An Outlyingness Matrix for Multivariate Functional Data Classification

Abstract

The classification of multivariate functional data is an important task in scientific research. Unlike point-wise data, functional data are usually classified by their shapes rather than by their scales. We define an outlyingness matrix by extending directional outlyingness, an effective measure of the shape variation of curves that combines the direction of outlyingness with conventional statistical depth. We propose two classifiers based on directional outlyingness and the outlyingness matrix, respectively. Our classifiers provide better performance compared with existing depth-based classifiers when applied on both univariate and multivariate functional data from simulation studies. We also test our methods on two data problems: speech recognition and gesture classification, and obtain results that are consistent with the findings from the simulated data.

Review on functional data classification

“…The variation between different groups of curves in functional data classification usually arises from variations in the data's diverse patterns or shapes. By extending the depth‐based scalar outlyingness to an outlyingness matrix, which contains pure information of shape variation of a curve, W. Dai and Genton (2018) proposed classifiers for both univariate and multivariate functional data. Moindjié et al (2022) considered partial least square classification and tree partial least square‐based methods for multivariate functional data which are defined in different domains.…”