Shift Invariance Property of a Non-Negative Matrix Factorization

Hideyuki IMAI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E103-A   No.2   pp.580-581
Publication Date: 2020/02/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.2019EAL2121
Type of Manuscript: LETTER
Category: General Fundamentals and Boundaries
non-negative matrix factorization,  semi non-negative matrix factorization,  parallel moving,  

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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.