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Dimensionality reduction and clustering techniques are frequently used toanalyze complex data sets, but their results are often not easy to interpret.We consider how to support users in interpreting apparent cluster structure onscatter plots where the axes are not directly interpretable, such as when thedata is projected onto a two-dimensional space using a dimensionality-reductionmethod. Specifically, we propose a new method to compute an interpretableclustering automatically, where the explanation is in the originalhigh-dimensional space and the clustering is coherent in the low-dimensionalprojection. It provides a tunable balance between the complexity and the amountof information provided, through the use of information theory. We study thecomputational complexity of this problem and introduce restrictions on thesearch space of solutions to arrive at an efficient, tunable, greedyoptimization algorithm. This algorithm is furthermore implemented in aninteractive tool called ExClus. Experiments on several data sets highlight thatExClus can provide informative and easy-to-understand patterns, and they exposewhere the algorithm is efficient and where there is room for improvementconsidering tunability and scalability.

ExClus: Explainable Clustering on Low-dimensional Data Representations