  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.
