The computational complexity of some explainable clustering problems

Let X is an element of R-d be a set of points and k >= 2 be an integer. Dasgupta et al. [1] considered the problem of building a partition of X into k groups, induced by an axis-aligned decision tree with k leaves. The motivation is obtaining partitions that are simple to explain. We study the computational complexity of this problem for k-means, k-medians and the k-center cost-functions. We prove that the optimization problems induced by these cost-functions are hard to approximate.(c) 2023 Elsevier B.V. All rights reserved.