On exploring complex relationships of correlation clusters

In high dimensional data, clusters often only exist in ar-bitrarily oriented subspaces of the feature space. In addi-tion, these so-called correlation clusters may have complex relationships between each other. For example, a correla-tion cluster in a 1-D subspace (forming a line) may be en-closed within one or even several correlation clusters in 2-D superspaces (forming planes). In general, such relation-ships can be seen as a complex hierarchy that allows mul-tiple inclusions, i.e. clusters may be embedded in several super-clusters rather than only in one. Obviously, uncover-ing the hierarchical relationships between the detected cor-relation clusters is an important information gain. Since ex-isting approaches cannot detect such complex hierarchical relationships among correlation clusters, we propose the al-gorithm ERiC to tackle this problem and to visualize the result by means of a graph-based representation. In our ex-perimental evaluation, we show that ERiC finds more infor-mation than state-of-the-art correlation clustering methods and outperforms existing competitors in terms of efficiency. 1