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Abstract:
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We show that, in the functional data context, by appropriately exploiting the functional nature of the data, it is possible to cluster the observations asymptotically perfectly. We demonstrate that this level of performance can often be achieved by the k-means algorithm as long as the data are projected on a carefully chosen finite dimensional space. We propose an iterative algorithm to choose the projection functions in a way that optimises clustering performance, where, to avoid peculiar solutions, we use a weighted least-squares criterion.
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