Elements of statistical computing: numerical computation
Elements of statistical computing: numerical computation
Introduction to statistical pattern recognition (2nd ed.)
Introduction to statistical pattern recognition (2nd ed.)
Linear methods in multimode data analysis for decision making
Computers and Operations Research
Neural Networks for Pattern Recognition
Neural Networks for Pattern Recognition
Pattern Recognition and Neural Networks
Pattern Recognition and Neural Networks
Multivariate Descriptive Statistical Analysis
Multivariate Descriptive Statistical Analysis
Pattern Classification (2nd Edition)
Pattern Classification (2nd Edition)
Clustering Large Graphs via the Singular Value Decomposition
Machine Learning
PCA and SVD with nonnegative loadings
Pattern Recognition
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Singular value decomposition (SVD) is widely used in data processing, reduction, and visualization. Applied to a positive matrix, the regular additive SVD by the first several dual vectors can yield irrelevant negative elements of the approximated matrix. We consider a multiplicative SVD modification that corresponds to minimizing the relative errors and produces always positive matrices at any approximation step. Another logistic SVD modification can be used for decomposition of the matrices of proportions, when a regular SVD can yield the elements beyond the zero-one range, while the modified SVD decomposition produces all the elements within the correct range at any step of approximation. Several additional modifications of matrix approximation are also considered.