Using Matrix Scaling to Identify Block Structure (SIAM Conference on Applied Linear Algebra, Atlanta, 26/10/15-30/10/15)
Résumé
We can apply a two-sided diagonal scaling to a nonnegativematrix to render it into doubly stochastic form if and onlyif the matrix is fully indecomposable. The scaling oftenreveals key structural properties of the matrix as the effectsof element size and connectivity are balanced. Exploitingkey spectral properties of doubly stochastic matrices, wewill show how to use the scaling to reveal hidden blockstructure in matrices without any prior knowledge.