Higher order co-occurrence tensors for hypergraphs via face-splitting
This provides a method for analyzing token relationships in hypergraphs, which is incremental as it extends existing pairwise techniques to higher orders.
The paper tackles the problem of computing higher-order tuple co-occurrences in hypergraphs by introducing an analog using the face-splitting product, generalizing mutual information, and demonstrates its application in NLP and hypergraph similarity models.
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.