Balancing Interpretability and Predictive Accuracy for Unsupervised Tensor Mining

Very frequently, tensor mining is done in an entirely unsupervised way, since ground truth and labels are either very expensive or hard to obtain. Our problem, thus, is: given a potentially very large and sparse tensor, and its R-component decomposition, compute a quality measure for that decomposition. Subsequently, using that quality metric, we would like to identify a "good" number R of components, and ultimately minimize human intervention and trial-and-error fine tuning. This problem is extremely hard. In fact, even computing the rank of a tensor has been shown to be an NPhard problem, in stark contrast to the matrix rank which can be easily computed in polynomial time. Fortunately, there exist heuristics that are able to assist with the above problem and have been shown to work well in practice, in the field of Chemometrics. Such a powerful and intuitive heuristic is the so-called "Core Consistency Diagnostic" [1], which given a tensor and its PARAFAC decomposition, provides a quality measure, which we can in turn use as a proxy of how interpretable our results are.