Optimal Interpretable Clustering Using Oblique Decision Trees

Recent years have seen a renewed interest in interpretable machine learning, which seeks insight into how a model achieves a prediction. Here, we focus on the relatively unexplored case of interpretable clustering. In our approach, the cluster assignments of the training instances are constrained to be the output of a decision tree. This has two advantages: 1) it makes it possible to understand globally how an instance is mapped to a cluster, in particular to see which features are used for which cluster; 2) it forces the clusters to respect a hierarchical structure while optimizing the original clustering objective function. Rather than the traditional axisaligned trees, we use sparse oblique trees, which have far more modelling power, particularly with high-dimensional data, while remaining interpretable. Our approach applies to any clustering method which is defined by optimizing a cost function and we demonstrate it with two -means variants.