  We introduce a cluster evaluation technique called Tree Index. Our Tree Index
algorithm aims at describing the structural information of the clustering
rather than the quantitative format of cluster-quality indexes (where the
representation power of clustering is some cumulative error similar to vector
quantization). Our Tree Index is finding margins amongst clusters for easy
learning without the complications of Minimum Description Length. Our Tree
Index produces a decision tree from the clustered data set, using the cluster
identifiers as labels. It combines the entropy of each leaf with their depth.
Intuitively, a shorter tree with pure leaves generalizes the data well (the
clusters are easy to learn because they are well separated). So, the labels are
meaningful clusters. If the clustering algorithm does not separate well, trees
learned from their results will be large and too detailed. We show that, on the
clustering results (obtained by various techniques) on a brain dataset, Tree
Index discriminates between reasonable and non-sensible clusters. We confirm
the effectiveness of Tree Index through graphical visualizations. Tree Index
evaluates the sensible solutions higher than the non-sensible solutions while
existing cluster-quality indexes fail to do so.
