Clustering Multivariate Functional Data with Phase Variation

• Published in: Biometrics Vol. 73; no. 1; pp. 324 - 333
• Main Authors: Park, Juhyun, Ahn, Jeongyoun
• Format: Journal Article
• Language: English
• Published: United States Wiley-Blackwell 01.03.2017; Blackwell Publishing Ltd
• Subjects: Anthropometry; BIOMETRIC PRACTICE; biometry; Body Weights and Measures; Cluster Analysis; Clustering; Curve alignment; data analysis; Data Interpretation, Statistical; Feature extraction; Functional clustering; Gene Expression Profiling; Gene Expression Regulation, Developmental; Growth and Development - genetics; Growth curves; Growth patterns; Human body; Humans; Mathematical analysis; Multivariate Analysis; Multivariate functional data; Phase variation; Phase variations; Variation; Phase variation; Functional clustering; Growth curves; Multivariate functional data; Curve alignment
• ISSN: 0006-341X; 1541-0420
• DOI: 10.1111/biom.12546

When functional data come as multiple curves per subject, characterizing the source of variations is not a trivial problem. The complexity of the problem goes deeper when there is phase variation in addition to amplitude variation. We consider clustering problem with multivariate functional data that have phase variations among the functional variables. We propose a conditional subject-specific warping framework in order to extract relevant features for clustering. Using multivariate growth curves of various parts of the body as a motivating example, we demonstrate the effectiveness of the proposed approach. The found clusters have individuals who show different relative growth patterns among different parts of the body.