Technical report : SVM in Krein spaces

Support vector machines (SVM) and kernel methods have been highly successful in many application areas. However, the requirement that the kernel is symmetric positive semidefinite, Mercer's condition, is not always verifi ed in practice. When it is not, the kernel is called indefi nite. Various heuristics and specialized methods have been proposed to address indefi nite kernels, from simple tricks such as removing negative eigenvalues, to advanced methods that de-noise the kernel by considering the negative part of the kernel as noise. Most approaches aim at correcting an inde finite kernel in order to provide a positive one. We propose a new SVM approach that deals directly with inde finite kernels. In contrast to previous approaches, we embrace the underlying idea that the negative part of an inde finite kernel may contain valuable information. To de fine such a method, the SVM formulation has to be adapted to a non usual form: the stabilization. The hypothesis space, usually a Hilbert space, becomes a Krei n space. This work explores this new formulation, and proposes two practical algorithms (ESVM and KSVM) that outperform the approaches that modify the kernel. Moreover, the solution depends on the original kernel and thus can be used on any new point without loss of accurac

Improved one-class SVM classifier for sounds classification

©2007 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.International audienceThis paper proposes to apply optimized One-Class Support Vector Machines (1-SVMs) as a discriminative framework in order to address a specific audio classification problem. First, since SVM-based classifier with gaussian RBF kernel is sensitive to the kernel width, the width will be scaled in a distribution-dependent way permitting to avoid underfitting and over-fitting problems. Moreover, an advanced dissimilarity measure will be introduced. We illustrate the performance of these methods on an audio database containing environmental sounds that may be of great importance for surveillance and security applications. The experiments conducted on a multi-class problem show that by choosing adequately the SVM parameters, we can efficiently address a sounds classification problem characterized by complex real-world datasets

One-Class Classification: Taxonomy of Study and Review of Techniques

One-class classification (OCC) algorithms aim to build classification models when the negative class is either absent, poorly sampled or not well defined. This unique situation constrains the learning of efficient classifiers by defining class boundary just with the knowledge of positive class. The OCC problem has been considered and applied under many research themes, such as outlier/novelty detection and concept learning. In this paper we present a unified view of the general problem of OCC by presenting a taxonomy of study for OCC problems, which is based on the availability of training data, algorithms used and the application domains applied. We further delve into each of the categories of the proposed taxonomy and present a comprehensive literature review of the OCC algorithms, techniques and methodologies with a focus on their significance, limitations and applications. We conclude our paper by discussing some open research problems in the field of OCC and present our vision for future research.Comment: 24 pages + 11 pages of references, 8 figure

Motion-Augmented Inference and Joint Kernels in Structured Learning for Object Tracking and Integration with Object Segmentation

Video object tracking is a fundamental task of continuously following an object of interest in a video sequence. It has attracted considerable attention in both academia and industry due to its diverse applications, such as in automated video surveillance, augmented and virtual reality, medical, automated vehicle navigation and tracking, and smart devices. Challenges in video object tracking arise from occlusion, deformation, background clutter, illumination variation, fast object motion, scale variation, low resolution, rotation, out-of-view, and motion blur. Object tracking remains, therefore, as an active research field. This thesis explores improving object tracking by employing 1) advanced techniques in machine learning theory to account for intrinsic changes in the object appearance under those challenging conditions, and 2) object segmentation. More specifically, we propose a fast and competitive method for object tracking by modeling target dynamics as a random stochastic process, and using structured support vector machines. First, we predict target dynamics by harmonic means and particle filter in which we exploit kernel machines to derive a new entropy based observation likelihood distribution. Second, we employ online structured support vector machines to model object appearance, where we analyze responses of several kernel functions for various feature descriptors and study how such kernels can be optimally combined to formulate a single joint kernel function. During learning, we develop a probability formulation to determine model updates and use sequential minimal optimization-step to solve the structured optimization problem. We gain efficiency improvements in the proposed object tracking by 1) exploiting particle filter for sampling the search space instead of commonly adopted dense sampling strategies, and 2) introducing a motion-augmented regularization term during inference to constrain the output search space. We then extend our baseline tracker to detect tracking failures or inaccuracies and reinitialize itself when needed. To that end, we integrate object segmentation into tracking. First, we use binary support vector machines to develop a technique to detect tracking failures (or inaccuracies) by monitoring internal variables of our baseline tracker. We leverage learned examples from our baseline tracker to train the employed binary support vector machines. Second, we propose an automated method to re-initialize the tracker to recover from tracking failures by integrating an active contour based object segmentation and using particle filter to sample bounding boxes for segmentation. Through extensive experiments on standard video datasets, we subjectively and objectively demonstrate that both our baseline and extended methods strongly compete against state-of-the-art object tracking methods on challenging video conditions

Positive Definite Kernels in Machine Learning

This survey is an introduction to positive definite kernels and the set of methods they have inspired in the machine learning literature, namely kernel methods. We first discuss some properties of positive definite kernels as well as reproducing kernel Hibert spaces, the natural extension of the set of functions $\{k(x,\cdot),x\in\mathcal{X}\}$ associated with a kernel $k$ defined on a space $\mathcal{X}$. We discuss at length the construction of kernel functions that take advantage of well-known statistical models. We provide an overview of numerous data-analysis methods which take advantage of reproducing kernel Hilbert spaces and discuss the idea of combining several kernels to improve the performance on certain tasks. We also provide a short cookbook of different kernels which are particularly useful for certain data-types such as images, graphs or speech segments.Comment: draft. corrected a typo in figure

Functional classification of G-Protein coupled receptors, based on their specific ligand coupling patterns

Functional identification of G-Protein Coupled Receptors (GPCRs) is one of the current focus areas of pharmaceutical research. Although thousands of GPCR sequences are known, many of them re- main as orphan sequences (the activating ligand is unknown). Therefore, classification methods for automated characterization of orphan GPCRs are imperative. In this study, for predicting Level 2 subfamilies of Amine GPCRs, a novel method for obtaining fixed-length feature vectors, based on the existence of activating ligand specific patterns, has been developed and utilized for a Support Vector Machine (SVM)-based classification. Exploiting the fact that there is a non-promiscuous relationship between the specific binding of GPCRs into their ligands and their functional classification, our method classifies Level 2 subfamilies of Amine GPCRs with a high predictive accuracy of 97.02% in a ten-fold cross validation test. The presented machine learning approach, bridges the gulf between the excess amount of GPCR sequence data and their poor functional characterization

Support Vector Machines in Analysis of Top Quark Production

Multivariate data analysis techniques have the potential to improve physics analyses in many ways. The common classification problem of signal/background discrimination is one example. The Support Vector Machine learning algorithm is a relatively new way to solve pattern recognition problems and has several advantages over methods such as neural networks. The SVM approach is described and compared to a conventional analysis for the case of identifying top quark signal events in the dilepton decay channel amidst a large number of background events.Comment: 8 pages, 8 figures, to be published in the proceedings of the "Advanced Statistical Techniques in Particle Physics" conference in Durham, UK (March, 2002