Journal
BIOMETRIKA
Volume 99, Issue 2, Pages 299-313Publisher
OXFORD UNIV PRESS
DOI: 10.1093/biomet/ass003
Keywords
Bandwidth; Classification error rate; Kernel method; Statistical smoothing; Tightness of clusters
Funding
- Australian Research Council
- National Science Foundation
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [0906795] Funding Source: National Science Foundation
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The infinite dimension of functional data can challenge conventional methods for classification and clustering. A variety of techniques have been introduced to address this problem, particularly in the case of prediction, but the structural models that they involve can be too inaccurate, or too abstract, or too difficult to interpret, for practitioners. In this paper, we develop approaches to adaptively choose components, enabling classification and clustering to be reduced to finite-dimensional problems. We explore and discuss properties of these methodologies. Our techniques involve methods for estimating classifier error rate and cluster tightness, and for choosing both the number of components, and their locations, to optimize these quantities. A major attraction of this approach is that it allows identification of parts of the function domain that convey important information for classification and clustering. It also permits us to determine regions that are relevant to one of these analyses but not the other.
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