Peak Criterion for Choosing Gaussian Kernel Bandwidth in Support Vector Data Description

Support Vector Data Description (SVDD) is a machine-learning technique used for single class classification and outlier detection. SVDD formulation with kernel function provides a flexible boundary around data. The value of kernel function parameters affects the nature of the data boundary. For example, it is observed that with a Gaussian kernel, as the value of kernel bandwidth is lowered, the data boundary changes from spherical to wiggly. The spherical data boundary leads to underfitting, and an extremely wiggly data boundary leads to overfitting. In this paper, we propose empirical criterion to obtain good values of the Gaussian kernel bandwidth parameter. This criterion provides a smooth boundary that captures the essential geometric features of the data

Fault detection in operating helicopter drive train components based on support vector data description

The objective of the paper is to develop a vibration-based automated procedure dealing with early detection of mechanical degradation of helicopter drive train components using Health and Usage Monitoring Systems (HUMS) data. An anomaly-detection method devoted to the quantification of the degree of deviation of the mechanical state of a component from its nominal condition is developed. This method is based on an Anomaly Score (AS) formed by a combination of a set of statistical features correlated with specific damages, also known as Condition Indicators (CI), thus the operational variability is implicitly included in the model through the CI correlation. The problem of fault detection is then recast as a one-class classification problem in the space spanned by a set of CI, with the aim of a global differentiation between normal and anomalous observations, respectively related to healthy and supposedly faulty components. In this paper, a procedure based on an efficient one-class classification method that does not require any assumption on the data distribution, is used. The core of such an approach is the Support Vector Data Description (SVDD), that allows an efficient data description without the need of a significant amount of statistical data. Several analyses have been carried out in order to validate the proposed procedure, using flight vibration data collected from a H135, formerly known as EC135, servicing helicopter, for which micro-pitting damage on a gear was detected by HUMS and assessed through visual inspection. The capability of the proposed approach of providing better trade-off between false alarm rates and missed detection rates with respect to individual CI and to the AS obtained assuming jointly-Gaussian-distributed CI has been also analysed

Graph Embedded One-Class Classifiers for media data classification

This paper introduces the Graph Embedded One-Class Support Vector Machine and Graph Embedded Support Vector Data Description methods. These methods constitute novel extensions of the One-Class Support Vectors Machines and Support Vector Data Description, incorporating generic graph structures that express geometric data relationships of interest in their optimization process. Local or global relationships between the training patterns can be expressed with single graphs or combinations of fully connected and kNN graphs. We show that the adoption of generic geometric class information acts as a regularizer to the solution of the original methods. Moreover, we prove that the regularized solutions for both One-Class Support Vector Machine and Support Vector Data Description are equivalent to applying the original methods in a transformed (and shared) feature space. Qualitative and quantitative evaluation of the proposed methods shows that they compare favorably to the standard OC-SVM and SVDD classifiers, respectively

Fault prognostic of bearings by using support vector data description.

International audienceThis paper presents a method for fault prognostic of bearings based on Principal Component Analysis (PCA) and Support Vector Data Description (SVDD). The purpose of the paper is to transform the monitoring vibration signals into features that can be used to track the health condition of bearings and to estimate their remaining useful life. PCA is used to reduce the dimensionality of original vibration features by removing the redundant ones. SVDD is a pattern recognition method based on structural risk minimization principles. In this contribution, the SVDD is used to fit the trained data to a hypersphere such that its radius can be used as a health indicator. The proposed method is then applied on real bearing degradation performed on an accelerated life test. The experimental results show that the health indicator reflects the bearing's degradation

Probabilistic Kernel Support Vector Machines

We propose a probabilistic enhancement of standard kernel Support Vector Machines for binary classification, in order to address the case when, along with given data sets, a description of uncertainty (e.g., error bounds) may be available on each datum. In the present paper, we specifically consider Gaussian distributions to model uncertainty. Thereby, our data consist of pairs $(x_i,\Sigma_i)$, $i\in\{1,\ldots,N\}$, along with an indicator $y_i\in\{-1,1\}$ to declare membership in one of two categories for each pair. These pairs may be viewed to represent the mean and covariance, respectively, of random vectors $\xi_i$ taking values in a suitable linear space (typically $\mathbb R^n$). Thus, our setting may also be viewed as a modification of Support Vector Machines to classify distributions, albeit, at present, only Gaussian ones. We outline the formalism that allows computing suitable classifiers via a natural modification of the standard "kernel trick." The main contribution of this work is to point out a suitable kernel function for applying Support Vector techniques to the setting of uncertain data for which a detailed uncertainty description is also available (herein, "Gaussian points").Comment: 6 pages, 6 figure