7. Multilinear Algebra for Analyzing Data with Multiple Linkages
Daniel Dunlavy, Tamara G. Kolda, W. Philip Kegelmeyer · Society for Industrial and Applied Mathematics eBooks · 2011
Tensors are a useful tool for representing multi-link graphs, and tensor decompositions facilitate a type of link analysis that incorporates all link types simultaneously. An adjacency tensor is formed by stacking the adjacency matrix for each link type to form a three-way array. The CANDECOMP/PARAFAC (CP) tensor decomposition provides information about adjacency tensors of multi-link graphs analogous to that produced for adjacency matrices of single-link graphs using the singular value decomposition (SVD). The CP tensor decomposition generates feature vectors that incorporate all linkages simultaneously for each node in a multi-link graph. Feature vectors can be used to analyze bibliometric data in a variety of ways, for example, to analyze five years of publication data from journals published by the Society for Industrial and Applied Mathematics (SIAM). Experiments presented include analyzing a body of work, distinguishing between papers written by different authors with the same name, and predicting the journal in which a paper is published.