# Algorithm 805: Computation and Uses of the Semidiscrete Matrix Decomposition

### Abstract

We present algorithms for computing a semidiscrete approximation to a matrix in a weighted norm, with the Frobenius norm as a special case. The approximation is formed as a weighted sum of outer products of vectors whose elements are +/- 1 or 0, so the storage required by the approximation is quite small. We also present a related algorithm for approximation of a tensor. Applications of the algorithms are presented to data compression, filtering, and information retrieval; software is provided in C and in Matlab.

Type
Publication
ACM Transactions on Mathematical Software
Date
Tags
Citation
T. G. Kolda, D. P. O’Leary. Algorithm 805: Computation and Uses of the Semidiscrete Matrix Decomposition. ACM Transactions on Mathematical Software, Vol. 26, No. 3, pp. 415-435, 2000. https://doi.org/10.1145/358407.358424

### Keywords

compression, latent semantic indexing, matrix decomposition, semidiscrete decomposition (SDD), singular value decomposition (SVD)

The published version has several typographical errors. You may wish instead to check the older version.

### BibTeX

@article{KoOl00,
author = {Tamara G. Kolda and Dianne P. O'Leary},
title = {Algorithm 805: Computation and Uses of the Semidiscrete Matrix Decomposition},
journal = {ACM Transactions on Mathematical Software},
volume = {26},
number = {3},
pages = {415--435},
month = {September},
year = {2000},
doi = {10.1145/358407.358424},
}