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Title: Explainable k-means: don’t be greedy, plant bigger trees!
We provide a new bi-criteria O(log2k) competitive algorithm for explainable k-means clustering. Explainable k-means was recently introduced by Dasgupta, Frost, Moshkovitz, and Rashtchian (ICML 2020). It is described by an easy to interpret and understand (threshold) decision tree or diagram. The cost of the explainable k-means clustering equals to the sum of costs of its clusters; and the cost of each cluster equals the sum of squared distances from the points in the cluster to the center of that cluster. The best non bi-criteria algorithm for explainable clustering O(k) competitive, and this bound is tight. Our randomized bi-criteria algorithm constructs a threshold decision tree that partitions the data set into (1+δ)k clusters (where δ∈(0,1) is a parameter of the algorithm). The cost of this clustering is at most O(1/δ⋅log2k) times the cost of the optimal unconstrained k-means clustering. We show that this bound is almost optimal.  more » « less
Award ID(s):
1955351
NSF-PAR ID:
10336877
Author(s) / Creator(s):
;
Date Published:
Journal Name:
STOC 2022
Page Range / eLocation ID:
1629 to 1642
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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