Permutation NMF

TL;DR

This paper introduces a translation-invariant extension of Nonnegative Matrix Factorization (NMF), enabling the detection of common features across images despite shifts, enhancing its application in image processing.

Contribution

It proposes a novel method to incorporate translation invariance into classical NMF, improving feature detection in shifted images.

Findings

Enhanced ability to detect shifted features in images

Maintains nonnegativity and clustering properties of NMF

Applicable to image processing tasks involving translation variations

Abstract

Nonnegative Matrix Factorization(NMF) is a common used technique in machine learning to extract features out of data such as text documents and images thanks to its natural clustering properties. In particular, it is popular in image processing since it can decompose several pictures and recognize common parts if they're located in the same position over the photos. This paper's aim is to present a way to add the translation invariance to the classical NMF, that is, the algorithms presented are able to detect common features, even when they're shifted, in different original images.