Auto-adjustable hypergraph regularized non-negative matrix factorization for image clustering

Abstract

Non-negative matrix factorization (NMF) is an effective method for image clustering. However, relatively fixed graph regularization terms and loss functions have been adopted by recently proposed variants of NMF, and their clustering performance can be improved by incorporating configurable parameters. In this paper, an auto-adjustable hypergraph regularized non-negative matrix factorization (AHRNMF) algorithm was proposed. In the AHRNMF framework, we proposed a piecewise loss function and an innovative auto-adjustable hypergraph. The loss function incorporates two adaptive parameters, harmonizing reconstruction error and anti-outlier efficacy. Hypergraph construction relies on the calculation of two k-nearest neighbors (KNN) with different scales. Furthermore, an KNN-based algorithm was developed to assist AHRNMF in achieving auto-adjustment, which can automatically detect outliers without determining the number of clusters in advance. It was demonstrated by extensive experiments that the proposed AHRNMF outperforms other state-of-the-art methods.