Understanding search engines: mathematical modeling and text retrieval
Understanding search engines: mathematical modeling and text retrieval
Matrix algorithms
Low-Rank Approximations with Sparse Factors I: Basic Algorithms and Error Analysis
SIAM Journal on Matrix Analysis and Applications
Efficiently finding web services using a clustering semantic approach
Proceedings of the 2008 international workshop on Context enabled source and service selection, integration and adaptation: organized with the 17th International World Wide Web Conference (WWW 2008)
The Boolean column and column-row matrix decompositions
Data Mining and Knowledge Discovery
Unsupervised feature selection for principal components analysis
Proceedings of the 14th ACM SIGKDD international conference on Knowledge discovery and data mining
Interpretable nonnegative matrix decompositions
Proceedings of the 14th ACM SIGKDD international conference on Knowledge discovery and data mining
Low-Rank matrix factorization and co-clustering algorithms for analyzing large data sets
ICDEM'10 Proceedings of the Second international conference on Data Engineering and Management
Exploratory factor and principal component analyses: some new aspects
Statistics and Computing
Improving CUR matrix decomposition and the Nyström approximation via adaptive sampling
The Journal of Machine Learning Research
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In many applications---latent semantic indexing, for example---it is required to obtain a reduced rank approximation to a sparse matrix A. Unfortunately, the approximations based on traditional decompositions, like the singular value and QR decompositions, are not in general sparse. Stewart [(1999), 313--323] has shown how to use a variant of the classical Gram--Schmidt algorithm, called the quasi--Gram-Schmidt--algorithm, to obtain two kinds of low-rank approximations. The first, the SPQR, approximation, is a pivoted, Q-less QR approximation of the form (XR11−1)(R11 R12), where X consists of columns of A. The second, the SCR approximation, is of the form the form A ≅ XTYT, where X and Y consist of columns and rows A and T, is small. In this article we treat the computational details of these algorithms and describe a MATLAB implementation.