Fréchet distance-based cluster analysis for multi-dimensional functional data

Multi-dimensional functional data analysis has become a contemporary research topic in medical research as patients’ various records are measured over time. We propose two clustering methods using the Fréchet distance for multi-dimensional functional data. The first method extends an existing K -mea...

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Bibliographic Details
Published inStatistics and computing Vol. 33; no. 4
Main Authors Kang, Ilsuk, Choi, Hosik, Yoon, Young Joo, Park, Junyoung, Kwon, Soon-Sun, Park, Cheolwoo
Format Journal Article
LanguageEnglish
Published New York Springer US 01.08.2023
Springer Nature B.V
Subjects
Artificial Intelligence
Cluster analysis
Clustering
Comparative studies
Computer Science
Data analysis
Dimensional analysis
Medical research
Multidimensional methods
Original Paper
Probability and Statistics in Computer Science
Statistical Theory and Methods
Statistics and Computing/Statistics Programs
Cluster analysis
Fréchet distance
Multi-dimensional longitudinal data
Sparsity
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Summary:Multi-dimensional functional data analysis has become a contemporary research topic in medical research as patients’ various records are measured over time. We propose two clustering methods using the Fréchet distance for multi-dimensional functional data. The first method extends an existing K -means type approach from one-dimensional to multi-dimensional longitudinal data. The second method enforces sparsity on functional variables while grouping observed trajectories and enables us to assess the contribution from each variable. Both methods utilize the generalized Fréchet distance to measure the distance between trajectories with irregularly spaced and asynchronous measurements. We demonstrate the effectiveness of the proposed methods through a comparative study using various simulation examples. Then, we apply the sparse clustering method to multi-dimensional thyroid cancer data collected in South Korea. It produces interpretable clusters and weighs the importance of functional variables.
ISSN:0960-3174
1573-1375
DOI:10.1007/s11222-023-10237-z