Paul Honeine

Online Prediction of Time Series Data With Kernels

Kernel-based algorithms have been a topic of considerable interest in the machine learning community over the last ten years. Their attractiveness resides in their elegant treatment of nonlinear problems. They have been successfully applied to pattern recognition, regression and density estimation. A common characteristic of kernel-based methods is that they deal with kernel expansions whose number of terms equals the number of input data, making them unsuitable for online applications. Recently, several solutions have been proposed to circumvent this computational burden in time series prediction problems. Nevertheless, most of them require excessively elaborate and costly operations. In this paper, we investigate a new model reduction criterion that makes computationally demanding sparsification procedures unnecessary. The increase in the number of variables is controlled by the coherence parameter, a fundamental quantity that characterizes the behavior of dictionaries in sparse approximation problems. We incorporate the coherence criterion into a new kernel-based affine projection algorithm for time series prediction. We also derive the kernel-based normalized LMS algorithm as a particular case. Finally, experiments are conducted to compare our approach to existing methods.

Nonlinear Unmixing of Hyperspectral Data Based on a Linear-Mixture/Nonlinear-Fluctuation Model

Spectral unmixing is an important issue to analyze remotely sensed hyperspectral data. Although the linear mixture model has obvious practical advantages, there are many situations in which it may not be appropriate and could be advantageously replaced by a nonlinear one. In this paper, we formulate a new kernel-based paradigm that relies on the assumption that the mixing mechanism can be described by a linear mixture of endmember spectra, with additive nonlinear fluctuations defined in a reproducing kernel Hilbert space. This family of models has clear interpretation, and allows to take complex interactions of endmembers into account. Extensive experiment results, with both synthetic and real images, illustrate the generality and effectiveness of this scheme compared with state-of-the-art methods.

Testing Stationarity With Surrogates: A Time-Frequency Approach

An operational framework is developed for testing stationarity relatively to an observation scale, in both stochastic and deterministic contexts. The proposed method is based on a comparison between global and local time-frequency features. The originality is to make use of a family of stationary surrogates for defining the null hypothesis of stationarity and to base on them two different statistical tests. The first one makes use of suitably chosen distances between local and global spectra, whereas the second one is implemented as a one-class classifier, the time- frequency features extracted from the surrogates being interpreted as a learning set for stationarity. The principle of the method and of its two variations is presented, and some results are shown on typical models of signals that can be thought of as stationary or nonstationary, depending on the observation scale used.

Geometric Unmixing of Large Hyperspectral Images: A Barycentric Coordinate Approach

In hyperspectral imaging, spectral unmixing is one of the most challenging and fundamental problems. It consists of breaking down the spectrum of a mixed pixel into a set of pure spectra, called endmembers, and their contributions, called abundances. Many endmember extraction techniques have been proposed in literature, based on either a statistical or a geometrical formulation. However, most, if not all, of these techniques for estimating abundances use a least-squares solution. In this paper, we show that abundances can be estimated using a geometric formulation. To this end, we express abundances with the barycentric coordinates in the simplex defined by endmembers. We propose to write them in terms of a ratio of volumes or a ratio of distances, which are quantities that are often computed to identify endmembers. This property allows us to easily incorporate abundance estimation within conventional endmember extraction techniques, without incurring additional computational complexity. We use this key property with various endmember extraction techniques, such as N-Findr, vertex component analysis, simplex growing algorithm, and iterated constrained endmembers. The relevance of the method is illustrated with experimental results on real hyperspectral images.

On-line Nonlinear Sparse Approximation of Functions

This paper provides new insights into on-line nonlinear sparse approximation of functions based on the coherence criterion. We revisit previous work, and propose tighter bounds on the approximation error based on the coherence criterion. Moreover, we study the connections between the coherence criterion and both the approximate linear dependence criterion and the principal component analysis. Finally, we derive a kernel normalized LMS algorithm based on the coherence criterion, which has linear computational complexity on the model order. Initial experimental results are presented on the performance of the algorithm.

Nonlinear Estimation of Material Abundances in Hyperspectral Images With

Integrating spatial information into hyperspectral unmixing procedures has been shown to have a positive effect on the estimation of fractional abundances due to the inherent spatial-spectral duality in hyperspectral scenes. However, current research works that take spatial information into account are mainly focused on the linear mixing model. In this paper, we investigate how to incorporate spatial correlation into a nonlinear abundance estimation process. A nonlinear unmixing algorithm operating in reproducing kernel Hilbert spaces, coupled with a l1-type spatial regularization, is derived. Experiment results, with both synthetic and real hyperspectral images, illustrate the effectiveness of the proposed scheme.

\ell_{1}

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 biomed-ical 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.

-Norm Spatial Regularization

The massive use of information and communication technologies in supervisory control and data acquisition (SCADA) systems opens new ways for carrying out cyberattacks against critical infrastructures relying on SCADA networks. The various vulnerabilities in these systems and the heterogeneity of cyberattacks make the task extremely difficult for traditional intrusion detection systems (IDS). Modeling cyberattacks has become nearly impossible and their potential consequences may be very severe. The primary objective of this work is to detect malicious intrusions once they have already bypassed traditional IDS and firewalls. This paper investigates the use of machine learning for intrusion detection in SCADA systems using one-class classification algorithms. Two approaches of one-class classification are investigated: 1) the support vector data description (SVDD); and 2) the kernel principle component analysis. The impact of the considered metric is examined in detail with the study of lp-norms in radial basis function (RBF) kernels. A heuristic is proposed to find an optimal choice of the bandwidth parameter in these kernels. Tests are conducted on real data with several types of cyberattacks.

Wireless sensor networks in biomedical: Body area networks

This paper describes an original method for target tracking in wireless sensor networks. The proposed method combines machine learning with a Kalman filter to estimate instantaneous positions of a moving target. The targets accelerations, along with information from the network, are used to obtain an accurate estimation of its position. To this end, radio-fingerprints of received signal strength indicators (RSSIs) are first collected over the surveillance area. The obtained database is then used with machine learning algorithms to compute a model that estimates the position of the target using only RSSI information. This model leads to a first position estimate of the target under investigation. The kernel-based ridge regression and the vector-output regularized least squares are used in the learning process. The Kalman filter is used afterward to combine predictions of the targets positions based on acceleration information with the first estimates, leading to more accurate ones. The performance of the method is studied for different scenarios and a thorough comparison with well-known algorithms is also provided.

l p -norms in One-Class Classification for Intrusion Detection in SCADA Systems.

Over the past few years, wireless sensor networks received tremendous attention for monitoring physical phenomena, such as the temperature field in a given region. Applying conventional kernel regression methods for functional learning such as support vector machines is inappropriate for sensor networks, since the order of the resulting model and its computational complexity scales badly with the number of available sensors, which tends to be large. In order to circumvent this drawback, we propose in this paper a reduced-order model approach. To this end, we take advantage of recent developments in sparse representation literature, and show the natural link between reducing the model order and the topology of the deployed sensors. To learn this model, we derive a gradient descent scheme and show its efficiency for wireless sensor networks. We illustrate the proposed approach through simulations involving the estimation of a spatial temperature distribution.