Maya Kallas | Université de Lorraine (original) (raw)

Papers by Maya Kallas

IEEE Signal Processing Magazine, 2011

In this paper, we consider the pre-image problem in kernel machines, such as denoising with kerne... more In this paper, we consider the pre-image problem in kernel machines, such as denoising with kernel-PCA. For a given reproducing kernel Hilbert space (RKHS), by solving the preimage problem one seeks a pattern whose image in the RKHS is approximately a given feature. Traditional techniques include an iterative technique (Mika et al.) and a multidimensional scaling (MDS) approach (Kwok et al.). In this paper, we propose a new technique to learn the pre-image. In the RKHS, we construct a basis having an isometry with the input space, with respect to a training data. Then representing any feature in this basis gives us information regarding its preimage in the input space. We show that doing a pre-image can be done directly using the kernel values, without having to compute distances in any of the spaces as with the MDS approach. Simulation results illustrates the relevance of the proposed method, as we compare it to these techniques.

Journal of Physics: Conference Series, 2015

2015 European Control Conference (ECC), 2015

Journal of Physics: Conference Series, 2014

Technological advances in the process industries during the past decade have resulted in increasi... more Technological advances in the process industries during the past decade have resulted in increasingly complicated processes, systems and products. Therefore, recent researches consider the challenges in their design and management for successful operation. While principal component analysis (PCA) technique is widely used for diagnosis, its structure cannot describe nonlinear related variables. Thus, an extension to the case of nonlinear systems is presented in a feature space for process monitoring. Working in a high-dimensional feature space, it is necessary to get back to the original space. Hence, an iterative pre-image technique is derived to provide a solution for fault diagnosis. The relevance of the proposed technique is illustrated on artificial and real dataset.

ABSTRACT This communication deals with the problem of analysis and prediction using an autoregres... more ABSTRACT This communication deals with the problem of analysis and prediction using an autoregressive model. The latter, being known for solving these problems, is designed for linear systems. However, real-life applications are non-linear by nature, therefore, we propose in this paper a nonlinear autoregressive model, using kernel machines. The proposed approach inherits the simplicity of autoregressive model, yet non-linear. By combining the principle of the kernel trick and the resolution of the pre-image problem required for the interpretation of the data, we predict future samples of known chaotic time series present in literature. A comparison with different methods for nonlinear prediction present in the literature illustrates the performance of the proposed nonlinear autoregressive model.

Conference proceedings : ... Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Annual Conference, 2010

The inherent physical characteristics of many real-life phenomena, including biological and physi... more The inherent physical characteristics of many real-life phenomena, including biological and physiological aspects, require adapted nonlinear tools. Moreover, the additive nature in some situations involve solutions expressed as positive combinations of data. In this paper, we propose a nonlinear feature extraction method, with a non-negativity constraint. To this end, the kernel principal component analysis is considered to define the most relevant features in the reproducing kernel Hilbert space. These features are the nonlinear principal components with high-order correlations between input variables. A pre-image technique is required to get back to the input space. With a non-negative constraint, we show that one can solve the pre-image problem efficiently, using a simple iterative scheme. Furthermore, the constrained solution contributes to the stability of the algorithm. Experimental results on event-related potentials (ERP) illustrate the efficiency of the proposed method.

2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2012

Dans cette communication, nous traitons le problème de la pré-image en méthodesà noyau pour la re... more Dans cette communication, nous traitons le problème de la pré-image en méthodesà noyau pour la reconnaissance de formes de systèmes non-linéaires. Ce passage d'un espace des caractéristiquesà l'espace des observations peut s'avérer nécessaire pour interpréter les résultats. Cependant certaines conditions sont exigées comme pour le cas du traitement d'images, où la non-négativité des pixels est fondamentale. Pour ce faire, une méthode de descente du gradient est proposée, en y imposant une contrainte de non-négativité du résultat afin de garantir ces conditions. La pertinence de l'approche proposée est illustrée pour le débruitage des images en niveau de gris comparéeà d'autres méthodes présentes dans la littérature.

ABSTRACT Wireless sensor networks have received considerable attention during the last decade for... more ABSTRACT Wireless sensor networks have received considerable attention during the last decade for efficient monitoring, due to their low cost, their easy deployment and their capacity to locally process information. This paper derives original mobility schemes that allow improving the tracking of a physical phenomenon. To this end, we use kernel-based methods to construct a local model for each sensor, using the learning process where the input is the position of the sensor and the output is the estimation of the physical phenomenon. We show that kernel-based methods provide an elegant way to optimize the model. This allows us to derive mobility schemes for sensors in such a way to improve the efficiency of the models, by minimizing the estimation error. Sensors are moved according to several optimization techniques, by considering the first and second derivatives of the approximation error. Experimentations aim at estimating a gas diffusion in the space at any location devoid of sensor.

2011 IEEE Workshop on Signal Processing Systems (SiPS), 2011

Cardiac problems are the main reason of people's death nowadays. However, one way that light save... more Cardiac problems are the main reason of people's death nowadays. However, one way that light save the life is the analysis of the an electrocardiograph. This analysis consist in the diagnosis of the arrhythmia when it presents. In this paper, we propose to combine the Support Vector Machines used in classification on one hand, with the Principal Component Analysis used in order to reduce the size of the data by choosing some axes that capture the most variance between data and on the other hand, with the kernel principal component analysis where a mapping to a high dimensional space is needed to capture the most relevant axes but for nonlinear separable data. The efficiency of the proposed SVM classification is illustrated on real electrocardiogram dataset taken from MIT-BIH Arrhythmia Database.

Signal Processing, 2013

This paper proposes nonlinear autoregressive (AR) models for time series, within the framework of... more This paper proposes nonlinear autoregressive (AR) models for time series, within the framework of kernel machines. Two models are investigated. In the first proposed model, the AR model is defined on the mapped samples in the feature space. In order to predict a future sample, this formulation requires to solve a pre-image problem to get back to the input space. We derive an iterative technique to provide a fine-tuned solution to this problem. The second model bypasses the pre-image problem, by defining the AR model with an hybrid model, as a tradeoff considering the computational time and the precision, by comparing it to the iterative, fine-tuned, model. By considering the stationarity assumption, we derive the corresponding Yule-Walker equations for each model, and show the ease of solving these problems. The relevance of the proposed models is studied on several time series, and compared with other well-known models in terms of accuracy and computational complexity.

Cette communication traite le problème d'analyse et de prédiction selon un modèle autorégressif. ... more Cette communication traite le problème d'analyse et de prédiction selon un modèle autorégressif. Ce dernier,étant reconnu pour la résolution de ces problèmes, est conçu pour des systèmes linéaires. Or, les applications de la vie courante sont non-linéaires par nature, par suite, on propose dans ce papier, un modèle autorégressif non-linéaire, utilisant les méthodesà noyau. L'approche proposée hérite de la simplicité algorithmique du modèle autorégressif classique, tout enétant non-linéaire. En combinant le principe du coup du noyau et la résolution du problème de la pré-image nécessaire pour l'interprétation des observations, on prédit les futurséchantillons des séries temporelles et chaotiques connues dans la littérature. Une comparaison avec différentes méthodes de prédiction non-linéaires présentes dans la littérature illustre la performance du modèle autorégressif non-linéaire proposé.

Many real-life applications are nonlinear by nature. Moreover, in order to have a physical interp... more Many real-life applications are nonlinear by nature. Moreover, in order to have a physical interpretation, some constraints should be incorporated in the signal or image processing technique, such as the non-negativity of the solution. This paper deals with the non-negative pre-image problem in kernel machines, for nonlinear pattern recognition. While kernel machines operate in a feature space, associated to the used kernel function, a pre-image technique is often required to map back features into the input space. We derive a gradient-based algorithm to solve the pre-image problem, and to guarantee the non-negativity of the solution. Its convergence speed is significantly improved due to a weighted stepsize approach. The relevance of the proposed method is demonstrated with experiments on real datasets, where only a couple of iterations are necessary.

2014 IEEE International Workshop on Machine Learning for Signal Processing (MLSP), 2014

The nonnegative matrix factorization (NMF) is widely used in signal and image processing, includi... more The nonnegative matrix factorization (NMF) is widely used in signal and image processing, including bio-informatics, blind source separation and hyperspectral image analysis in remote sensing. A great challenge arises when dealing with nonlinear NMF. In this paper, we propose an efficient nonlinear NMF, which is based on kernel machines. As opposed to previous work, the proposed method does not suffer from the pre-image problem. We propose two iterative algorithms: an additive and a multiplicative update rule. Several extensions of the kernel-NMF are developed in order to take into account auxiliary structural constraints, such as smoothness, sparseness and spatial regularization. The relevance of the presented techniques is demonstrated in unmixing a synthetic hyperspectral image.

2012 19th International Conference on Telecommunications (ICT), 2012

One may monitor the heart normal activity by analyzing the electrocardiogram. We propose in this ... more One may monitor the heart normal activity by analyzing the electrocardiogram. We propose in this paper to combine the principle of kernel machines, that maps data into a high dimensional feature space, with the autoregressive (AR) technique defined using the Yule-Walker equations, which predicts future samples using a combination of some previous samples. A pre-image technique is applied in order

International Workshop on Systems, Signal Processing and their Applications, WOSSPA, 2011

The rapid growth in biomedical sensors, low-power circuits and wireless communications has enable... more The rapid growth in biomedical sensors, low-power circuits and wireless communications has enabled a new generation of wireless sensor networks: the body area networks. These networks are composed of tiny, cheap and low-power biomedical nodes, mainly dedicated for healthcare monitoring applications. The objective of these applications is to ensure a continuous monitoring of vital parameters of patients, while giving them the freedom of motion and thereby better quality of healthcare. This paper shows a comparison of body area networks to the wireless sensor networks. In particular, it shows how body area networks borrow and enhance ideas from wireless sensor networks. A study of energy consumption and heat absorption problems is developed for illustration.