From Large to Small Datasets: Size Generalization for Clustering Algorithm Selection

• URL: http://arxiv.org/abs/2402.14332v2
• Date: Mon, 26 Feb 2024 02:11:10 GMT
• Title: From Large to Small Datasets: Size Generalization for Clustering Algorithm Selection
• Authors: Vaggos Chatziafratis, Ishani Karmarkar, and Ellen Vitercik
• Abstract summary: We study a problem in a semi-supervised setting, with an unknown ground-truth clustering. We introduce a notion of size generalization for clustering algorithm accuracy. We use a subsample of as little as 5% of the data to identify which algorithm is best on the full dataset.
• Score: 12.993073967843292
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In clustering algorithm selection, we are given a massive dataset and must efficiently select which clustering algorithm to use. We study this problem in a semi-supervised setting, with an unknown ground-truth clustering that we can only access through expensive oracle queries. Ideally, the clustering algorithm's output will be structurally close to the ground truth. We approach this problem by introducing a notion of size generalization for clustering algorithm accuracy. We identify conditions under which we can (1) subsample the massive clustering instance, (2) evaluate a set of candidate algorithms on the smaller instance, and (3) guarantee that the algorithm with the best accuracy on the small instance will have the best accuracy on the original big instance. We provide theoretical size generalization guarantees for three classic clustering algorithms: single-linkage, k-means++, and (a smoothed variant of) Gonzalez's k-centers heuristic. We validate our theoretical analysis with empirical results, observing that on real-world clustering instances, we can use a subsample of as little as 5% of the data to identify which algorithm is best on the full dataset.

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