Generative hypergraph clustering: From blockmodels to modularity

Hypergraphs are a natural modeling paradigm for networked systems with multiway interactions. A standard task in network analysis is the identification of closely related or densely interconnected nodes. We propose a probabilistic generative model of clustered hypergraphs with heterogeneous node degrees and edge sizes. Approximate maximum likelihood inference in this model leads to a clustering objective that generalizes the popular modularity objective for graphs. From this, we derive an inference algorithm that generalizes the Louvain graph community detection method, and a faster, specialized variant in which edges are expected to lie fully within clusters. Using synthetic and empirical data, we demonstrate that the specialized method is highly scalable and can detect clusters where graph-based methods fail. We also use our model to find interpretable higher-order structure in school contact networks, U.S. congressional bill cosponsorship and committees, product categories in copurchasing behavior, and hotel locations from web browsing sessions.

Introducing a computational model of aesthetic value

People invest precious time and resources on sensory experiences such as watching movies or listening to music. Yet, we still have a poor understanding of how sensory experiences gain aesthetic value. We propose a model of aesthetic value that integrates existing theories with literature on conventional primary and secondary rewards such as food and money. We assume that the states of observers' sensory and cognitive systems adapt to process stimuli effectively in both the present and the future. These system states collectively comprise a probabilistic generative model of stimuli in the environment. Two interlinked components generate value: immediate sensory reward and the change in expected future reward. Immediate sensory reward is taken as the fluency with which a stimulus is processed, quantified by the likelihood of that stimulus given an observer's state. The change in expected future reward is taken as the change in fluency with which likely future stimuli will be processed. It is quantified by the change in the divergence between the observer's system state and the distribution of stimuli that the observer expects to see over the long term.Simulations show that a simple version of the model can account for empirical data on the effects of exposure, complexity, and symmetry on aesthetic value judgments. Taken together, our model melds processing fluency theories (immediate reward) and learning theories (change in expected future reward). Its application offers insight as to how the interplay of immediate processing fluency and learning gives rise to aesthetic value judgments.

An Image-Based Approach to Variational Path Synthesis of Linkages

This paper brings together computer vision, mechanism synthesis, and machine learning to create an image-based variational path synthesis approach for linkage mechanisms. An image-based approach is particularly amenable to mechanism synthesis when the input from mechanism designers is deliberately imprecise or inherently uncertain due to the nature of the problem. In addition, it also lends itself naturally to the creation of a unified approach to mechanism synthesis since pixels do not care if they were generated from a four-bar or six-bar. Path synthesis problem has generally been solved for a set of precision points on the intended path such that the designed mechanism passes through those points. This approach usually leads to a small set of over-fitting solutions to the particular precision points. However, most kinematic synthesis problems are concept generation problem where a designer cares more about generating a large number of plausible solutions. This paper models the input curve as a probability distribution of image pixels and employs a probabilistic generative model to capture the inherent uncertainty in the input. In addition, it gives feedback on the input quality and provides corrections for a more conducive input. The image representation allows for capturing local spatial correlations, which plays an important role in finding a variety of solutions with similar semantics as the input curve.