Achieving Near-Perfect Classification for Functional Data

• Activity Number: 273
• Type: Invited
• Date/Time: Tuesday, August 2, 2011 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Peter Hall*+ and Aurore Delaigle
• Companies: The University of Melbourne/University of California at Davis and University of Melbourne

Abstract

It can be shown that, in functional data classification problems, perfect asymptotic classification is possible, making use of the intrinsic very high dimensional nature of functional data. This performance is often achieved by linear methods, which are optimal in important cases. These results point to a marked difference between classification for functional data and its counterpart in conventional multivariate analysis, where dimension is kept fixed as sample size diverges. In the latter setting, linear methods can sometimes be quite inefficient, and there are no prospects for asymptotically perfect classification, except in pathological cases where, for example, a variance vanishes. By way of contrast, in finite samples of functional data, good performance can be achieved by truncated versions of linear methods. Truncation can be implemented by partial least-squares or projection onto a finite number of principal components, using, in both cases, cross-validation to determine the truncation point.