Jérémie Jakubowicz

LSD: A Fast Line Segment Detector with a False Detection Control

We propose a linear-time line segment detector that gives accurate results, a controlled number of false detections, and requires no parameter tuning. This algorithm is tested and compared to state-of-the-art algorithms on a wide set of natural images.

Convergence of a Multi-Agent Projected Stochastic Gradient Algorithm for Non-Convex Optimization

We introduce a new framework for the convergence analysis of a class of distributed constrained non-convex optimization algorithms in multi-agent systems. The aim is to search for local minimizers of a non-convex objective function which is supposed to be a sum of local utility functions of the agents. The algorithm under study consists of two steps: a local stochastic gradient descent at each agent and a gossip step that drives the network of agents to a consensus. Under the assumption of decreasing stepsize, it is proved that consensus is asymptotically achieved in the network and that the algorithm converges to the set of Karush-Kuhn-Tucker points. As an important feature, the algorithm does not require the double-stochasticity of the gossip matrices. It is in particular suitable for use in a natural broadcast scenario for which no feedback messages between agents are required. It is proved that our results also holds if the number of communications in the network per unit of time vanishes at moderate speed as time increases, allowing potential savings of the networks energy. Applications to power allocation in wireless ad-hoc networks are discussed. Finally, we provide numerical results which sustain our claims.

On Straight Line Segment Detection

In this paper we propose a comprehensive method for detecting straight line segments in any digital image, accurately controlling both false positive and false negative detections. Based on Helmholtz principle, the proposed method is parameterless. At the core of the work lies a new way to interpret binary sequences in terms of unions of segments, for which a dynamic programming implementation is given. The proposed algorithm is extensively tested on synthetic and real images and compared with the state of the art.

Analysis of Max-Consensus Algorithms in Wireless Channels

In this paper, we address the problem of estimating the maximal value over a sensor network using wireless links between them. We introduce two heuristic algorithms and analyze their theoretical performance. More precisely, i) we prove that their convergence time is finite with probability one, ii) we derive an upper-bound on their mean convergence time, and iii) we exhibit a bound on their convergence time dispersion.

Convergence of a distributed parameter estimator for sensor networks with local averaging of the estimates

The paper addresses the convergence of a decentralized Robbins-Monro algorithm for networks of agents. This algorithm combines local stochastic approximation steps for finding the root of an objective function, and a gossip step for consensus seeking between agents. We provide verifiable sufficient conditions on the stochastic approximation procedure and on the network so that the decentralized Robbins-Monro algorithm converges to a consensus. We also prove that the limit points of the algorithm correspond to the roots of the objective function. We apply our results to Maximum Likelihood estimation in sensor networks.

Linear Precoders for the Detection of a Gaussian Process in Wireless Sensors Networks

We investigate the performance of Neyman-Pearson detection of a stationary Gaussian process in noise, using a large wireless sensor network (WSN). In our model, each sensor compresses its observation sequence using a linear precoder and a final decision is taken by a fusion center (FC) based on the compressed information. Two families of precoders are studied: random i.i.d. precoders and orthogonal precoders. We analyse their performance under a regime where both the number of sensors k and the number of samples n per sensor tend to infinity at the same rate, that is, k/n→ c ∈ [0,1]. Contributions are as follows. 1) Using results from random matrix theory and large Toeplitz matrices, we prove that, when the above families of precoders are used, the miss probability of the Neyman-Pearson detector converges exponentially to zero. Closed form expressions of the corresponding error exponents are derived. 2) In particular, we propose a practical orthogonal precoding strategy, the Principal Frequencies Strategy (PFS), which achieves the best error exponent among all orthogonal strategies, and which requires very little signaling overhead between the central processor and the nodes of the network. 3) When the PFS is used, a simplified low-complexity testing procedure can be implemented at the FC. We show that the proposed suboptimal test enjoys the same error exponent as the Neyman-Pearson test, which indicates a similar asymptotic behavior of the performance. We illustrate our findings by numerical experiments on several examples.

Dynamic cluster-based over-demand prediction in bike sharing systems

Bike sharing is booming globally as a green transportation mode, but the occurrence of over-demand stations that have no bikes or docks available greatly affects user experiences. Directly predicting individual over-demand stations to carry out preventive measures is difficult, since the bike usage pattern of a station is highly dynamic and context dependent. In addition, the fact that bike usage pattern is affected not only by common contextual factors (e.g., time and weather) but also by opportunistic contextual factors (e.g., social and traffic events) poses a great challenge. To address these issues, we propose a dynamic cluster-based framework for over-demand prediction. Depending on the context, we construct a weighted correlation network to model the relationship among bike stations, and dynamically group neighboring stations with similar bike usage patterns into clusters. We then adopt Monte Carlo simulation to predict the over-demand probability of each cluster. Evaluation results using real-world data from New York City and Washington, D.C. show that our framework accurately predicts over-demand clusters and outperforms the baseline methods significantly.

Classification of Periodic Activities Using the Wasserstein Distance

In this paper, we introduce a novel nonparametric classification technique based on the use of the Wasserstein distance. The proposed scheme is applied in a biomedical context for the analysis of recorded accelerometer data: the aim is to retrieve three types of periodic activities (walking, biking, and running) from a time-frequency representation of the data. The main interest of the use of the Wasserstein distance lies in the fact that it is less sensitive to the location of the frequency peaks than to the global structure of the frequency pattern, allowing us to detect activities almost independently of their speed or incline. Our system is tested on a 24-subject corpus: results show that the use of Wasserstein distance combined with some supervised learning techniques allows us to compare with some more complex classification systems.

On-line learning gossip algorithm in multi-agent systems with local decision rules

This paper is devoted to investigate binary classification in a distributed and on-line setting. In the Big Data era, datasets can be so large that it may be impossible to process them using a single processor. The framework considered accounts for situations where both the training and test phases have to be performed by taking advantage of a network architecture by the means of local computations and exchange of limited information between neighbor nodes. An online learning gossip algorithm (OLGA) is introduced, together with a variant which implements a node selection procedure. Beyond a discussion of the practical advantages of the algorithm we promote, the paper proposes an asymptotic analysis of the accuracy of the rules it produces, together with preliminary experimental results.

New broadcast based distributed averaging algorithm over wireless sensor networks

The distributed estimation of the average value of the sensors initial measures is one of the most popular issues in the Wireless Sensor Networks (WSN) area. In WSNs, broadcasting data seems natural to exchange information quickly because of the broadcast nature of the Wireless channel. Nevertheless, although broadcast-based algorithms converge faster than pairwise algorithms, the obtained consensus is not necessarily the true average. By the means of additional side-information exchange, we propose a broadcast-based algorithm converging rapidly to the true average. The convergence of this new algorithm is established and its convergence speed is exhibited. We remark that the proposed algorithm outperforms the existing ones.