The Centroid Decomposition: Relationships between Discrete Variational Decompositions and Svd

The centroid decomposition, an approximation for the singular value decomposition, had a long history among the statistics/psychometrics community for factor analysis research. We revisit the centroid method first 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 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. A major purpose of this work is to show fundamental relationships between the singular value, centroid and semi-discrete decompositions. This unifies an entire class of truncated SVD approximations. Applications include semantic indexing in information retrieval.