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Spectral clustering and co-clustering are well-known techniques in dataanalysis, and recent work has extended spectral clustering to square, symmetrictensors and hypermatrices derived from a network. We develop a new tensorspectral co-clustering method that applies to any non-negative tensor of data.The result of applying our method is a simultaneous clustering of the rows,columns, and slices of a three-mode tensor, and the idea generalizes to anynumber of modes. The algorithm we design works by recursively bisecting thetensor into two pieces. We also design a new measure to understand the role ofeach cluster in the tensor. Our new algorithm and pipeline are demonstrated inboth synthetic and real-world problems. On synthetic problems with a plantedhigher-order cluster structure, our method is the only one that can reliablyidentify the planted structure in all cases. On tensors based on n-gram textdata, we identify stop-words and semantically independent sets; on tensors froman airline-airport multimodal network, we find worldwide and regionalco-clusters of airlines and airports; and on tensors from an email network, weidentify daily-spam and focused-topic sets.

General Tensor Spectral Co-clustering for Higher-Order Data