-way arrays
Multiway data analysis
Communications of the ACM
NIPS '97 Proceedings of the 1997 conference on Advances in neural information processing systems 10
A Multilinear Singular Value Decomposition
SIAM Journal on Matrix Analysis and Applications
On the Best Rank-1 and Rank-(R1,R2,. . .,RN) Approximation of Higher-Order Tensors
SIAM Journal on Matrix Analysis and Applications
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Competitive recommendation systems
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Eigentaste: A Constant Time Collaborative Filtering Algorithm
Information Retrieval
Amazon.com Recommendations: Item-to-Item Collaborative Filtering
IEEE Internet Computing
Learning Collaborative Information Filters
ICML '98 Proceedings of the Fifteenth International Conference on Machine Learning
Recommendation Systems: A Probabilistic Analysis
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Collaborative filtering with decoupled models for preferences and ratings
CIKM '03 Proceedings of the twelfth international conference on Information and knowledge management
An efficient boosting algorithm for combining preferences
The Journal of Machine Learning Research
Using mixture models for collaborative filtering
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
IEEE Transactions on Knowledge and Data Engineering
Fast Monte Carlo Algorithms for Matrices I: Approximating Matrix Multiplication
SIAM Journal on Computing
Fast Monte Carlo Algorithms for Matrices II: Computing a Low-Rank Approximation to a Matrix
SIAM Journal on Computing
SIAM Journal on Computing
On the Nyström Method for Approximating a Gram Matrix for Improved Kernel-Based Learning
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
Preference-based graphic models for collaborative filtering
UAI'03 Proceedings of the Nineteenth conference on Uncertainty in Artificial Intelligence
Randomized algorithms for matrices and massive data sets
VLDB '06 Proceedings of the 32nd international conference on Very large data bases
Unsupervised feature selection for principal components analysis
Proceedings of the 14th ACM SIGKDD international conference on Knowledge discovery and data mining
Incremental tensor analysis: Theory and applications
ACM Transactions on Knowledge Discovery from Data (TKDD)
An improved approximation algorithm for the column subset selection problem
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
MobiOpp '10 Proceedings of the Second International Workshop on Mobile Opportunistic Networking
Online evolutionary collaborative filtering
Proceedings of the fourth ACM conference on Recommender systems
Fast track article: Connectivity in time-graphs
Pervasive and Mobile Computing
Dynamic texture analysis and synthesis using tensor decomposition
ISVC'06 Proceedings of the Second international conference on Advances in Visual Computing - Volume Part II
Randomized Algorithms for Matrices and Data
Foundations and Trends® in Machine Learning
ParCube: sparse parallelizable tensor decompositions
ECML PKDD'12 Proceedings of the 2012 European conference on Machine Learning and Knowledge Discovery in Databases - Volume Part I
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Motivated by numerous applications in which the data may be modeled by a variable subscripted by three or more indices, we develop a tensor-based extension of the matrix CUR decomposition. The tensor-CUR decomposition is most relevant as a data analysis tool when the data consist of one mode that is qualitatively different than the others. In this case, the tensor-CUR decomposition approximately expresses the original data tensor in terms of a basis consisting of underlying subtensors that are actual data elements and thus that have natural interpretation in terms ofthe processes generating the data. In order to demonstrate the general applicability of this tensor decomposition, we apply it to problems in two diverse domains of data analysis: hyperspectral medical image analysis and consumer recommendation system analysis. In the hyperspectral data application, the tensor-CUR decomposition is used to compress the data, and we show that classification quality is not substantially reduced even after substantial data compression. In the recommendation system application, the tensor-CUR decomposition is used to reconstruct missing entries in a user-product-product preference tensor, and we show that high quality recommendations can be made on the basis of a small number of basis users and a small number of product-product comparisons from a new user.