Jean-Michel Renders

Random-Walk Computation of Similarities between Nodes of a Graph with Application to Collaborative Recommendation

This work presents a new perspective on characterizing the similarity between elements of a database or, more generally, nodes of a weighted and undirected graph. It is based on a Markov-chain model of random walk through the database. More precisely, we compute quantities (the average commute time, the pseudoinverse of the Laplacian matrix of the graph, etc.) that provide similarities between any pair of nodes, having the nice property of increasing when the number of paths connecting those elements increases and when the length of paths decreases. It turns out that the square root of the average commute time is a Euclidean distance and that the pseudoinverse of the Laplacian matrix is a kernel matrix (its elements are inner products closely related to commute times). A principal component analysis (PCA) of the graph is introduced for computing the subspace projection of the node vectors in a manner that preserves as much variance as possible in terms of the Euclidean commute-time distance. This graph PCA provides a nice interpretation to the Fiedler vector, widely used for graph partitioning. The model is evaluated on a collaborative-recommendation task where suggestions are made about which movies people should watch based upon what they watched in the past. Experimental results on the MovieLens database show that the Laplacian-based similarities perform well in comparison with other methods. The model, which nicely fits into the so-called statistical relational learning framework, could also be used to compute document or word similarities, and, more generally, it could be applied to machine-learning and pattern-recognition tasks involving a relational database

Hybridizing genetic algorithms with hill-climbing methods for global optimization: two possible ways

Two methods of hybridizing genetic algorithms (GA) with hill-climbing for global optimization are investigated. The first one involves two interwoven levels of optimization-evolution (GA) and individual learning (hill-climbing)-which cooperate in the global optimization process. The second one consists of modifying a GA by the introduction of new genetic operators or by the alteration of traditional ones in such a way that these new operators capture the basic mechanisms of hill-climbing. The simplex-GA is one of the possibilities explained and tested. These two methods are applied and compared for the maximization of complex functions defined in high-dimensional real space.<<ETX>>

Kinematic calibration and geometrical parameter identification for robots

A technique is presented for the calibration of robots based on a maximum-likelihood approach for the identification of geometrical errors. A new experimental setup is presented for measurement of the end-reflector position errors. The errors of position and orientation of the measuring device are included in the algorithm and identified. Tests have been carried out on a robot with six degrees of freedom. Tests show that this technique can reduce the mean error distance by a factor of more than 15. Compensation algorithms are presented, based on the improved knowledge of the geometrical model. >

Links between Kleinberg's hubs and authorities, correspondence analysis, and Markov chains

We show that Kleinbergs hubs and authorities model is closely related to both correspondence analysis, a well-known multivariate statistical technique, and a particular Markov chain model of navigation through the Web. The only difference between correspondence analysis and Kleinbergs method is the use of the average value of the hubs (authorities) scores for computing the authorities (hubs) scores, instead of the sum for Kleinbergs method. We also show that correspondence analysis and our Markov model are related to SALSA, a variant of Kleinbergs model.

Some Preliminary Comparisons Between a Neural Adaptive Controller and a Model Reference Adaptive Controller

Our aim in this paper is to make some preliminary comparisons between a neural adaptive controller and a Model Reference Adaptive Controller, on a simple and well defined first-order problem. We focus on the rate of convergence, and on the capacity to control non-linear and time-varying systems. Results from a first experiment show that the MRAC always converges faster and performs better for linear systems, but that its performances decline in case of non-linearity: the more abrupt the non-linearity, the stronger the decline in performance. On the contrary, this phenomenon is not observed for the neural net, whose performances do not vary significantly when the plant changes from linear to non-linear. Results from a second experiment show that the neural net adapts his parameters well for fast time-varying processes. This shows that a neural network, although it converges much more slowly, could be more appropriate in the case of control of that much has to be done to study the conditions of convergence of networks, in order to understand what can be really done by neural nets in non-linear control.

Fuzzy adaptive control of a certain class of SISO discrete-time processes

In this manuscript, we address the problem of the stability of a certain class of SISO discrete-time processes controlled by an adaptive fuzzy controller, by using Lyapunov stability theory. These results were recently obtained for adaptive neural controllers, and are extended here to adaptive fuzzy controllers of Sugenos type. In order to achieve tracking of a reference signal with this kind of fuzzy system, we allow both the membership functions and the consequent part of the rules to be adjusted by a parameter adaptation law. We first present the gradient-based (steepest descent) adaptation law, and we argue that this gradient-based adaptation law can be simplified dramatically. Thereafter, we show the asymptotic stability of the overall system (the convergence of the tracking error to zero) when using this simplified parameters adjustment law. Unfortunately, this result can only be proved when the outputs of the fuzzy controller can be expanded to the first order around the optimal parameter values that allow perfect tracking; that is, when the parameters are initialized not too far from their optimal values (local stability). However, when the set of tunable parameters is restricted to the set appearing in the linear consequent part of the rules (i.e. the membership functions of the premises are not modified) and when the reference signal is the delayed desired output, the stability result is strictly valid: the parameters do not have to be initialized around the perfectly tuned values. In this case, the algorithm can be simplified further by only considering the sign of the derivative of the output of the process in terms of its last influential input.

Adaptive Neurocontrol of a Certain Class of MIMO Discrete-Time Processes Based on Stability Theory

In this chapter, we prove the stability of a certain class of nonlinear discrete MIMO (Multi-Input Multi-Output) systems controlled by a multilayer neural net with a simple weight adaptation strategy. The proof is based on the Lyapunov stability theory. However, the stability statement is only valid if the initial weight values are not too far from their optimal values which allow perfect model matching (local stability). We therefore propose to initialize the weights with values that solve the linear problem. This extends our previous work (Renders, 1993; Saerens, Renders & Bersini, 1994), where single-input single-output (SISO) systems were considered.

Adaptive neurocontrol of MIMO systems based on stability theory

In this paper, we prove the input-output stability of a certain class of nonlinear discrete MIMO systems controlled by a multilayer neural net with a simple weight adaptation strategy. The proof is based on the Lyapunov formalism. The stability statement is, however, only valid if the initial weight values are not too far from their optimal values that allow perfect model matching. We therefore propose to initialize the weights with values that solve the linear problem. This extends our previous work (Renders, 1993; Saerens, Renders and Bersini, 1993), where SISO systems were considered.<<ETX>>

Non-Geometrical Parameters Identification for Robot Kinematic Calibration by use of Neural Network Techniques

This paper presents a new technique for the calibration of robots based on a neural network approach for the identification of non-geometrical errors. Identification of geometrical errors is not a problem any more since several methods have been presented recently. The remaining problem is the identification of the non-geometrical errors. Non-geometrical errors modeling is a very complex and heavy process. The originality of this paper is the use of a neural network approach avoiding explicit modeling of this kind of errors. Simulations have been carried out on a robot with 6 degrees of freedom. Finally, two compensation algorithms are presented, based on the improved knowledge of the model: the first one is based on the construction of false target, the second one compensates directly into the joint space.