Extensions of the SVM Method to the Non-Linearly Separable Data

The main aim of the paper is to briefly investigate the most significant topics of the currently used methodologies of solving and implementing SVM-based classifier. Following a brief introductory part, the basics of linear SVM and non-linear SVM models are briefly exposed in the next two sections. The problem of soft margin SVM is exposed in the fourth section of the paper. The currently used methods for solving the resulted QP-problem require access to all labeled samples at once and a computation of an optimal solution is of complexity O(N2). Several ap-proaches have been proposed aiming to reduce the computation complexity, as the interior point (IP) methods, and the decomposition methods such as Sequential Minimal Optimization – SMO, as well as gradient-based methods to solving primal SVM problem. Several approaches based on genetic search in solving the more general problem of identifying the optimal type of kernel from pre-specified set of kernel types (linear, polynomial, RBF, Gaussian, Fourier, Bspline, Spline, Sigmoid) have been recently proposed. The fifth section of the paper is a brief survey on the most outstanding new techniques reported so far in this respect

Analysis of nonlinear modes of variation for functional data

A set of curves or images of similar shape is an increasingly common functional data set collected in the sciences. Principal Component Analysis (PCA) is the most widely used technique to decompose variation in functional data. However, the linear modes of variation found by PCA are not always interpretable by the experimenters. In addition, the modes of variation of interest to the experimenter are not always linear. We present in this paper a new analysis of variance for Functional Data. Our method was motivated by decomposing the variation in the data into predetermined and interpretable directions (i.e. modes) of interest. Since some of these modes could be nonlinear, we develop a new defined ratio of sums of squares which takes into account the curvature of the space of variation. We discuss, in the general case, consistency of our estimates of variation, using mathematical tools from differential geometry and shape statistics. We successfully applied our method to a motivating example of biological data. This decomposition allows biologists to compare the prevalence of different genetic tradeoffs in a population and to quantify the effect of selection on evolution.Comment: Published in at http://dx.doi.org/10.1214/07-EJS080 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org

Machine Learning Methods for Attack Detection in the Smart Grid

Attack detection problems in the smart grid are posed as statistical learning problems for different attack scenarios in which the measurements are observed in batch or online settings. In this approach, machine learning algorithms are used to classify measurements as being either secure or attacked. An attack detection framework is provided to exploit any available prior knowledge about the system and surmount constraints arising from the sparse structure of the problem in the proposed approach. Well-known batch and online learning algorithms (supervised and semi-supervised) are employed with decision and feature level fusion to model the attack detection problem. The relationships between statistical and geometric properties of attack vectors employed in the attack scenarios and learning algorithms are analyzed to detect unobservable attacks using statistical learning methods. The proposed algorithms are examined on various IEEE test systems. Experimental analyses show that machine learning algorithms can detect attacks with performances higher than the attack detection algorithms which employ state vector estimation methods in the proposed attack detection framework.Comment: 14 pages, 11 Figure