  A popular trick for computing a pairwise co-occurrence matrix is the product
of an incidence matrix and its transpose. We present an analog for higher order
tuple co-occurrences using the face-splitting product, or alternately known as
the transpose Khatri-Rao product. These higher order co-occurrences encode the
commonality of tokens in the company of other tokens, and thus generalize the
mutual information commonly studied. We demonstrate this tensor's use via a
popular NLP model, and hypergraph models of similarity.
