  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.
