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Co-clustering of High-order Data via Regularized Tucker Decompositions

Computational methods for identifying hidden structures in high-order data are critical for exploratory data analysis tasks. This work proposes a joint dimensionality reduction and co-clustering algorithm for tensors. A compressed representation of a tensor is obtained via a Tucker-like decomposition model, whose factor matrices capture the tensor co-clustering structure. Factor matrices correspond to the cluster centroids of the tensor fibers per mode, whose entries interact nonlinearly to build the tensor approximation. The algorithm, developed based on the alternating-direction method of multipliers, has computational complexity similar to that of a single Tucker decomposition.