ﻻ يوجد ملخص باللغة العربية
In this paper we solve support vector machines in reproducing kernel Banach spaces with reproducing kernels defined on nonsymmetric domains instead of the traditional methods in reproducing kernel Hilbert spaces. Using the orthogonality of semi-inner-products, we can obtain the explicit representations of the dual (normalized-duality-mapping) elements of support vector machine solutions. In addition, we can introduce the reproduction property in a generalized native space by Fourier transform techniques such that it becomes a reproducing kernel Banach space, which can be even embedded into Sobolev spaces, and its reproducing kernel is set up by the related positive definite function. The representations of the optimal solutions of support vector machines (regularized empirical risks) in these reproducing kernel Banach spaces are formulated explicitly in terms of positive definite functions, and their finite numbers of coefficients can be computed by fixed point iteration. We also give some typical examples of reproducing kernel Banach spaces induced by Matern functions (Sobolev splines) so that their support vector machine solutions are well computable as the classical algorithms. Moreover, each of their reproducing bases includes information from multiple training data points. The concept of reproducing kernel Banach spaces offers us a new numerical tool for solving support vector machines.
We present necessary and sufficient conditions to hold true a Kramer type sampling theorem over semi-inner product reproducing kernel Banach spaces. Under some sampling-type hypotheses over a sequence of functions on these Banach spaces it results ne
We provide the first mathematically complete derivation of the Nystrom method for low-rank approximation of indefinite kernels and propose an efficient method for finding an approximate eigendecomposition of such kernel matrices. Building on this res
Sparse classifiers such as the support vector machines (SVM) are efficient in test-phases because the classifier is characterized only by a subset of the samples called support vectors (SVs), and the rest of the samples (non SVs) have no influence on
Many problems that appear in biomedical decision making, such as diagnosing disease and predicting response to treatment, can be expressed as binary classification problems. The costs of false positives and false negatives vary across application dom
A widely-used tool for binary classification is the Support Vector Machine (SVM), a supervised learning technique that finds the maximum margin linear separator between the two classes. While SVMs have been well studied in the batch (offline) setting