Clustering Functional Data via Multivariate Functional Halfspace Depth

• Activity Number: 482
• Type: Invited
• Date/Time: Wednesday, August 3, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Gerda Claeskens*+
• Companies: Katholieke Universiteit Leuven
• Keywords: Functional data analysis ; clustering ; depth ; phase variation ; amplitude variation

Abstract

Depth functions provide an ordering to observations in a sample from the center outwards. They play an important role in outlier detection, robust classification and clustering to name just a few. We introduce a new functional data depth, called multivariate functional halfspace depth (MFHD). The new depth function acknowledges some important characteristics of functional data, namely differences in the amount of phase variation ("horizontal" variation), local amplitude variation ("vertical" variation) and shape variation. Phase variation in functional data arises when the curves are not perfectly aligned, that is, when peaks and troughs occur at different time points. As opposed to treating it as a nuisance effect, we explicitly recognize it as a possible important source of information for clustering. A weight function incorporates the effects of local amplitude variation. The multivariate aspect of our method allows to include warping functions, warped curves and their derivatives, hereby including shape aspects.