The Relevance Dependent Infinite Relational Model for Discovering Co-Cluster Structure from Relationships with Structured Noise

Abstract

Iku OHAMA†a) , Hiromi IIDA † †b) , Nonmembers, Takuya KIDA † † †c) , and Hiroki ARIMURA † † †d) , Members SUMMARY Latent variable models for relational data enable us to extract the co-cluster structures underlying observed relational data. The Infinite Relational Model (IRM) is a well-known relational model for discovering co-cluster structures with an unknown number of clusters. The IRM assumes that the link probability between two objects (e.g., a customer and an item) depends only on their cluster assignment. However, relational models based on this assumption often lead us to extract many non-informative and unexpected clusters. This is because the underlying co-cluster structures in real-world relationships are often destroyed by structured noise that blurs the cluster structure stochastically depending on the pair of related objects. To overcome this problem, in this paper, we propose an extended IRM that simultaneously estimates denoised clear co-cluster structure and a structured noise component. In other words, our proposed model jointly estimates cluster assignment and noise level for each object. We also present posterior probabilities for running collapsed Gibbs sampling to infer the model. Experiments on real-world datasets show that our model extracts a clear co-cluster structure. Moreover, we confirm that the estimated noise levels enable us to extract representative objects for each cluster. key words: relational data, co-clustering, infinite relational model, structured noise

Discovering Co-Cluster Structure from Relationships between Biased Objects

“…For co-clustering relational data, there have been several extensions of the IRM so that the background layer affect link probabilities. The Subset IRM (SIRM) proposed by Ishiguro et al [22] and the Relevance Dependent IRM (RDIRM) proposed by Ohama et al [23], [24] both consider a generative model in which link probability is a mixture distribution of a clustering layer η k,l and a background layer η 0 . In the SIRM, binary variables s 1 i , s 2 j ∈ {0, 1} are introduced to indicate whether each object is relevant to the underlying cluster structure.…”