Non-Convex Distributed Optimization

We study distributed non-convex optimization on a time-varying multi-agent network. Each node has access to its own smooth local cost function, and the collective goal is to minimize the sum of these functions. We generalize the results obtained previously to the case of non-convex functions. Under some additional technical assumptions on the gradients we prove the convergence of the distributed push-sum algorithm to some critical point of the objective function. By utilizing perturbations on the update process, we show the almost sure convergence of the perturbed dynamics to a local minimum of the global objective function. Our analysis shows that this noised procedure converges at a rate of $O(1/t)$

Public Transit Arrival Prediction: a Seq2Seq RNN Approach

Arrival/Travel times for public transit exhibit variability on account of factors like seasonality, dwell times at bus stops, traffic signals, travel demand fluctuation etc. The developing world in particular is plagued by additional factors like lack of lane discipline, excess vehicles, diverse modes of transport and so on. This renders the bus arrival time prediction (BATP) to be a challenging problem especially in the developing world. A novel data-driven model based on recurrent neural networks (RNNs) is proposed for BATP (in real-time) in the current work. The model intelligently incorporates both spatial and temporal correlations in a unique (non-linear) fashion distinct from existing approaches. In particular, we propose a Gated Recurrent Unit (GRU) based Encoder-Decoder(ED) OR Seq2Seq RNN model (originally introduced for language translation) for BATP. The geometry of the dynamic real time BATP problem enables a nice fit with the Encoder-Decoder based RNN structure. We feed relevant additional synchronized inputs (from previous trips) at each step of the decoder (a feature classically unexplored in machine translation applications). Further motivated from accurately modelling congestion influences on travel time prediction, we additionally propose to use a bidirectional layer at the decoder (something unexplored in other time-series based ED application contexts). The effectiveness of the proposed algorithms is demonstrated on real field data collected from challenging traffic conditions. Our experiments indicate that the proposed method outperforms diverse existing state-of-art data-driven approaches proposed for the same problem

Survey Assessment for Decision Support Using Self-Organizing Maps Profile Characterization with an Odds and Cluster Heat Map: Application to Children’s Perception of Urban School Environments

The interpretation of opinion and satisfaction surveys based exclusively on statistical analysis often faces difficulties due to the nature of the information and the requirements of the available statistical methods. These difficulties include the concurrence of categorical information with answers based on Likert scales with only a few levels, or the distancing of the necessary heuristic approach of the decision support system (DSS). The artificial neural network used for data analysis, called Kohonen or self-organizing maps (SOM), although rarely used for survey analysis, has been applied in many fields, facilitating the graphical representation and the simple interpretation of high-dimensionality data. This clustering method, based on unsupervised learning, also allows obtaining profiles of respondents without the need to provide additional information for the creation of these clusters. In this work, we propose the identification of profiles using SOM for evaluating opinion surveys. Subsequently, non-parametric chi-square tests were first conducted to contrast whether answer was independent of each profile found, and in the case of statistical significance (p ≤ 0.05), the odds ratio was evaluated as an indicator of the effect size of such dependence. Finally, all results were displayed in an odds and cluster heat map so that they could be easily interpreted and used to make decisions regarding the survey results. The methodology was applied to the analysis of a survey based on forms administered to children (N = 459) about their perception of the urban environment close to their school, obtaining relevant results, facilitating results interpretation, and providing support to the decision-process.This research was funded by Campus de Excelencia Internacional BIOTIC Granada, University of Granada, grant number V1.2015 and the APC was funded by University of Granada