On the Study of Solving Weighted Kernel k-means via Symmetric Non-negative Matrix Factorization


Tsu-Ming Kuo

13:45:00 - 14:15:00

308 , Mathematics Research Center Building (ori. New Math. Bldg.)

In this talk, the equivalence between weighted kernel k-means and symmetric non-negative matrix factorization (SNMF) will be reviewed. We will show that SNMF is equivalent to a relaxed version of weighted kernel k-means clustering. With this relaxation and equivalence, we will then discuss the issue of converting a relaxed solution of weighted kernel k-means to a legitimate clustering solution. The recovering of a legitimate clustering solution consists of two major steps. One is to find the nearest feasible solution on a Stiefel manifold to the relaxed solution. The other is to discretize this feasible solution. Some gradient update algorithms will be discussed. Empirical experiments will be presented.