Object based validation algorithm and its application to consensus clustering

In this paper, we propose a new object based validity index using linear discriminant analysis (OVI-LDA). In OVI-LDA, each object is assigned an index value which is the log ratio of between-group distance to within-group distance. Unlike another object based validity index - Silhouette, OVI-LDA is suitable for both crisp and fuzzy clustering. Furthermore, its object based feature and dual-type capability lead to a consensus clustering by aggregating multiple crisp and fuzzy clustering results. For the demonstration purposes, we study a set of benchmark datasets with a variety of signal-to-noise ratio (SNR) levels and compare the results with other well known indices. The results show that the proposed OVI-LDA possesses not only all capabilities that other validity indices have, but also the capability to guide consensus clustering. The consensus clustering is also validated using a third-party validity index.