Explainable k-means and k-medians clustering

Sanjoy Dasgupta, Nave Frost, Michal Moshkovitz, Cyrus Rashtchian

    Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

    Abstract

    Many clustering algorithms lead to cluster assignments that are hard to explain, partially because they depend on all the features of the data in a complicated way. To improve interpretability, we consider using a small decision tree to partition a data set into clusters, so that clusters can be characterized in a straightforward manner. We study this problem from a theoretical viewpoint, measuring cluster quality by the k-means and k-medians objectives. In terms of negative results, we show that popular top-down decision tree algorithms may lead to clusterings with arbitrarily large cost, and any clustering based on a tree with k leaves must incur an (log k) approximation factor compared to the optimal clustering. On the positive side, for two means/medians, we show that a single threshold cut can achieve a constant factor approximation, and we give nearly-matching lower bounds; for general k 2, we design an efficient algorithm that leads to an O(k) approximation to the optimal k-medians and an O(k2) approximation to the optimal k-means. Prior to our work, no algorithms were known with provable guarantees independent of dimension and input size.

    Original languageEnglish
    Title of host publication37th International Conference on Machine Learning, ICML 2020
    EditorsHal Daume, Aarti Singh
    PublisherInternational Machine Learning Society (IMLS)
    Pages7012-7022
    Number of pages11
    ISBN (Electronic)9781713821120
    StatePublished - 2020
    Event37th International Conference on Machine Learning, ICML 2020 - Virtual, Online
    Duration: 13 Jul 202018 Jul 2020

    Publication series

    Name37th International Conference on Machine Learning, ICML 2020
    VolumePartF168147-10

    Conference

    Conference37th International Conference on Machine Learning, ICML 2020
    CityVirtual, Online
    Period13/07/2018/07/20

    Fingerprint

    Dive into the research topics of 'Explainable k-means and k-medians clustering'. Together they form a unique fingerprint.

    Cite this