  There are various cluster validity indices used for evaluating clustering
results. One of the main objectives of using these indices is to seek the
optimal unknown number of clusters. Some indices work well for clusters with
different densities, sizes, and shapes. Yet, one shared weakness of those
validity indices is that they often provide only one optimal number of
clusters. That number is unknown in real-world problems, and there might be
more than one possible option. We develop a new cluster validity index based on
a correlation between an actual distance between a pair of data points and a
centroid distance of clusters that the two points occupy. Our proposed index
constantly yields several local peaks and overcomes the previously stated
weakness. Several experiments in different scenarios, including UCI real-world
data sets, have been conducted to compare the proposed validity index with
several well-known ones. An R package related to this new index called NCvalid
is available at https://github.com/nwiroonsri/NCvalid.
