A Basis Approach to Surface Clustering

TL;DR

This paper introduces a basis function approach for surface clustering that reduces data dimensionality and improves clustering accuracy, demonstrating strong consistency and outperforming traditional methods in simulations and real data.

Contribution

The paper proposes a novel basis function method for surface clustering that extends to tensor data and proves its strong consistency under various conditions.

Findings

Outperforms standard k-means on vectorized data in simulations

Demonstrates strong consistency in clustering as sample size increases

Effectively applied to real EGG data for practical validation

Abstract

This paper presents a novel method for clustering surfaces. The proposal involves first using 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 the k-means algorithm. An extension of the algorithm to clustering 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 algorithm which uses the original vectorized data. In addition, an EGG real data example is considered to illustrate the practical application of the proposal.