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Philipp Thomann

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JMLR Journal 2023 Journal Article

Adaptive Clustering Using Kernel Density Estimators

  • Ingo Steinwart
  • Bharath K. Sriperumbudur
  • Philipp Thomann

We derive and analyze a generic, recursive algorithm for estimating all splits in a finite cluster tree as well as the corresponding clusters. We further investigate statistical properties of this generic clustering algorithm when it receives level set estimates from a kernel density estimator. In particular, we derive finite sample guarantees, consistency, rates of convergence, and an adaptive data-driven strategy for choosing the kernel bandwidth. For these results we do not need continuity assumptions on the density such as Hölder continuity, but only require intuitive geometric assumptions of non-parametric nature. In addition, we compare our results to other guarantees found in the literature and also present some experiments comparing our algorithm to $k$-means and hierarchical clustering. [abs] [ pdf ][ bib ] &copy JMLR 2023. ( edit, beta )

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JMLR Journal 2015 Journal Article

Towards an Axiomatic Approach to Hierarchical Clustering of Measures

  • Philipp Thomann
  • Ingo Steinwart
  • Nico Schmid

We propose some axioms for hierarchical clustering of probability measures and investigate their ramifications. The basic idea is to let the user stipulate the clusters for some elementary measures. This is done without the need of any notion of metric, similarity or dissimilarity. Our main results then show that for each suitable choice of user-defined clustering on elementary measures we obtain a unique notion of clustering on a large set of distributions satisfying a set of additivity and continuity axioms. We illustrate the developed theory by numerous examples including some with and some without a density. [abs] [ pdf ][ bib ] &copy JMLR 2015. ( edit, beta )

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