Normalized Asymmetric Mutual Information

The entropy of either, clustering and categorization , provides another tight bound on mutual information that can be used for normalization. Since the categorization is a stable, user given distribution, let's consider

(8.10) |

Hence, one can alternatively define [0,1]-normalized asymmetric mutual information based quality as

(8.11) |

which translates into frequency counts as

Note that this definition of mutual information is asymmetric and does not penalize overrefined clusterings . Also, is biased towards high .

Alexander Strehl 2002-05-03