Variation Pattern Classification of Functional Data

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)943-958
Number of pages16
Journal / PublicationCanadian Journal of Statistics
Issue number4
Online published25 Oct 2022
Publication statusPublished - Dec 2023
Externally publishedYes


A new classification method for functional data is proposed in this article. This work is motivated by the need to identify features that discriminate between neurological conditions on which local field potentials (LFPs) were recorded. Regardless of the condition, these LFPs have zero mean, and thus the first moments of these random processes do not have discriminating power. We propose the variation pattern classification (VPC) method which employs the second-moment structure as the discriminating feature and uses the Hilbert–Schmidt norm to measure the discrepancy between the second-moment structure of different groups. The proposed VPC method is demonstrated to be sensitive to the discrepancy, potentially leading to a higher rate of classification. One important innovation lies in the dimension reduction where the VPC method adaptively determines the basis functions (discriminative feature functions) that account for the major discrepancy. In addition, the selected discriminative feature functions provide insights into the discrepancy between different groups because they reveal the features of variation pattern that differentiate groups. Consistency properties are established and, furthermore, simulation studies and the analysis of rat brain LFP trajectories empirically demonstrate the advantages and effectiveness of the proposed method. © 2022 Statistical Society of Canada / Société statistique du Canada.

Research Area(s)

  • Dimension reduction, discriminative feature function, functional data analysis, nearest centroid classifier, second-moment structure

Citation Format(s)

Variation Pattern Classification of Functional Data. / JIAO, Shuhao; FROSTIG, Ron D.; OMBAO, Hernando.
In: Canadian Journal of Statistics, Vol. 51, No. 4, 12.2023, p. 943-958.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review