Customer mobility and congestion in supermarkets

The analysis and characterization of human mobility using population-level mobility models is important for numerous applications, ranging from the estimation of commuter flows in cities to modeling trade flows between countries. However, almost all of these applications have focused on large spatial scales, which typically range between intra-city scales to inter-country scales. In this paper, we investigate population-level human mobility models on a much smaller spatial scale by using them to estimate customer mobility flow between supermarket zones. We use anonymized, ordered customer-basket data to infer empirical mobility flow in supermarkets, and we apply variants of the gravity and intervening-opportunities models to fit this mobility flow and estimate the flow on unseen data. We find that a doubly-constrained gravity model and an extended radiation model (which is a type of intervening-opportunities model) can successfully estimate 65--70\% of the flow inside supermarkets. Using a gravity model as a case study, we then investigate how to reduce congestion in supermarkets using mobility models. We model each supermarket zone as a queue, and we use a gravity model to identify store layouts with low congestion, which we measure either by the maximum number of visits to a zone or by the total mean queue size. We then use a simulated-annealing algorithm to find store layouts with lower congestion than a supermarket's original layout. In these optimized store layouts, we find that popular zones are often in the perimeter of a store. Our research gives insight both into how customers move in supermarkets and into how retailers can arrange stores to reduce congestion. It also provides a case study of human mobility on small spatial scales

Characterizing Human Mobility Patterns in a Large Street Network

Previous studies demonstrated empirically that human mobility exhibits Levy flight behaviour. However, our knowledge of the mechanisms governing this Levy flight behaviour remains limited. Here we analyze over 72 000 people's moving trajectories, obtained from 50 taxicabs during a six-month period in a large street network, and illustrate that the human mobility pattern, or the Levy flight behaviour, is mainly attributed to the underlying street network. In other words, the goal-directed nature of human movement has little effect on the overall traffic distribution. We further simulate the mobility of a large number of random walkers, and find that (1) the simulated random walkers can reproduce the same human mobility pattern, and (2) the simulated mobility rate of the random walkers correlates pretty well (an R square up to 0.87) with the observed human mobility rate.Comment: 13 figures, 17 page

Automatic Deformation of Riemann-Hilbert Problems with Applications to the Painlev\'e II Transcendents

The stability and convergence rate of Olver's collocation method for the numerical solution of Riemann-Hilbert problems (RHPs) is known to depend very sensitively on the particular choice of contours used as data of the RHP. By manually performing contour deformations that proved to be successful in the asymptotic analysis of RHPs, such as the method of nonlinear steepest descent, the numerical method can basically be preconditioned, making it asymptotically stable. In this paper, however, we will show that most of these preconditioning deformations, including lensing, can be addressed in an automatic, completely algorithmic fashion that would turn the numerical method into a black-box solver. To this end, the preconditioning of RHPs is recast as a discrete, graph-based optimization problem: the deformed contours are obtained as a system of shortest paths within a planar graph weighted by the relative strength of the jump matrices. The algorithm is illustrated for the RHP representing the Painlev\'e II transcendents.Comment: 20 pages, 16 figure

Bayesian Optimization for Adaptive MCMC

This paper proposes a new randomized strategy for adaptive MCMC using Bayesian optimization. This approach applies to non-differentiable objective functions and trades off exploration and exploitation to reduce the number of potentially costly objective function evaluations. We demonstrate the strategy in the complex setting of sampling from constrained, discrete and densely connected probabilistic graphical models where, for each variation of the problem, one needs to adjust the parameters of the proposal mechanism automatically to ensure efficient mixing of the Markov chains.Comment: This paper contains 12 pages and 6 figures. A similar version of this paper has been submitted to AISTATS 2012 and is currently under revie

Diffusion Component Analysis: Unraveling Functional Topology in Biological Networks

Complex biological systems have been successfully modeled by biochemical and genetic interaction networks, typically gathered from high-throughput (HTP) data. These networks can be used to infer functional relationships between genes or proteins. Using the intuition that the topological role of a gene in a network relates to its biological function, local or diffusion based "guilt-by-association" and graph-theoretic methods have had success in inferring gene functions. Here we seek to improve function prediction by integrating diffusion-based methods with a novel dimensionality reduction technique to overcome the incomplete and noisy nature of network data. In this paper, we introduce diffusion component analysis (DCA), a framework that plugs in a diffusion model and learns a low-dimensional vector representation of each node to encode the topological properties of a network. As a proof of concept, we demonstrate DCA's substantial improvement over state-of-the-art diffusion-based approaches in predicting protein function from molecular interaction networks. Moreover, our DCA framework can integrate multiple networks from heterogeneous sources, consisting of genomic information, biochemical experiments and other resources, to even further improve function prediction. Yet another layer of performance gain is achieved by integrating the DCA framework with support vector machines that take our node vector representations as features. Overall, our DCA framework provides a novel representation of nodes in a network that can be used as a plug-in architecture to other machine learning algorithms to decipher topological properties of and obtain novel insights into interactomes.Comment: RECOMB 201