Multistability of αα-divergence based NMF algorithms

In this paper, the multistability of a class of Amari’s αα-divergence based nonnegative matrix factorization learning algorithms is analyzed. The analysis results show that invariant sets for the update algorithms can be constructed. In these invariant sets, the non-convergence of the discussed algorithms can be guaranteed. Based on Lyapunov’s stability theorem, the local convergence of this class of learning algorithms is proved in the domain of their update rules. In the simulation, the analysis results are applied to image representation. Experiment results demonstrate that selecting suitable initial data for different applications of these nonnegative matrix factorization algorithms is very important.