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- W2950590167 abstract "In many applications of clustering (for example, ontologies or clusterings of animal or plant species), hierarchical clusterings are more descriptive than a flat clustering. A hierarchical clustering over $n$ elements is represented by a rooted binary tree with $n$ leaves, each corresponding to one element. The subtrees rooted at interior nodes capture the clusters. In this paper, we study active learning of a hierarchical clustering using only ordinal queries. An ordinal query consists of a set of three elements, and the response to a query reveals the two elements (among the three elements in the query) which are to each other than to the third one. We say that elements and $x'$ are closer to each other than $x$ if there exists a cluster containing and $x'$, but not $x$. When all the query responses are correct, there is a deterministic algorithm that learns the underlying hierarchical clustering using at most $n log_2 n$ adaptive ordinal queries. We generalize this algorithm to be robust in a model in which each query response is correct independently with probability $p > frac{1}{2}$, and adversarially incorrect with probability $1 - p$. We show that in the presence of noise, our algorithm outputs the correct hierarchical clustering with probability at least $1 - delta$, using $O(n log n + n log(1/delta))$ adaptive ordinal queries. For our results, adaptivity is crucial: we prove that even in the absence of noise, every non-adaptive algorithm requires $Omega(n^3)$ ordinal queries in the worst case." @default.
- W2950590167 created "2019-06-27" @default.
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- W2950590167 date "2017-08-01" @default.
- W2950590167 modified "2023-09-27" @default.
- W2950590167 title "Adaptive Hierarchical Clustering Using Ordinal Queries" @default.
- W2950590167 hasPublicationYear "2017" @default.
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