Cluster analysis: significance, empty space, clustering tendency, non-uniformity. II--Empty Space index.

The here presented Empty Space index (ES) evaluates the fraction of the information space without experimental points, i.e. the space where the distance from an experimental point is significantly larger than the mean distance between the experimental points themselves. ES can be used to eliminate the ambiguity of the some clustering indexes, that aim to evaluate the separation of the data set in clusters, but these clustering indexes are really a mixed measure of clustering, of empty space (the empty space does not necessarily correspond to the break between clusters) and of the degree of uniformity of the objects. The ES index can be used also to correct the MST index, the clustering index based on the distribution of edge lengths in the minimum spanning tree connecting the objects. The corrected MST index seems to be a reliable measure of the clustering degree.