Search results for "Kernel embedding of distributions"
showing 8 items of 18 documents
Learning non-linear time-scales with kernel -filters
2009
A family of kernel methods, based on the @c-filter structure, is presented for non-linear system identification and time series prediction. The kernel trick allows us to develop the natural non-linear extension of the (linear) support vector machine (SVM) @c-filter [G. Camps-Valls, M. Martinez-Ramon, J.L. Rojo-Alvarez, E. Soria-Olivas, Robust @c-filter using support vector machines, Neurocomput. J. 62(12) (2004) 493-499.], but this approach yields a rigid system model without non-linear cross relation between time-scales. Several functional analysis properties allow us to develop a full, principled family of kernel @c-filters. The improved performance in several application examples suggest…
Spectral density estimation for stationary stable random fields
1995
International audience
Spectral clustering with the probabilistic cluster kernel
2015
Abstract This letter introduces a probabilistic cluster kernel for data clustering. The proposed kernel is computed with the composition of dot products between the posterior probabilities obtained via GMM clustering. The kernel is directly learned from the data, is parameter-free, and captures the data manifold structure at different scales. The projections in the kernel space induced by this kernel are useful for general feature extraction purposes and are here exploited in spectral clustering with the canonical k-means. The kernel structure, informative content and optimality are studied. Analysis and performance are illustrated in several real datasets.
Fuzzy sigmoid kernel for support vector classifiers
2004
This Letter proposes the use of the fuzzy sigmoid function presented in (IEEE Trans. Neural Networks 14(6) (2003) 1576) as non-positive semi-definite kernel in the support vector machines framework. The fuzzy sigmoid kernel allows lower computational cost, and higher rate of positive eigenvalues of the kernel matrix, which alleviates current limitations of the sigmoid kernel.
Feature extraction from remote sensing data using Kernel Orthonormalized PLS
2007
This paper presents the study of a sparse kernel-based method for non-linear feature extraction in the context of remote sensing classification and regression problems. The so-called kernel orthonormalized PLS algorithm with reduced complexity (rKOPLS) has two core parts: (i) a kernel version of OPLS (called KOPLS), and (ii) a sparse (reduced) approximation for large scale data sets, which ultimately leads to rKOPLS. The method demonstrates good capabilities in terms of expressive power of the extracted features and scalability.
Semisupervised Kernel Feature Extraction for Remote Sensing Image Analysis
2014
This paper presents a novel semisupervised kernel partial least squares (KPLS) algorithm for nonlinear feature extraction to tackle both land-cover classification and biophysical parameter retrieval problems. The proposed method finds projections of the original input data that align with the target variable (labels) and incorporates the wealth of unlabeled information to deal with low-sized or underrepresented data sets. The method relies on combining two kernel functions: the standard radial-basis-function kernel based on labeled information and a generative, i.e., probabilistic, kernel directly learned by clustering the data many times and at different scales across the data manifold. Th…
A family of kernel anomaly change detectors
2014
This paper introduces the nonlinear extension of the anomaly change detection algorithms in [1] based on the theory of reproducing kernels. The presented methods generalize their linear counterparts, under both the Gaussian and elliptically-contoured assumptions, and produce both improved detection accuracies and reduced false alarm rates. We study the Gaussianity of the data in Hilbert spaces with kernel dependence estimates, provide low-rank kernel versions to cope with the high computational cost of the methods, and give prescriptions about the selection of the kernel functions and their parameters. We illustrate the performance of the introduced kernel methods in both pervasive and anom…
Semi-Supervised Remote Sensing Image Classification based on Clustering and the Mean Map Kernel
2008
This paper presents a semi-supervised classifier based on the combination of the expectation-maximization (EM) algorithm for Gaussian mixture models (GMM) and the mean map kernel. The proposed method uses the most reliable samples in terms of maximum likelihood to compute a kernel function that accurately reflects the similarity between clusters in the kernel space. The proposed method improves classification accuracy in situations where the available labeled information does not properly describe the classes in the test image.