Performing Multi-Objective Optimization Alongside Dimension Reduction to Determine Number of Clusters

Abstract

One of the consequences of the widespread automation of manufacturing operations has been the proliferation and availability of historical databases that can be exploited by analytical methods to improve process understanding. Data science tools such as dimension reduction and clustering are among many such approaches that can aid in the identification of unique process features and patterns that can be associated with faulty states. However, determining the number of such states still requires significant engineering knowledge and insight. In this study, a new unsupervised method is proposed that reveals the number of classes in a data set. The method utilizes a variety of dimension reduction techniques to create projections of a data set and performs multiple clustering operations on the lower-dimensional data as well as the original data. The relevant internal clustering metrics are incorporated into a multi-objective optimization problem to determine the solutions that simultaneously optimize all metrics. The cluster number that shows Pareto optimality based on the performance metrics is selected as the final one. The method is tested on three data sets with distinct features. The results demonstrate the ability of the proposed method to correctly identify the expected number of clusters.