6,057 research outputs found
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
Generalization properties of finite size polynomial Support Vector Machines
The learning properties of finite size polynomial Support Vector Machines are
analyzed in the case of realizable classification tasks. The normalization of
the high order features acts as a squeezing factor, introducing a strong
anisotropy in the patterns distribution in feature space. As a function of the
training set size, the corresponding generalization error presents a crossover,
more or less abrupt depending on the distribution's anisotropy and on the task
to be learned, between a fast-decreasing and a slowly decreasing regime. This
behaviour corresponds to the stepwise decrease found by Dietrich et al.[Phys.
Rev. Lett. 82 (1999) 2975-2978] in the thermodynamic limit. The theoretical
results are in excellent agreement with the numerical simulations.Comment: 12 pages, 7 figure
Perceptron learning with random coordinate descent
A perceptron is a linear threshold classifier that separates examples with a hyperplane. It is perhaps the simplest learning model that is used standalone. In this paper, we propose a family of random coordinate descent algorithms for perceptron learning on binary classification problems. Unlike most perceptron learning algorithms which require smooth cost functions, our algorithms directly minimize the training error, and usually achieve the lowest training error compared with other algorithms. The algorithms are also computational efficient. Such advantages make them favorable for both standalone use and ensemble learning, on problems that are not linearly separable. Experiments show that our algorithms work very well with AdaBoost, and achieve the lowest test errors for half of the datasets
Statistical Mechanics of Soft Margin Classifiers
We study the typical learning properties of the recently introduced Soft
Margin Classifiers (SMCs), learning realizable and unrealizable tasks, with the
tools of Statistical Mechanics. We derive analytically the behaviour of the
learning curves in the regime of very large training sets. We obtain
exponential and power laws for the decay of the generalization error towards
the asymptotic value, depending on the task and on general characteristics of
the distribution of stabilities of the patterns to be learned. The optimal
learning curves of the SMCs, which give the minimal generalization error, are
obtained by tuning the coefficient controlling the trade-off between the error
and the regularization terms in the cost function. If the task is realizable by
the SMC, the optimal performance is better than that of a hard margin Support
Vector Machine and is very close to that of a Bayesian classifier.Comment: 26 pages, 12 figures, submitted to Physical Review
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