Monitoring network optimisation for spatial data classification using support vector machines

The paper presents a novel method for monitoring network optimisation, based on a recent machine learning technique known as support vector machine. It is problem-oriented in the sense that it directly answers the question of whether the advised spatial location is important for the classification model. The method can be used to increase the accuracy of classification models by taking a small number of additional measurements. Traditionally, network optimisation is performed by means of the analysis of the kriging variances. The comparison of the method with the traditional approach is presented on a real case study with climate data.

Modelling ecological niches with support vector machines

1. The ecological niche is a fundamental biological concept. Modelling species' niches is central to numerous ecological applications, including predicting species invasions, identifying reservoirs for disease, nature reserve design and forecasting the effects of anthropogenic and natural climate change on species' ranges. 2. A computational analogue of Hutchinson's ecological niche concept (the multidimensional hyperspace of species' environmental requirements) is the support of the distribution of environments in which the species persist. Recently developed machine-learning algorithms can estimate the support of such high-dimensional distributions. We show how support vector machines can be used to map ecological niches using only observations of species presence to train distribution models for 106 species of woody plants and trees in a montane environment using up to nine environmental covariates. 3. We compared the accuracy of three methods that differ in their approaches to reducing model complexity. We tested models with independent observations of both species presence and species absence. We found that the simplest procedure, which uses all available variables and no pre-processing to reduce correlation, was best overall. Ecological niche models based on support vector machines are theoretically superior to models that rely on simulating pseudo-absence data and are comparable in empirical tests. 4. Synthesis and applications. Accurate species distribution models are crucial for effective environmental planning, management and conservation, and for unravelling the role of the environment in human health and welfare. Models based on distribution estimation rather than classification overcome theoretical and practical obstacles that pervade species distribution modelling. In particular, ecological niche models based on machine-learning algorithms for estimating the support of a statistical distribution provide a promising new approach to identifying species' potential distributions and to project changes in these distributions as a result of climate change, land use and landscape alteration.

Classification of very high spatial resolution imagery using mathematical morphology and support vector machines

We investigate the relevance of morphological operators for the classification of land use in urban scenes using submetric panchromatic imagery. A support vector machine is used for the classification. Six types of filters have been employed: opening and closing, opening and closing by reconstruction, and opening and closing top hat. The type and scale of the filters are discussed, and a feature selection algorithm called recursive feature elimination is applied to decrease the dimensionality of the input data. The analysis performed on two QuickBird panchromatic images showed that simple opening and closing operators are the most relevant for classification at such a high spatial resolution. Moreover, mixed sets combining simple and reconstruction filters provided the best performance. Tests performed on both images, having areas characterized by different architectural styles, yielded similar results for both feature selection and classification accuracy, suggesting the generalization of the feature sets highlighted.

Support vector machines in spectral data classification

Työssä käydään läpi tukivektorikoneiden teoreettista pohjaa sekä tutkitaan eri parametrien vaikutusta spektridatan luokitteluun.

Non invasive classification system of scoliosis curve types using least-squares support vector machines

Objective To determine scoliosis curve types using non invasive surface acquisition, without prior knowledge from X-ray data. Methods Classification of scoliosis deformities according to curve type is used in the clinical management of scoliotic patients. In this work, we propose a robust system that can determine the scoliosis curve type from non invasive acquisition of the 3D back surface of the patients. The 3D image of the surface of the trunk is divided into patches and local geometric descriptors characterizing the back surface are computed from each patch and constitute the features. We reduce the dimensionality by using principal component analysis and retain 53 components using an overlap criterion combined with the total variance in the observed variables. In this work, a multi-class classifier is built with least-squares support vector machines (LS-SVM). The original LS-SVM formulation was modified by weighting the positive and negative samples differently and a new kernel was designed in order to achieve a robust classifier. The proposed system is validated using data from 165 patients with different scoliosis curve types. The results of our non invasive classification were compared with those obtained by an expert using X-ray images. Results The average rate of successful classification was computed using a leave-one-out cross-validation procedure. The overall accuracy of the system was 95%. As for the correct classification rates per class, we obtained 96%, 84% and 97% for the thoracic, double major and lumbar/thoracolumbar curve types, respectively. Conclusion This study shows that it is possible to find a relationship between the internal deformity and the back surface deformity in scoliosis with machine learning methods. The proposed system uses non invasive surface acquisition, which is safe for the patient as it involves no radiation. Also, the design of a specific kernel improved classification performance.

Comparing Support Vector Machines with Gaussian Kernels to Radial Basis Function Classifiers

The Support Vector (SV) machine is a novel type of learning machine, based on statistical learning theory, which contains polynomial classifiers, neural networks, and radial basis function (RBF) networks as special cases. In the RBF case, the SV algorithm automatically determines centers, weights and threshold such as to minimize an upper bound on the expected test error. The present study is devoted to an experimental comparison of these machines with a classical approach, where the centers are determined by $k$--means clustering and the weights are found using error backpropagation. We consider three machines, namely a classical RBF machine, an SV machine with Gaussian kernel, and a hybrid system with the centers determined by the SV method and the weights trained by error backpropagation. Our results show that on the US postal service database of handwritten digits, the SV machine achieves the highest test accuracy, followed by the hybrid approach. The SV approach is thus not only theoretically well--founded, but also superior in a practical application.

Properties of Support Vector Machines

Support Vector Machines (SVMs) perform pattern recognition between two point classes by finding a decision surface determined by certain points of the training set, termed Support Vectors (SV). This surface, which in some feature space of possibly infinite dimension can be regarded as a hyperplane, is obtained from the solution of a problem of quadratic programming that depends on a regularization parameter. In this paper we study some mathematical properties of support vectors and show that the decision surface can be written as the sum of two orthogonal terms, the first depending only on the margin vectors (which are SVs lying on the margin), the second proportional to the regularization parameter. For almost all values of the parameter, this enables us to predict how the decision surface varies for small parameter changes. In the special but important case of feature space of finite dimension m, we also show that there are at most m+1 margin vectors and observe that m+1 SVs are usually sufficient to fully determine the decision surface. For relatively small m this latter result leads to a consistent reduction of the SV number.

Notes on PCA, Regularization, Sparsity and Support Vector Machines

We derive a new representation for a function as a linear combination of local correlation kernels at optimal sparse locations and discuss its relation to PCA, regularization, sparsity principles and Support Vector Machines. We first review previous results for the approximation of a function from discrete data (Girosi, 1998) in the context of Vapnik"s feature space and dual representation (Vapnik, 1995). We apply them to show 1) that a standard regularization functional with a stabilizer defined in terms of the correlation function induces a regression function in the span of the feature space of classical Principal Components and 2) that there exist a dual representations of the regression function in terms of a regularization network with a kernel equal to a generalized correlation function. We then describe the main observation of the paper: the dual representation in terms of the correlation function can be sparsified using the Support Vector Machines (Vapnik, 1982) technique and this operation is equivalent to sparsify a large dictionary of basis functions adapted to the task, using a variation of Basis Pursuit De-Noising (Chen, Donoho and Saunders, 1995; see also related work by Donahue and Geiger, 1994; Olshausen and Field, 1995; Lewicki and Sejnowski, 1998). In addition to extending the close relations between regularization, Support Vector Machines and sparsity, our work also illuminates and formalizes the LFA concept of Penev and Atick (1996). We discuss the relation between our results, which are about regression, and the different problem of pattern classification.

From Regression to Classification in Support Vector Machines

We study the relation between support vector machines (SVMs) for regression (SVMR) and SVM for classification (SVMC). We show that for a given SVMC solution there exists a SVMR solution which is equivalent for a certain choice of the parameters. In particular our result is that for $epsilon$ sufficiently close to one, the optimal hyperplane and threshold for the SVMC problem with regularization parameter C_c are equal to (1-epsilon)^{- 1} times the optimal hyperplane and threshold for SVMR with regularization parameter C_r = (1-epsilon)C_c. A direct consequence of this result is that SVMC can be seen as a special case of SVMR.

A Unified Framework for Regularization Networks and Support Vector Machines

Regularization Networks and Support Vector Machines are techniques for solving certain problems of learning from examples -- in particular the regression problem of approximating a multivariate function from sparse data. We present both formulations in a unified framework, namely in the context of Vapnik's theory of statistical learning which provides a general foundation for the learning problem, combining functional analysis and statistics.

An Equivalence Between Sparse Approximation and Support Vector Machines

In the first part of this paper we show a similarity between the principle of Structural Risk Minimization Principle (SRM) (Vapnik, 1982) and the idea of Sparse Approximation, as defined in (Chen, Donoho and Saunders, 1995) and Olshausen and Field (1996). Then we focus on two specific (approximate) implementations of SRM and Sparse Approximation, which have been used to solve the problem of function approximation. For SRM we consider the Support Vector Machine technique proposed by V. Vapnik and his team at AT&T Bell Labs, and for Sparse Approximation we consider a modification of the Basis Pursuit De-Noising algorithm proposed by Chen, Donoho and Saunders (1995). We show that, under certain conditions, these two techniques are equivalent: they give the same solution and they require the solution of the same quadratic programming problem.