Abstract:

There is an extensive body of literature on clustering univariate and multivariate data. However, attention the use of multidimensional arrays for clustering has thus far been limited to two-dimensional arrays, i.e., matrices or order-two tensors. Work on clustering data matrices, or three-way data, is presented before an approach for clustering multi-way data is introduced. The latter is based on a finite mixture of multidimensional arrays., i.e., a finite mixture of d-dimensional arrays, for d>2. For both matrix- and tensor-variate approaches, the Gaussian component approach is introduced first but approaches that use non-Gaussian components are also discussed. Simulated and real data are used for illustration.