Support Vector Machines: Training and Applications

The Support Vector Machine (SVM) is a new and very promising classification technique developed by Vapnik and his group at AT&T Bell Labs. This new learning algorithm can be seen as an alternative training technique for Polynomial, Radial Basis Function and Multi-Layer Perceptron classifiers. An interesting property of this approach is that it is an approximate implementation of the Structural Risk Minimization (SRM) induction principle. The derivation of Support Vector Machines, its relationship with SRM, and its geometrical insight, are discussed in this paper. Training a SVM is equivalent to solve a quadratic programming problem with linear and box constraints in a number of variables equal to the number of data points. When the number of data points exceeds few thousands the problem is very challenging, because the quadratic form is completely dense, so the memory needed to store the problem grows with the square of the number of data points. Therefore, training problems arising in some real applications with large data sets are impossible to load into memory, and cannot be solved using standard non-linear constrained optimization algorithms. We present a decomposition algorithm that can be used to train SVM's over large data sets. The main idea behind the decomposition is the iterative solution of sub-problems and the evaluation of, and also establish the stopping criteria for the algorithm. We present previous approaches, as well as results and important details of our implementation of the algorithm using a second-order variant of the Reduced Gradient Method as the solver of the sub-problems. As an application of SVM's, we present preliminary results we obtained applying SVM to the problem of detecting frontal human faces in real images.

Preconditioning and iterative solution of symmetric indefinite linear systems arising from interior point methods for linear programming

We study the preconditioning of symmetric indefinite linear systems of equations that arise in interior point solution of linear optimization problems. The preconditioning method that we study exploits the block structure of the augmented matrix to design a similar block structure preconditioner to improve the spectral properties of the resulting preconditioned matrix so as to improve the convergence rate of the iterative solution of the system. We also propose a two-phase algorithm that takes advantage of the spectral properties of the transformed matrix to solve for the Newton directions in the interior-point method. Numerical experiments have been performed on some LP test problems in the NETLIB suite to demonstrate the potential of the preconditioning method discussed.

Optimal piecewise locally linear modeling

Associative memory networks such as Radial Basis Functions, Neurofuzzy and Fuzzy Logic used for modelling nonlinear processes suffer from the curse of dimensionality (COD), in that as the input dimension increases the parameterization, computation cost, training data requirements, etc. increase exponentially. Here a new algorithm is introduced for the construction of a Delaunay input space partitioned optimal piecewise locally linear models to overcome the COD as well as generate locally linear models directly amenable to linear control and estimation algorithms. The training of the model is configured as a new mixture of experts network with a new fast decision rule derived using convex set theory. A very fast simulated reannealing (VFSR) algorithm is utilized to search a global optimal solution of the Delaunay input space partition. A benchmark non-linear time series is used to demonstrate the new approach.

Linear-wavelet models applied to the identification of a two-link manipulator

This paper shows that a wavelet network and a linear term can be advantageously combined for the purpose of non linear system identification. The theoretical foundation of this approach is laid by proving that radial wavelets are orthogonal to linear functions. A constructive procedure for building such nonlinear regression structures, termed linear-wavelet models, is described. For illustration, sim ulation data are used to identify a model for a two-link robotic manipulator. The results show that the introduction of wavelets does improve the prediction ability of a linear model.

Adaptive modelling with tunable RBF network using multi-innovation RLS algorithm assisted by swarm intelligence

In this paper, we propose a new on-line learning algorithm for the non-linear system identification: the swarm intelligence aided multi-innovation recursive least squares (SI-MRLS) algorithm. The SI-MRLS algorithm applies the particle swarm optimization (PSO) to construct a flexible radial basis function (RBF) model so that both the model structure and output weights can be adapted. By replacing an insignificant RBF node with a new one based on the increment of error variance criterion at every iteration, the model remains at a limited size. The multi-innovation RLS algorithm is used to update the RBF output weights which are known to have better accuracy than the classic RLS. The proposed method can produces a parsimonious model with good performance. Simulation result are also shown to verify the SI-MRLS algorithm.

Measures of observation impact in non-Gaussian data assimilation

ABSTRACT Non-Gaussian/non-linear data assimilation is becoming an increasingly important area of research in the Geosciences as the resolution and non-linearity of models are increased and more and more non-linear observation operators are being used. In this study, we look at the effect of relaxing the assumption of a Gaussian prior on the impact of observations within the data assimilation system. Three different measures of observation impact are studied: the sensitivity of the posterior mean to the observations, mutual information and relative entropy. The sensitivity of the posterior mean is derived analytically when the prior is modelled by a simplified Gaussian mixture and the observation errors are Gaussian. It is found that the sensitivity is a strong function of the value of the observation and proportional to the posterior variance. Similarly, relative entropy is found to be a strong function of the value of the observation. However, the errors in estimating these two measures using a Gaussian approximation to the prior can differ significantly. This hampers conclusions about the effect of the non-Gaussian prior on observation impact. Mutual information does not depend on the value of the observation and is seen to be close to its Gaussian approximation. These findings are illustrated with the particle filter applied to the Lorenz ’63 system. This article is concluded with a discussion of the appropriateness of these measures of observation impact for different situations.

Tests of non-linearity using LIFFE futures transactions price data

This paper presents and implements a number of tests for non-linear dependence and a test for chaos using transactions prices on three LIFFE futures contracts: the Short Sterling interest rate contract, the Long Gilt government bond contract, and the FTSE 100 stock index futures contract. While previous studies of high frequency futures market data use only those transactions which involve a price change, we use all of the transaction prices on these contracts whether they involve a price change or not. Our results indicate irrefutable evidence of non-linearity in two of the three contracts, although we find no evidence of a chaotic process in any of the series. We are also able to provide some indications of the effect of the duration of the trading day on the degree of non-linearity of the underlying contract. The trading day for the Long Gilt contract was extended in August 1994, and prior to this date there is no evidence of any structure in the return series. However, after the extension of the trading day we do find evidence of a non-linear return structure.

Testing for non-linearity in daily sterling exchange rates

A number of tests for non-linear dependence in time series are presented and implemented on a set of 10 daily sterling exchange rates covering the entire post Bretton-Woods era until the present day. Irrefutable evidence of non-linearity is shown in many of the series, but most of this dependence can apparently be explained by reference to the GARCH family of models. It is suggested that the literature in this area has reached an impasse, with the presence of ARCH effects clearly demonstrated in a large number of papers, but with the tests for non-linearity which are currently available being unable to classify any additional non-linear structure.

An evaluation of three upwinding approximations for numerical modeling the flow in tubular membrane of Newtonian and non-Newtonian fluids

In this paper, the laminar fluid flow of Newtonian and non-Newtonian of aqueous solutions in a tubular membrane is numerically studied. The mathematical formulation, with associated initial and boundary conditions for cylindrical coordinates, comprises the mass conservation, momentum conservation and mass transfer equations. These equations are discretized by using the finite-difference technique on a staggered grid system. Comparisons of the three upwinding schemes for discretization of the non-linear (convective) terms are presented. The effects of several physical parameters on the concentration profile are investigated. The numerical results compare favorably with experimental data and the analytical solutions. (C) 2011 Elsevier Inc. All rights reserved.

Study of the spectroscopic properties and first hyperpolarizabilities of disperse azo dyes derived from 2-amino-5-nitrothiazole

The solvatochromism and other spectroscopic and photophysical characteristics of four azo disperse dyes, derived from 2-amino-5-nitrothiazole, were evaluated and interpreted with the aid of experimental data and quantum mechanical calculations. For the non-substituted compound two conformers, E and Z, were proposed for the isolated molecules, being the second one considerably less stable. The optimization of these structures in combination with a SCRF methodology (IEFPCM, Simulating the molecules in a continuum dielectric with characteristics of methanol), suggests that the Z form is not stable in solution. This same behaviour is expected for the substituted compounds, which is corroborated by experimental data presented in previous investigations [A.E.H. Machado, L.M. Rodrigues, S. Gupta, A.M.F. Oliveira-Campos, A.M.S. Silva, J. Mol. Struct. 738 (2005) 239-245]. For the substituted compounds, two forms derived from E conformer (A and R) are possible. Quantum mechanical data suggest for the isolated molecules, that the low energy absorption hand of the E conformers involve at least two close electronic states. having the low-lying excited state a (1)(n,pi*) nature, and being the S-2 state attributed to a (1)(pi,pi*) transition. The data also suggest a small energy gap between the absorption peaks of A and B, related to the easy conversion between these forms. For the structures optimized in combination with the applied SCRF methodology, an states inversion is observed for the Substituted compounds, with a considerable diminish of the energy gap between A and B absorption peaks. The electronic spectra of these compounds are quite sensitive to changes in the solvent polarity. The positive solvatochromism is more evident in aprotic solvents, probably due to the polarization induced by the solute. These compounds do not fluoresce at 298 K, but present a small but perceptible fluorescence at 77 K, which seems to be favoured by the nature of the group in the 2 `-position of the phenyl ring. Moreover, such compounds present expressive values for first hyperpolarizability, which implies in good non-linear optics (NLO) responses and photoswitching capability. (C) 2008 Elsevier B.V. All rights reserved.

New and improved results for packing identical unitary radius circles within triangles, rectangles and strips

The focus of study in this paper is the class of packing problems. More specifically, it deals with the placement of a set of N circular items of unitary radius inside an object with the aim of minimizing its dimensions. Differently shaped containers are considered, namely circles, squares, rectangles, strips and triangles. By means of the resolution of non-linear equations systems through the Newton-Raphson method, the herein presented algorithm succeeds in improving the accuracy of previous results attained by continuous optimization approaches up to numerical machine precision. The computer implementation and the data sets are available at http://www.ime.usp.br/similar to egbirgin/packing/. (C) 2009 Elsevier Ltd, All rights reserved.

Minimizing the object dimensions in circle and sphere packing problems

Given a fixed set of identical or different-sized circular items, the problem we deal with consists on finding the smallest object within which the items can be packed. Circular, triangular, squared, rectangular and also strip objects are considered. Moreover, 2D and 3D problems are treated. Twice-differentiable models for all these problems are presented. A strategy to reduce the complexity of evaluating the models is employed and, as a consequence, instances with a large number of items can be considered. Numerical experiments show the flexibility and reliability of the new unified approach. (C) 2007 Elsevier Ltd. All rights reserved.

Multi-Objective Pipe Smoothing Genetic Algorithm For Water Distribution Network Design

This paper describes the formulation of a Multi-objective Pipe Smoothing Genetic Algorithm (MOPSGA) and its application to the least cost water distribution network design problem. Evolutionary Algorithms have been widely utilised for the optimisation of both theoretical and real-world non-linear optimisation problems, including water system design and maintenance problems. In this work we present a pipe smoothing based approach to the creation and mutation of chromosomes which utilises engineering expertise with the view to increasing the performance of the algorithm whilst promoting engineering feasibility within the population of solutions. MOPSGA is based upon the standard Non-dominated Sorting Genetic Algorithm-II (NSGA-II) and incorporates a modified population initialiser and mutation operator which directly targets elements of a network with the aim to increase network smoothness (in terms of progression from one diameter to the next) using network element awareness and an elementary heuristic. The pipe smoothing heuristic used in this algorithm is based upon a fundamental principle employed by water system engineers when designing water distribution pipe networks where the diameter of any pipe is never greater than the sum of the diameters of the pipes directly upstream resulting in the transition from large to small diameters from source to the extremities of the network. MOPSGA is assessed on a number of water distribution network benchmarks from the literature including some real-world based, large scale systems. The performance of MOPSGA is directly compared to that of NSGA-II with regard to solution quality, engineering feasibility (network smoothness) and computational efficiency. MOPSGA is shown to promote both engineering and hydraulic feasibility whilst attaining good infrastructure costs compared to NSGA-II.

Joint dynamic probabilistic constraints with projected linear decision rules

We consider multistage stochastic linear optimization problems combining joint dynamic probabilistic constraints with hard constraints. We develop a method for projecting decision rules onto hard constraints of wait-and-see type. We establish the relation between the original (in nite dimensional) problem and approximating problems working with projections from di erent subclasses of decision policies. Considering the subclass of linear decision rules and a generalized linear model for the underlying stochastic process with noises that are Gaussian or truncated Gaussian, we show that the value and gradient of the objective and constraint functions of the approximating problems can be computed analytically.

Utilização de modelos de programação não-linear para sistematização de terras para irrigação em áreas regulares

Objetivou-se com este trabalho, desenvolver modelos de programação não-linear para sistematização de terras, aplicáveis para áreas com formato regular e que minimizem a movimentação de terra, utilizando o software GAMS para o cálculo. Esses modelos foram comparados com o Método dos Quadrados Mínimos Generalizado, desenvolvido por Scaloppi & Willardson (1986), sendo o parâmetro de avaliação o volume de terra movimentado. Concluiu-se que, ambos os modelos de programação não-linear desenvolvidos nesta pesquisa mostraram-se adequados para aplicação em áreas regulares e forneceram menores valores de movimentação de terra quando comparados com o método dos quadrados mínimos.