Approximate low-rank factorization with structured factors

An approximate rank revealing factorization problem with structure constraints on the normalized factors is considered. Examples of structure, motivated by an application in microarray data analysis, are sparsity, nonnegativity, periodicity, and smoothness. In general, the approximate rank revealing factorization problem is nonconvex. An alternating projections algorithm is developed, which is globally convergent to a locally optimal solution. Although the algorithm is developed for a specific application in microarray data analysis, the approach is applicable to other types of structure. Key words: rank revealing factorization; numerical rank; low-rank approximation; maximum likelihood PCA; total least squares; errors-in-variables; microarray data.

• Type: Journal
• Year: 2010
• Where: CSDA
• Authors: Ivan Markovsky, Mahesan Niranjan
• Keywords: Approximate Rank, CSDA 2010, Factorization Problem, Microarray Data Analysis