Aaron Gerow

Aaron Gerow, Mingyang Zhou, Stan Matwin et al.

Bipartite data is common in data engineering and brings unique challenges, particularly when it comes to clustering tasks that impose on strong structural assumptions. This work presents an unsupervised method for assessing similarity in bipartite data. Similar to some co-clustering methods, the method is based on regular equivalence in graphs. The algorithm uses spectral properties of a bipartite adjacency matrix to estimate similarity in both dimensions. The method is reflexive in that similarity in one dimension is used to inform similarity in the other. Reflexive regular equivalence can also use the structure of transitivities -- in a network sense -- the contribution of which is controlled by the algorithm's only free-parameter, $α$. The method is completely unsupervised and can be used to validate assumptions of co-similarity, which are required but often untested, in co-clustering analyses. Three variants of the method with different normalizations are tested on synthetic data. The method is found to be robust to noise and well-suited to asymmetric co-similar structure, making it particularly informative for cluster analysis and recommendation in bipartite data of unknown structure. In experiments, the convergence and speed of the algorithm are found to be stable for different levels of noise. Real-world data from a network of malaria genes are analyzed, where the similarity produced by the reflexive method is shown to out-perform other measures' ability to correctly classify genes.

Jingwei Zhang, Aaron Gerow, Jaan Altosaar et al.

Weak topic correlation across document collections with different numbers of topics in individual collections presents challenges for existing cross-collection topic models. This paper introduces two probabilistic topic models, Correlated LDA (C-LDA) and Correlated HDP (C-HDP). These address problems that can arise when analyzing large, asymmetric, and potentially weakly-related collections. Topic correlations in weakly-related collections typically lie in the tail of the topic distribution, where they would be overlooked by models unable to fit large numbers of topics. To efficiently model this long tail for large-scale analysis, our models implement a parallel sampling algorithm based on the Metropolis-Hastings and alias methods (Yuan et al., 2015). The models are first evaluated on synthetic data, generated to simulate various collection-level asymmetries. We then present a case study of modeling over 300k documents in collections of sciences and humanities research from JSTOR.