  We present a method for hierarchical clustering of data called {\it mutual
information clustering} (MIC) algorithm. It uses mutual information (MI) as a
similarity measure and exploits its grouping property: The MI between three
objects $X, Y,$ and $Z$ is equal to the sum of the MI between $X$ and $Y$, plus
the MI between $Z$ and the combined object $(XY)$. We use this both in the
Shannon (probabilistic) version of information theory and in the Kolmogorov
(algorithmic) version. We apply our method to the construction of phylogenetic
trees from mitochondrial DNA sequences and to the output of independent
components analysis (ICA) as illustrated with the ECG of a pregnant woman.
