Shift Invariance Property of a Non-Negative Matrix Factorization

Abstract

We consider a property about a result of non-negative matrix factorization under a parallel moving of data points. The shape of a cloud of original data points and that of data points moving parallel to a vector are identical. Thus it is sometimes required that the coefficients to basis vectors of both data points are also identical from the viewpoint of classification. We show a necessary and sufficient condition for such an invariance property under a translation of the data points.