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Description: |
Despite its popularity, the investigation of some theoretical aspects of clustering has been relatively sparse. One of the main reasons for this lack of theoretical results is surely the fact that, unlike the situation with other statistical problems as regression or classification, for some of the clustering methodologies it is difficult to specify the population goal to which the data-based clustering algorithms try to get close. In this talk we investigate the theoretical foundations of clustering by focusing on two main objectives: first, to provide an explicit formulation for the ideal population goal of density-based clustering, which understands clusters as regions of high density (here, Morse theory plays a crucial role); and second, to present two new loss functions, applicable to any clustering methodology, to evaluate the performance of a data-based clustering algorithm with respect to the ideal population goal. In particular, it is shown that only mild conditions on a sequence of density estimators are needed to ensure that the sequence of clusterings that they induce is consistent.
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Date: |
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| Start Time: |
14:30 |
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Speaker: |
José E. Chacón (Univ. de Extremadura, Spain)
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Institution: |
Univ. de Extremadura, Spain
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Place: |
Sala 5.4
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| Research Groups: |
-Probability and Statistics
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See more:
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<Main>
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