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Clustering functional data into groups by using projections
Author(s) -
Delaigle Aurore,
Hall Peter,
Pham Tung
Publication year - 2019
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/rssb.12310
Subject(s) - cluster analysis , ideal (ethics) , projection (relational algebra) , computer science , context (archaeology) , cluster (spacecraft) , clustering high dimensional data , algorithm , mathematics , data mining , artificial intelligence , paleontology , philosophy , epistemology , biology , programming language
Summary 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 sometimes be achieved by the k ‐means algorithm as long as the data are projected on a carefully chosen finite dimensional space. In general, the notion of an ideal cluster is not clearly defined. We derive our results in the setting where the data come from two populations whose distributions differ at least in terms of means, and where an ideal cluster corresponds to one of these two populations. We propose an iterative algorithm to choose the projection functions in a way that optimizes clustering performance, where, to avoid peculiar solutions, we use a weighted least squares criterion. We apply our iterative clustering procedure on simulated and real data, where we show that it works well.