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Cevikalp H.,Eskiehir Osmangazi University | Triggs B.,Laboratoire Jean Kuntzmann
Pattern Recognition | Year: 2013

We introduce a large margin linear binary classification framework that approximates each class with a hyperdisk - the intersection of the affine support and the bounding hypersphere of its training samples in feature space - and then finds the linear classifier that maximizes the margin separating the two hyperdisks. We contrast this with Support Vector Machines (SVMs), which find the maximum-margin separator of the pointwise convex hulls of the training samples, arguing that replacing convex hulls with looser convex class models such as hyperdisks provides safer margin estimates that improve the accuracy on some problems. Both the hyperdisks and their separators are found by solving simple quadratic programs. The method is extended to nonlinear feature spaces using the kernel trick, and multi-class problems are dealt with by combining binary classifiers in the same ways as for SVMs. Experiments on a range of data sets show that the method compares favourably with other popular large margin classifiers. © 2012 Elsevier Ltd. Source

Doyen L.,Laboratoire Jean Kuntzmann
Computational Statistics and Data Analysis | Year: 2012

An imperfect maintenance model for repairable systems is considered. Corrective Maintenances (CM) are assumed to be minimal, i.e. As Bad As Old (ABAO). They are considered to be left and right censored. Preventive Maintenances (PM) are assumed to be done at predetermined planned times and to follow a Brown-Proschan (BP) model, i.e. they renew (As Good As New, AGAN) the system with probability p, and they are minimal (ABAO) with probability 1-p. BP PM effects (AGAN or ABAO) are assumed to be not observed. In this context, different methods (maximum likelihood, moment estimation, and expectation-maximization algorithm) are considered in order to estimate jointly the PM efficiency parameter p and the parameters of the first time to failure distribution corresponding to the new unmaintained system. A method to individually assess the effect of each PM is also proposed. Finally, some reliability characteristics are computed: failure and cumulative failure intensities, reliability and expected cumulative number of failures. All the corresponding algorithms are detailed and applied to a real maintenance data set from an electricity power plant. © 2012 Elsevier B.V. All rights reserved. Source

Cevikalp H.,Eskiehir Osmangazi University | Triggs B.,Laboratoire Jean Kuntzmann | Yavuz H.S.,Eskiehir Osmangazi University | Kucuk Y.,Anadolu University | And 2 more authors.
Neurocomputing | Year: 2010

This paper introduces a geometrically inspired large margin classifier that can be a better alternative to the support vector machines (SVMs) for the classification problems with limited number of training samples. In contrast to the SVM classifier, we approximate classes with affine hulls of their class samples rather than convex hulls. For any pair of classes approximated with affine hulls, we introduce two solutions to find the best separating hyperplane between them. In the first proposed formulation, we compute the closest points on the affine hulls of classes and connect these two points with a line segment. The optimal separating hyperplane between the two classes is chosen to be the hyperplane that is orthogonal to the line segment and bisects the line. The second formulation is derived by modifying the ν-SVM formulation. Both formulations are extended to the nonlinear case by using the kernel trick. Based on our findings, we also develop a geometric interpretation of the least squares SVM classifier and show that it is a special case of the proposed method. Multi-class classification problems are dealt with constructing and combining several binary classifiers as in SVM. The experiments on several databases show that the proposed methods work as good as the SVM classifier if not any better. © 2010 Elsevier B.V. Source

Hussain S.U.,University of Caen Lower Normandy | Triggs B.,Laboratoire Jean Kuntzmann
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2012

Features such as Local Binary Patterns (LBP) and Local Ternary Patterns (LTP) have been very successful in a number of areas including texture analysis, face recognition and object detection. They are based on the idea that small patterns of qualitative local gray-level differences contain a great deal of information about higher-level image content. Current local pattern features use hand-specified codings that are limited to small spatial supports and coarse graylevel comparisons. We introduce Local Quantized Patterns (LQP), a generalization that uses lookup-table-based vector quantization to code larger or deeper patterns. LQP inherits some of the flexibility and power of visual word representations without sacrificing the run-time speed and simplicity of local pattern ones. We show that it outperforms well-established features including HOG, LBP and LTP and their combinations on a range of challenging object detection and texture classification problems. © 2012 Springer-Verlag. Source

Bonnivard M.,Laboratoire Jean Kuntzmann | Bucur D.,CNRS Mathematics Laboratory
Journal of Mathematical Fluid Mechanics | Year: 2012

Relying on the effect of microscopic asperities, one can mathematically justify that viscous fluids adhere completely on the boundary of an impermeable domain. The rugosity effect accounts asymptotically for the transformation of complete slip boundary conditions on a rough surface in total adherence boundary conditions, as the amplitude of the rugosities vanishes. The decreasing rate (average velocity divided by the amplitude of the rugosities) computed on close flat layers is definitely influenced by the geometry. Recent results prove that this ratio has a uniform upper bound for certain geometries, like periodical and "almost Lipschitz" boundaries. The purpose of this paper is to prove that such a result holds for arbitrary (non-periodical) crystalline boundaries and general (non-smooth) periodical boundaries. © 2011 Springer Basel AG. Source

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