Suppose you are given some data set drawn from an underlying probability distribution P and you want to estimate a "simple" subset S of input space such that the probability that a test point drawn from P lies outside of S equals some a priori specified value between 0 and 1. We propose a method to approach this problem by trying to estimate a function f that is positive on S and negative on the complement. The functional form of f is given by a kernel expansion in terms of a potentially small subset of the training data; it is regularized by controlling the length of the weight vector in an associated feature space. The expansion coefficients are found by solving a quadratic programming problem, which we do by carrying out sequential optimization over pairs of input patterns. We also provide a theoretical analysis of the statistical performance of our algorithm. The algorithm is a natural extension of the support vector algorithm to the case of unlabeled data.

/pdf/estimating-the-support-of-a-high-dimensional-distribution-1tg8d7chbx.pdf

Estimating the Support of a High-Dimensional Distribution

Suppose you are given some data set drawn from an underlying probability distribution P and you want to estimate a simple subset S of input space such that the probability that a test point drawn from P lies outside of S equals some a priori specified value between 0 and 1. We propose a method to approach this problem by trying to estimate a function f that is positive on S and negative on the complement. The functional form of f is given by a kernel expansion in terms of a potentially small subset of the training data; it is regularized by controlling the length of the weight vector in an associated feature space. The expansion coefficients are found by solving a quadratic programming problem, which we do by carrying out sequential optimization over pairs of input patterns. We also provide a theoretical analysis of the statistical performance of our algorithm. The algorithm is a natural extension of the support vector algorithm to the case of unlabeled data.

Williamson, estimating the support of a high-dimensional distribution

The increasing interest in Support Vector Machines (SVMs) over the past 15 years is described. Methods are illustrated using simulated case studies, and 4 experimental case studies, namely mass spectrometry for studying pollution, near infrared analysis of food, thermal analysis of polymers and UV/visible spectroscopy of polyaromatic hydrocarbons. The basis of SVMs as two-class classifiers is shown with extensive visualisation, including learning machines, kernels and penalty functions. The influence of the penalty error and radial basis function radius on the model is illustrated. Multiclass implementations including one vs. all, one vs. one, fuzzy rules and Directed Acyclic Graph (DAG) trees are described. One-class Support Vector Domain Description (SVDD) is described and contrasted to conventional two- or multi-class classifiers. The use of Support Vector Regression (SVR) is illustrated including its application to multivariate calibration, and why it is useful when there are outliers and non-linearities.

Support Vector Machines for classification and regression

The characteristics of the OPLS method have been investigated for the purpose of discriminant analysis (OPLS-DA). We demonstrate how class-orthogonal variation can be exploited to augment classific ...

OPLS discriminant analysis: combining the strengths of PLS-DA and SIMCA classification†

Support vector machines (SVMs) have considerable potential as classifiers of remotely sensed data. A constraint on their application in remote sensing has been their binary nature, requiring multiclass classifications to be based upon a large number of binary analyses. Here, an approach for multiclass classification of airborne sensor data by a single SVM analysis is evaluated against a series of classifiers that are widely used in remote sensing, with particular regard to the effect of training set size on classification accuracy. In addition to the SVM, the same datasets were classified using a discriminant analysis, decision tree, and multilayer perceptron neural network. The accuracy statements of the classifications derived from the different classifiers were compared in a statistically rigorous fashion that accommodated for the related nature of the samples used in the analyses. For each classification technique, accuracy was positively related with the size of the training set. In general, the most accurate classifications were derived from the SVM approach, and with the largest training set the SVM classification was significantly (p 90% correct, the classifiers differed in the ability to correctly label individual cases and so may be suitable candidates for an ensemble-based approach to classification.

/pdf/a-relative-evaluation-of-multiclass-image-classification-by-cxhcuggzt4.pdf

A relative evaluation of multiclass image classification by support vector machines

A flexible classification approach with optimal generalisation performance: support vector machines

Signatures of Bovine Spongiform Encephalopathy (BSE) have been identified in serum by means of “Diagnostic Pattern Recognition (DPR)”. For DPR-analysis, mid-infrared spectroscopy of dried films of 641 serum samples was performed using disposable silicon sample carriers and a semi-automated DPR research system operating at room temperature. The combination of four mathematical classification approaches (principal component analysis plus linear discriminant analysis, robust linear discriminant analysis, artificial neural network, support vector machine) allowed for a reliable assignment of spectra to the class “BSE-positive” or “BSE-negative”. An independent, blinded validation study was carried out on a second DPR research system at the Veterinary Laboratory Agency, Weybridge, UK. Out of 84 serum samples originating from terminally-ill, BSE-positive cattle, 78 were classified correctly. Similarly, 73 out of 76 BSE-negative samples were correctly identified by DPR such that, numerically, an accuracy of 94.4 % can be calculated. At a confidence level of 0.95 (α
				= 0.05) these results correspond to a sensitivity > 85% and a specificity > 90%. Identical class assignment by all four classifiers occurred in 75% of the cases while ambiguous results were obtained in only 8 of the 160 cases. With an area under the ROC (receiver operating charateristics) curve of 0.991, DPR may potentially supply a valuable surrogate marker for BSE even in cases in which a deliberate bias towards improved sensitivity or specificity is desired. To the best of our knowledge, DPR is the first and—up to now—only method which has demonstrated its capability of detecting BSE-related signatures in serum.

/pdf/classification-of-signatures-of-bovine-spongiform-3hr86iy2yd.pdf

Classification of signatures of Bovine Spongiform Encephalopathy in serum using infrared spectroscopy.

A lattice boson model is used to study ordering phenomena in regular 2D array of superconductive mesoscopic granules, Josephson junctions or pores filled with a superfluid helium. Phase diagram of the system, when quantum fluctuations of both the phase and local superfluid density are essential, is analyzed both analytically and by quantum Monte Carlo technique. For the system of strongly interacting bosons it is found that as the boson density n0 is increased the boundary of ordered superconducting state shifts to lower temperatures and at n0 > 8 approaches its limiting position corresponding to negligible relative fluctuations of moduli of the order parameter (as in an array of ”macroscopic” granules). In the region of weak quantum fluctuations of phases mesoscopic phenomena manifest themselves up to n0 ∼ 10. The mean field theory and functional integral 1/n0 expansion results are shown to agree with that of quantum Monte Carlo calculations of the boson Hubbard model and its quasiclassical limit, the quantum XY model.

A ug 1 99 8 Phase diagram of 2 D array of mesoscopic granules .

The special emphasis of support vector machines (SVMs) on generalization ability makes this approach particularly interesting for real-world applications with limited amounts of training data. In this paper we analyse the applicational aspects of SVMs, illustrating them with the step-by-step construction of a classifier for polymers by means of their mid-infrared spectra. With this example we show how the main difficulties of a typical industrial classification task can be addressed using SVMs.

Applicational aspects of support vector machines

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A flexible classification approach with optimal generalisation performance: support vector machines

Classification of signatures of Bovine Spongiform Encephalopathy in serum using infrared spectroscopy.

A ug 1 99 8 Phase diagram of 2 D array of mesoscopic granules .

Applicational aspects of support vector machines