Abstract

Traditional clustering methods are mainly developed for multivariate data and often struggle to

capture the continuity and dynamics of functional data, thus neglecting key features. To address

this issue, we propose a two-stage functional data spectral clustering (TSFDSC) method that can

effectively cluster both dense and sparse functional data using the graph Laplacian operator. For

dense functional data, they are projected onto a set of pre-determined basis functions, and then the

resulting coefficients are clustered by spectral clustering, whereas for sparse functional data, functional principal component scores are used instead. By leveraging low-dimensional representations

from spectral embedding, TSFDSC achieves computational efficiency. We establish asymptotic

properties for the proposed procedure. Simulation studies demonstrate that TSFDSC outperforms

some commonly used functional clustering methods under various settings. The effectiveness of

TSFDSC is further illustrated by two real applications.

Information

Preprint No.SS-2025-0153
Manuscript IDSS-2025-0153
Complete AuthorsYang Ren, Jinguan Lin, Peijun Sang, Jiangyan Wang
Corresponding AuthorsJiangyan Wang
Emailswangjiangyan2007@126.com

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Acknowledgments

This work was supported by the National Natural Science Foundation of China

(12271255, 12371267), Qing Lan Project of Jiangsu Province, Postgraduate Research and

Practice Innovation Program of Jiangsu Province (KYCX25_2447), the National Statistical Science Research Project of China (2024LY059), project of Joint Lab for Statistics

and Finance, and Jiangsu Provincial Key Discipline Construction Project (Statistics).

Supplementary Materials

The supplementary file contains the proofs of Theorems 2.1-2.2 and more extensive

numerical results.

Supplementary materials are available for download.