Clustering Higher Order Data: Finite Mixtures of Multidimensional Arrays

An approach for clustering multi-way data is introduced based on a finite mixture of multidimensional arrays. Attention to the use of multidimensional arrays for clustering has thus far been limited to two-dimensional arrays, i.e., matrices or order-two tensors. Accordingly, this is the first paper to develop an approach for clustering d-dimensional arrays for d>2 or, in other words, for clustering using order-d tensors.