Clustering Higher-Order Data
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.