Probabilistic Dyadic Data Analysis with Local and Global Consistency

Dyadic data arises in many real world applications such as social network analysis and information retrieval. In order to discover the underlying or hidden structure in the dyadic data, many topic modeling techniques were proposed. The typical algorithms include Probabilistic Latent Semantic Analysis (PLSA) and Latent Dirichlet Allocation (LDA). The probability density functions obtained by both of these two algorithms are supported on the Euclidean space. However, many previous studies have shown naturally occurring data may reside on or close to an underlying submanifold. We introduce a probabilistic framework for modeling both the topical and geometrical structure of the dyadic data that explicitly takes into account the local manifold structure. Specifically, the local manifold structure is modeled by a graph. The graph Laplacian, analogous to the Laplace-Beltrami operator on manifolds, is applied to smooth the probability density functions. As a result, the obtained probabilistic distributions are concentrated around the data manifold. Experimental results on real data sets demonstrate the effectiveness of the proposed approach.