Support Vector Machines for Business Applications

This chapter discusses the usage of Support Vector Machines (SVM) for business applications. It provides a brief historical background on inductive learning and pattern recognition, and then an intuitive motivation for SVM methods. The method is compared to other approaches, and the tools and background theory required to successfully apply SVMs to business applications are introduced. The authors hope that the chapter will help practitioners to understand when the SVM should be the method of choice, as well as how to achieve good results in minimal time

Kernel Based Algebraic Curve Fitting

An algebraic curve is defined as the zero set of a multivariate polynomial. We consider the problem of fitting an algebraic curve to a set of vectors given an additional set of vectors labelled as interior or exterior to the curve. The problem of fitting a linear curve in this way is shown to lend itself to a support vector representation, allowing non-linear curves and high dimensional surfaces to be estimated using kernel functions. The approach is attractive due to the stability of solutions obtained, the range of functional forms made possible (including polynomials), and the potential for applying well understood regularisation operators from the theory of Support Vector Machines

Implicit Surface Modelling as an Eigenvalue Problem

We discuss the problem of fitting an implicit shape model to a set of points sampled from a co-dimension one manifold of arbitrary topology. The method solves a non-convex optimisation problem in the embedding function that defines the implicit by way of its zero level set. By assuming that the solution is a mixture of radial basis functions of varying widths we attain the globally optimal solution by way of an equivalent eigenvalue problem, without using or constructing as an intermediate step the normal vectors of the manifold at each data point. We demonstrate the system on two and three dimensional data, with examples of missing data interpolation and set operations on the resultant shapes

Algebraic Curve Fitting Support Vector Machines

An algebraic curve is defined as the zero set of a multivariate polynomial. We consider the problem of fitting an algebraic curve to a set of vectors given an additional set of vectors labelled as interior or exterior to the curve. The problem of fitting a linear curve in this way is shown to lend itself to a support vector representation, allowing non-linear curves and high dimensional surfaces to be estimated using kernel functions. The approach is attractive due to the stability of solutions obtained, the range of functional forms made ossible (including polynomials), and the potential for applying well understood regularisation operators from the theory of Support Vector Machines

Towards a Maximum Entropy Method for Estimating HMM Parameters

Training a Hidden Markov Model (HMM) to maximise the probability of a given sequence can result in over-fitting. That is, the model represents the training sequence well, but fails to generalise. In this paper, we present a possible solution to this problem, which is to maximise a linear combination of the likelihood of the training data, and the entropy of the model. We derive the necessary equations for gradient based maximisation of this combined term. The performance of the system is then evaluated in comparison with three other algorithms, on a classification task using synthetic data. The results indicate that the method is potentially useful. The main problem with the method is the computational intractability of the entropy calculation

Old World megadroughts and pluvials during the Common Era

Climate model projections suggest widespread drying in the Mediterranean Basin and wetting in Fennoscandia in the coming decades largely as a consequence of greenhouse gas forcing of climate. To place these and other “Old World” climate projections into historical perspective based on more complete estimates of natural hydroclimatic variability, we have developed the “Old World Drought Atlas” (OWDA), a set of year-to-year maps of tree-ring reconstructed summer wetness and dryness over Europe and the Mediterranean Basin during the Common Era. The OWDA matches historical accounts of severe drought and wetness with a spatial completeness not previously available. In addition, megadroughts reconstructed over north-central Europe in the 11th and mid-15th centuries reinforce other evidence from North America and Asia that droughts were more severe, extensive, and prolonged over Northern Hemisphere land areas before the 20th century, with an inadequate understanding of their causes. The OWDA provides new data to determine the causes of Old World drought and wetness and attribute past climate variability to forced and/or internal variability

Post-stroke inhibition of induced NADPH oxidase type 4 prevents oxidative stress and neurodegeneration

Ischemic stroke is the second leading cause of death worldwide. Only one moderately effective therapy exists, albeit with contraindications that exclude 90% of the patients. This medical need contrasts with a high failure rate of more than 1,000 pre-clinical drug candidates for stroke therapies. Thus, there is a need for translatable mechanisms of neuroprotection and more rigid thresholds of relevance in pre-clinical stroke models. One such candidate mechanism is oxidative stress. However, antioxidant approaches have failed in clinical trials, and the significant sources of oxidative stress in stroke are unknown. We here identify NADPH oxidase type 4 (NOX4) as a major source of oxidative stress and an effective therapeutic target in acute stroke. Upon ischemia, NOX4 was induced in human and mouse brain. Mice deficient in NOX4 (Nox4(-/-)) of either sex, but not those deficient for NOX1 or NOX2, were largely protected from oxidative stress, blood-brain-barrier leakage, and neuronal apoptosis, after both transient and permanent cerebral ischemia. This effect was independent of age, as elderly mice were equally protected. Restoration of oxidative stress reversed the stroke-protective phenotype in Nox4(-/-) mice. Application of the only validated low-molecular-weight pharmacological NADPH oxidase inhibitor, VAS2870, several hours after ischemia was as protective as deleting NOX4. The extent of neuroprotection was exceptional, resulting in significantly improved long-term neurological functions and reduced mortality. NOX4 therefore represents a major source of oxidative stress and novel class of drug target for stroke therapy