S.R. Gunn

The problem of empirical data modelling is germane to many engineering applications.
\nIn empirical data modelling a process of induction is used to build up a model of the
\nsystem, from which it is hoped to deduce responses of the system that have yet to be observed.
\nUltimately the quantity and quality of the observations govern the performance
\nof this empirical model. By its observational nature data obtained is finite and sampled;
\ntypically this sampling is non-uniform and due to the high dimensional nature of the
\nproblem the data will form only a sparse distribution in the input space. Consequently
\nthe problem is nearly always ill posed (Poggio et al., 1985) in the sense of Hadamard
\n(Hadamard, 1923). Traditional neural network approaches have suffered difficulties with
\ngeneralisation, producing models that can overfit the data. This is a consequence of the
\noptimisation algorithms used for parameter selection and the statistical measures used
\nto select the ’best’ model. The foundations of Support Vector Machines (SVM) have
\nbeen developed by Vapnik (1995) and are gaining popularity due to many attractive
\nfeatures, and promising empirical performance. The formulation embodies the Structural
\nRisk Minimisation (SRM) principle, which has been shown to be superior, (Gunn
\net al., 1997), to traditional Empirical Risk Minimisation (ERM) principle, employed by
\nconventional neural networks. SRM minimises an upper bound on the expected risk,
\nas opposed to ERM that minimises the error on the training data. It is this difference
\nwhich equips SVM with a greater ability to generalise, which is the goal in statistical
\nlearning. SVMs were developed to solve the classification problem, but recently they
\nhave been extended to the domain of regression problems (Vapnik et al., 1997). In the
\nliterature the terminology for SVMs can be slightly confusing. The term SVM is typically
\nused to describe classification with support vector methods and support vector
\nregression is used to describe regression with support vector methods. In this report
\nthe term SVM will refer to both classification and regression methods, and the terms
\nSupport Vector Classification (SVC) and Support Vector Regression (SVR) will be used
\nfor specification. This section continues with a brief introduction to the structural risk

Spectral band selection is a fundamental problem in hyperspectral data processing. In this letter, a new band-selection method based on mutual information (MI) is proposed. MI measures the statistical dependence between two random variables and can therefore be used to evaluate the relative utility of each band to classification. A new strategy is described to estimate the MI using a priori knowledge of the scene, reducing reliance on a "ground truth" reference map, by retaining bands with high associated MI values (subject to the so-called "complementary" conditions). Simulations of classification performance on 16 classes of vegetation from the AVIRIS 92AV3C data set show the effectiveness of the method, which outperforms an MI-based method using the associated reference map, an entropy-based method, and a correlation-based method. It is also competitive with the steepest ascent algorithm at much lower computational cost

Mixture modeling is becoming an increasingly important tool in the remote sensing community as researchers attempt to resolve subpixel, area information. This paper compares a well-established technique, linear spectral mixture models (LSMM), with a much newer idea based on data selection, support vector machines (SVM). It is shown that the constrained least squares LSMM is equivalent to the linear SVM, which relies on proving that the LSMM algorithm possesses the "maximum margin" property. This in turn shows that the LSMM algorithm can be derived from the same optimality conditions as the linear SVM, which provides important insights about the role of the bias term and rank deficiency in the pure pixel matrix within the LSMM algorithm. It also highlights one of the main advantages for using the linear SVM algorithm in that it performs automatic "pure pixel" selection from a much larger database. In addition, extensions to the basic SVM algorithm allow the technique to be applied to data sets that exhibit spectral confusion (overlapping sets of pure pixels) and to data sets that have nonlinear mixture regions. Several illustrative examples, based on an area-labeled Landsat dataset, are used to demonstrate the potential of this approach.

A conventional active contour formulation suffers difficulty in appropriate choice of an initial contour and values of parameters. Recent approaches have aimed to resolve these problems but can compromise other performance aspects. To relieve the problem in initialization, we use a dual active contour, which is combined with a local shape model to improve the parameterization. One contour expands from inside the target feature, the other contracts from the outside. The two contours are interlinked to provide a balanced technique with an ability to reject "weak" local energy minima.