Interpretable Clustering via Multi-Polytope Machines

Clustering is a popular unsupervised learning tool often used to discover groups within larger population such as customer segments, or patient subtypes. However, despite its use for subgroup discovery and description few state-of-the-art algorithms provide any rationale behind the clusters found. We propose novel approach interpretable clustering that both data points constructs polytopes around discovered explain them. Our framework allows additional constraints on including ensuring hyperplanes constructing polytope are axis-parallel sparse with integer coefficients. formulate problem of via Mixed-Integer Non-Linear Program (MINLP). To solve our formulation we two phase where first initialize using alternating minimization, then coordinate descent boost performance. benchmark suite synthetic real world problems, algorithm outperforms state art non-interpretable algorithms.