Evaluating Evolving Structure in Streaming Data With Modified Dunn's Indices

Abstract

Dunn's internal cluster validity index is used to assess partition quality and identify a “best” crisp c-partition of n objects built from static data sets. This index is quite sensitive to inliers and outliers in the input data, so a subsequent study developed a family of 17 generalized Dunn's indices that extend and improve the original measure in various ways. This paper presents online versions of two modified generalized Dunn's indices that can be used for the dynamic evaluation of an evolving (cluster) structure in streaming data. We argue that this method is a good way to monitor the ongoing performance of streaming clustering algorithms, and we illustrate several types of inferences that can be drawn from such indices. Streaming clustering algorithms are incremental, process incoming data points only once and then discard them, adapt as the data stream evolves, flag outliers, and most importantly, spawn new emerging structures. We compare the two new indices to the incremental Xie-Beni and Davies-Boudin indices, which to our knowledge offer the only comparable approach, with numerical examples on a variety of synthetic and real datasets.