Incremental Cluster Validity Indices for Hard Partitions: Extensions and Comparative Study

TL;DR

This paper extends the family of incremental cluster validity indices to include several new measures and compares their effectiveness in detecting under- and over-partitioning in clustering results, especially using fuzzy ART-based methods.

Contribution

The paper introduces new incremental cluster validity indices and provides a comprehensive comparative analysis of their performance in different partitioning scenarios.

Findings

Most iCVIs detect under-partitioning effectively.

Over-partitioning detection is more challenging, mainly indicated by iConn_Index.

Expansion of iCVIs enhances assessment of unsupervised learning results.

Abstract

Validation is one of the most important aspects of clustering, but most approaches have been batch methods. Recently, interest has grown in providing incremental alternatives. This paper extends the incremental cluster validity index (iCVI) family to include incremental versions of Calinski-Harabasz (iCH), I index and Pakhira-Bandyopadhyay-Maulik (iI and iPBM), Silhouette (iSIL), Negentropy Increment (iNI), Representative Cross Information Potential (irCIP) and Representative Cross Entropy (irH), and Conn_Index (iConn_Index). Additionally, the effect of under- and over-partitioning on the behavior of these six iCVIs, the Partition Separation (PS) index, as well as two other recently developed iCVIs (incremental Xie-Beni (iXB) and incremental Davies-Bouldin (iDB)) was examined through a comparative study. Experimental results using fuzzy adaptive resonance theory (ART)-based clustering methods showed that while evidence of most under-partitioning cases could be inferred from the behaviors of all these iCVIs, over-partitioning was found to be a more challenging scenario indicated only by the iConn_Index. The expansion of incremental validity indices provides significant novel opportunities for assessing and interpreting the results of unsupervised learning.