Generalized information theoretic cluster validity indices for soft clusterings

There have been a large number of external validity indices proposed for cluster validity. One such class of cluster comparison indices is the information theoretic measures, due to their strong mathematical foundation and their ability to detect non-linear relationships. However, they are devised for evaluating crisp (hard) partitions. In this paper, we generalize eight information theoretic crisp indices to soft clusterings, so that they can be used with partitions of any type (i.e., crisp or soft, with soft including fuzzy, probabilistic and possibilistic cases). We present experimental results to demonstrate the effectiveness of the generalized information theoretic indices.