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Shift Invariance Property of a Non-Negative Matrix Factorization
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2020/02/01
Online ISSN: 1745-1337
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.