Open AccessA Basis Approach to Surface Clustering
Author(s) -
Adriano Zanin Zambom,
Qing Wang,
Ronaldo Dias
Publication year - 2022
Publication title -
statistics, optimization and information computing
Language(s) - English
Resource type - Journals
eISSN - 2311-004X
pISSN - 2310-5070
DOI - 10.19139/soic-2310-5070-1486
Subject(s) - cluster analysis , basis (linear algebra) , spectral clustering , cure data clustering algorithm , benchmark (surveying) , dimension (graph theory) , algorithm , data stream clustering , computer science , consistency (knowledge bases) , basis function , correlation clustering , mathematics , data mining , artificial intelligence , mathematical analysis , combinatorics , geography , geometry , geodesy
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.