We present an approach for learning an anisotropic RBF kernel in a game theoretical setting where the value of the game is the degree of separation between positive and negative training examples. The method extends a previously proposed method (KOMD) to perform feature re-weighting and distance metric learning in a kernel-based classification setting. Experiments on several benchmark datasets ...

We determine the asymptotic behaviour 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 h...

The image-based plant identification challenge was focused on tree, herbs and ferns species identification based on different types of images. The aim of the task was to produce relevant species for each observation of a plant of the test dataset. We have elaborated a viewpoints combined classification method for this challenge. We have applied dense SIFT for feature detection and description; ...

Dynamic mode decomposition (DMD) has become synonymous with the Koopman operator, where continuous time dynamics are discretized and examined using (i.e. composition) operators. Using newly introduced “occupation kernels,” present manuscript develops an approach to DMD that treats directly through Liouville operator. This outlines technical theoretical differences between Koopman-based for disc...

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 ...

In the classical Gaussian SVM classification we use the feature space projection transforming points to normal distributions with fixed covariance matrices (identity in the standard RBF and the covariance of the whole dataset in Mahalanobis RBF). In this paper we add additional information to Gaussian SVM by considering local geometry-dependent feature space projection. We emphasize that our ap...

As the support vector (SV) number of a support vector machine (SVM) determines the execution speed of the testing phase, there have been diverse methods to reduce it. Although iterative preimage addition (IPA), belonging to the ‘reduced set construction’, is reported to be able to reduce a large portion of the SV number of a standard SVM when the kernel is a radial basis function (RBF), the fac...