Shallow decision trees for explainable $k$-means clustering
This work addresses the need for more interpretable machine learning models in clustering, though it is incremental as it builds on prior decision-tree-based approaches.
The paper tackles the problem of constructing explainable partitions for k-means clustering using decision trees, focusing on minimizing both cost and tree depth. It presents an efficient algorithm that achieves lower or equivalent costs with shallower trees compared to existing methods on 16 datasets.
A number of recent works have employed decision trees for the construction of explainable partitions that aim to minimize the $k$-means cost function. These works, however, largely ignore metrics related to the depths of the leaves in the resulting tree, which is perhaps surprising considering how the explainability of a decision tree depends on these depths. To fill this gap in the literature, we propose an efficient algorithm that takes into account these metrics. In experiments on 16 datasets, our algorithm yields better results than decision-tree clustering algorithms such as the ones presented in \cite{dasgupta2020explainable}, \cite{frost2020exkmc}, \cite{laber2021price} and \cite{DBLP:conf/icml/MakarychevS21}, typically achieving lower or equivalent costs with considerably shallower trees. We also show, through a simple adaptation of existing techniques, that the problem of building explainable partitions induced by binary trees for the $k$-means cost function does not admit an $(1+ε)$-approximation in polynomial time unless $P=NP$, which justifies the quest for approximation algorithms and/or heuristics.