AbstractThis paper describes an experiment on face recognition using a simple feature vector and Support Vector Machine (SVM) classifier. Polynomial and Radial Basis Function (RBF) kernels of SVM are used for classification. The dataset in this experiment consists of a set of images of eight different faces (eight classes) containing ten different images for a single class. The experiment is pe...

We consider the model selection problem for support vector machines applied to binary classification. As the data generating process is unknown, we have to rely on heuristics as model section criteria. In this study, we analyze the behavior of two criteria, radius margin quotient and kernel polarization, applied to SVMs with radial Gaussian kernel. We proof necessary and sufficient conditions f...

Maximum Mean Discrepancy (MMD) is a distance on the space of probability measures which has found numerous applications in machine learning and nonparametric testing. This distance is based on the notion of embedding probabilities in a reproducing kernel Hilbert space. In this paper, we present the first known lower bounds for the estimation of MMD based on finite samples. Our lower bounds hold...

We study the heat semigroup generated by two-dimensional Schrödinger operators with compactly supported magnetic field. We show that if the field is radial, then the large time behavior of the associated heat kernel is determined by its total flux. We also establish some on-diagonal heat kernel estimates and discuss their applications for solutions to the heat equation. An exact formula for the...

To accelerate the training of kernel machines, we propose to map the input data to a randomized low-dimensional feature space and then apply existing fast linear methods. The features are designed so that the inner products of the transformed data are approximately equal to those in the feature space of a user specified shiftinvariant kernel. We explore two sets of random features, provide conv...

-In this paper, we introduce a new classification kernel by embedding self organized map (SOM) clustering with mixture of radial basis function (RBF) networks. The model’s efficacy is demonstrated in solving a multi-class TIMIT speech recognition problem where the kernel is used to learn the multidimensional cepstral feature vectors to estimate their posterior class probabilities. The tests res...

We propose the “generalized min-max” (GMM) kernel as a measure of data similarity, where data vectors can have both positive and negative entries. GMM is positive definite as there is an associate hashing method named “generalized consistent weighted sampling” (GCWS) which linearizes this (nonlinear) kernel. A natural competitor of GMM is the radial basis function (RBF) kernel, whose correspond...

In this paper, we use Radial Basis Function Networks (RBFN) for solving the problem of environmental interference cancellation of speech signal. We show that the Second Order ThinPlate Spline (SOTPS) kernel cancels the interferences effectively. For make comparison, we test our experiments on two conventional most used RBFN kernels: the Gaussian and First order TPS (FOTPS) basis functions. The ...

Kernel-based methods and ensemble learning are two important paradigms for the classification of hyperspectral remote sensing images. However, they were developed in parallel with different principles. In this paper, we aim to combine the advantages of kernel and ensemble methods by proposing a kernel supervised ensemble classification method. In particular, the proposed method, namely RoF-KOPL...

We determine the asymptotic limit of the function computed by support vector machines (SVM) and related algorithms that minimize a regularized empirical convex loss function in the reproducing kernel Hilbert space of the Gaussian RBF kernel, in the situation where the number of examples tends to infinity, the bandwidth of the Gaussian kernel tends to 0, and the regularization parameter is held ...