Non-Negative Matrix Factorization with Scale Data Structure Preservation

TL;DR

This paper introduces a novel non-negative matrix factorization method that preserves data structure during reduction, enhancing clustering and classification performance on real datasets.

Contribution

It proposes a new NMF model with a penalty term for scale relationship preservation, improving data representation quality.

Findings

Enhanced clustering accuracy compared to existing NMF methods

Effective data structure preservation demonstrated on real datasets

Improved classification results using the proposed NMF approach

Abstract

The model described in this paper belongs to the family of non-negative matrix factorization methods designed for data representation and dimension reduction. In addition to preserving the data positivity property, it aims also to preserve the structure of data during matrix factorization. The idea is to add, to the NMF cost function, a penalty term to impose a scale relationship between the pairwise similarity matrices of the original and transformed data points. The solution of the new model involves deriving a new parametrized update scheme for the coefficient matrix, which makes it possible to improve the quality of reduced data when used for clustering and classification. The proposed clustering algorithm is compared to some existing NMF-based algorithms and to some manifold learning-based algorithms when applied to some real-life datasets. The obtained results show the effectiveness of the proposed algorithm.