Adaptive Symmetric NMF for the Clustering of Sets of Points

Organizing data into clusters is a key task for data compression and classication. In this note we consider the case where the data are points belonging to a linear space, whose distance is measured through the Euclidean norm. A symmetric nonnegative similarity matrix is obtained from the data and a symmetric nonnegative matrix factorization (SymNMF) is computed in an alternating framework, through a penalized nonsymmetric formulation. An adaptive strategy to deal with the penalization parameter is proposed and validated by the numerical experimentation.