Parameter-Less Tensor Co-clustering

Tensors co-clustering has been proven useful in many applications, due to its ability of coping with high-dimensional data and sparsity. However, setting up a co-clustering algorithm properly requires the specification of the desired number of clusters for each mode as input parameters. This choice is already difficult in relatively easy settings, like flat clustering on data matrices, but on tensors it could be even more frustrating. To face this issue, we propose a tensor co-clustering algorithm that does not require the number of desired co-clusters as input, as it optimizes an objective function based on a measure of association across discrete random variables (called Goodman and Kruskal’s τ) that is not affected by their cardinality. The effectiveness of our algorithm is shown on both synthetic and real-world datasets, also in comparison with state-of-the-art co-clustering methods based on tensor factorization.