A Non Negative Matrix Factorization-Based Data Augmentation Procedure for Two-Dimensional Data

Abstract

In this paper, we investigate how geometric transformations—such as translations and rotations—affect matrix factorizations, with a particular focus on Non negative Matrix Factorization (NMF) in the context of supervised learning. We describe a novel feature extraction and data augmentation framework that leverages the invariance properties of matrix decompositions under linear transformations. Specifically, we show how applying such transformations in the input space induces systematic variations in the factorization structure, which we exploit to generate new feature vectors from the left factors of NMF applied to transformed data. This provides both augmented training examples and their interpretable non negative representations. Our approach thus enhances feature interpretability while preserving nonnegativity and structure. Preliminary numerical experiments on a binary image classification task related to archaeological data demonstrate the effectiveness of the method.