Algorithms for Bounded-Error Correlation of High Dimensional Data in Microarray Experiments
CSB '03 Proceedings of the IEEE Computer Society Conference on Bioinformatics
PROXIMUS: a framework for analyzing very high dimensional discrete-attributed datasets
Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining
Compression, Clustering, and Pattern Discovery in Very High-Dimensional Discrete-Attribute Data Sets
IEEE Transactions on Knowledge and Data Engineering
Nonorthogonal decomposition of binary matrices for bounded-error data compression and analysis
ACM Transactions on Mathematical Software (TOMS)
L1-norm projection pursuit principal component analysis
Computational Statistics & Data Analysis
Discrete Eckart-Young Theorem for Integer Matrices
SIAM Journal on Matrix Analysis and Applications
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The centroid decomposition, an approximation for the singular value decomposition (SVD), has a long history among the statistics/psychometrics community for factor analysis research. We revisit the centroid method in its original context of factor analysis and then adapt it to other than a covariance matrix. The centroid method can be cast as an ${\cal O}(n)$-step ascent method on a hypercube. It is shown empirically that the centroid decomposition provides a measurement of second order statistical information of the original data in the direction of the corresponding left centroid vectors. One major purpose of this work is to show fundamental relationships between the singular value, centroid, and semidiscrete decompositions. This unifies an entire class of truncated SVD approximations. Applications include semantic indexing in information retrieval.