Positive matrix factorization via extremal polyhedral cones

✍ Scribed by Jacqueline M. van den Hof; Jan H. van Schuppen

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 142 KB
• Volume: 293
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(99)00038-5

✦ Synopsis

The positive matrix factorization problem is for a given positive matrix to determine those factorizations of the given matrix as a product of two positive matrices for which the space of the positive real numbers over which is factored has the lowest possible dimension. Geometrically the problem is to embed a polyhedral cone in another polyhedral cone which has as few spanning vectors as possible. It is proven that this problem can be reduced to the search for an embedding in either an extremal polyhedral cone or in a facet of the positive orthant.