A Basis Approach to Surface Clustering

  • Adriano Zanin Zambom Department of Mathematics, California State University Northridge, USA
  • Qing Wang Department of Mathematics, Wellesley College, USA
  • Ronaldo Dias Department of Statistics, State University of Campinas, Brazil
Keywords: natural splines, k-means, spectral clustering, surface clustering


This paper presents a novel method for clustering surfaces. The proposal involves first using natural splines basis functions in a tensor product to smooth the data and thus reduce the dimension to a finite number of coefficients, and then using these estimated coefficients to cluster the surfaces via k-means or spectral clustering. An extension of the algorithm to clustering higher-dimensional tensors is also discussed. We show that the proposed algorithm exhibits the property of strong consistency, with or without measurement errors, in correctly clustering the data as the sample size increases. Simulation studies suggest that the proposed method outperforms the benchmark k-means and spectral algorithm which use the original data. In addition, an EGG real data example is considered to illustrate the practical application of the proposal.


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How to Cite
Zambom, A. Z., Wang, Q., & Dias, R. (2022). A Basis Approach to Surface Clustering. Statistics, Optimization & Information Computing, 10(2), 339-351. https://doi.org/10.19139/soic-2310-5070-1486
Research Articles