Discovery of path-important nodes using structured semi-nonnegative matrix factorization

Identifying critical components in networked systems is a key problem for many important applications in a diverse set of fields, including epidemiology, e-commerce and traffic systems. This paper describes the development and application of a semi-nonnegative matrix factorization for structural discovery featuring nodes that are important for transmission over social networks. The technique allows the practitioner to perform structured matrix factorization by specifying context-specific network statistics that guide the solution. The techniques are demonstrated on a network derived from Twitter data.