Evolutionary nonnegative matrix factorization with adaptive control of cluster quality

Abstract

Nonnegative matrix factorization (NMF) approximates a given data matrix using linear combinations of a small number of nonnegative basis vectors, weighted by nonnegative encoding coefficients. This enables the exploration of the cluster structure of the data through the examination of the values of the encoding coefficients and therefore, NMF is often used as a popular tool for clustering analysis. However, its encoding coefficients do not always reveal a satisfactory cluster structure. To improve its effectiveness, a novel evolutionary strategy is proposed here to drive the iterative updating scheme of NMF and generate encoding coefficients of higher quality that are capable of offering more accurate and sharper cluster structures. The proposed hybridization procedure that relies on multiple initializations reinforces the robustness of the solution. Additionally, three evolving rules are designed to simultaneously boost the cluster quality and the reconstruction error during the iterative updates. Any clustering performance measure, such as either an internal one relying on the data itself or an external based on the availability of ground truth information, can be employed to drive the evolving procedure. The effectiveness of the proposed method is demonstrated via careful experimental designs and thorough comparative analyses using multiple benchmark datasets.