SUMMARY We have developed two novel methods for Singular Value Decomposition analysis (SVD) of microarray data. The first is a threshold-based method for obtaining gene groups, and the second is a method for obtaining a measure of confidence in SVD analysis. Gene groups are obtained by identifying elements of the left singular vectors, or gene coefficient vectors, that are greater in magnitude ...

The problem of jointly sparse support recovery is to determine the common support of jointly sparse signal vectors from multiple measurement vectors (MMV) related to the signals by a linear transformation. The fundamental limit of performance has been studied in terms of a so-called algebraic bound, relating the maximum recoverable sparsity level to the spark of the sensing matrix and the rank ...

As whole genome sequences continue to expand in number and complexity, effective methods for comparing and categorizing both genes and species represented within extremely large datasets are required. Methods introduced to date have generally utilized incomplete and likely insufficient subsets of the available data. We have developed an accurate and efficient method for producing robust gene an...

Explicit expressions for the singular vectors in the highest weight representations of A (1) 1 are obtained using the fusion formalism of conformal field theory.

In this paper, we present the results of classifying electroencephalographic (EEG) signals into four motor imagery tasks using a new method for feature extraction. This method is based on a signal-dependent orthogonal transform, referred to as LP-SVD, defined as the left singular vectors of the LPC filter impulse response matrix. Using a logistic tree based model classifier, the extracted featu...

This paper concerns the use of a method for the solution of ill-conditioned linear systems. We show that the Generalized Minimum Residual Method (GMRES) in conjunction with a truncated singular value decomposition can beused to solve large nonsymmetric linear systems of equations which are nearly singular. Error bounds are given for the right s i n g u l a r v ectors and singular values compute...

We show how the interplay between the fusion formalism of conformal field theory and the Knizhnik–Zamolodchikov equation leads to explicit formulae for the singular vectors in the highest weight representations of A (1) 1. Infinite dimensional Lie algebras occur everywhere in the study of 2-d conformal field theories: the Virasoro algebra and the affine algebras are the most common examples. Ho...

We present a parallel software implementation for computing the singular value decomposition (SVD) of general, banded or bidiagonal matrices. First, the matrix is reduced to bidiagonal form. This reduction can be rearranged in a way that allows heavy use of matrix-matrix operations. Then the singular values are computed in an iterative process. Finally the singular vectors are computed independ...