  A new clustering accuracy measure is proposed to determine the unknown number
of clusters and to assess the quality of clustering of a data set given in any
dimensional space. Our validity index applies the classical nonparametric
univariate kernel density estimation method to the interpoint distances
computed between the members of data. Being based on interpoint distances, it
is free of the curse of dimensionality and therefore efficiently computable for
high-dimensional situations where the number of study variables can be larger
than the sample size. The proposed measure is compatible with any clustering
algorithm and with every kind of data set where the interpoint distance measure
can be defined to have a density function. Simulation study proves its
superiority over widely used cluster validity indices like the average
silhouette width and the Dunn index, whereas its applicability is shown with
respect to a high-dimensional Biostatistical study of Alon data set and a large
Astrostatistical application of time series with light curves of new variable
stars.
