Fault clustering by small‐entropy nonnegative matrix factorizations

Abstract

Fault clustering attempts to partition a set of faulty samples into several clusters, allowing the exploration of the underlying pattern of faults. Nonnegative matrix factorizations (NMFs) are good candidates for fault clustering since they are inherently capable of data clustering and variants of the k-means algorithm. However, NMFs always show poor performance in real-world clustering applications for their naive data clustering mechanism. To improve the clustering performance of the existing NMFs and solve the fault clustering problem, this paper proposes a new type of NMFs, called small-entropy nonnegative matrix factorizations (SENMFs). SENMFs impose a small amount of entropy on the cluster probability distribution of each sample to avoid ambiguous clustering results. Moreover, the algorithm for SENMFs is convergent in theory. We selected three types of faulty samples of the penicillin fermentation process for fault clustering. The case study results showed that SENMFs exceed the state-of-the-art NMFs and k-means in terms of fault clustering performance.