Kernels between ensembles (or a collection of entities) have recently attracted growing interests in the literature on machine learning . In this paper, we focus on the ‘ensemble’ that is defined as a collection of vectors. One natural way to interpret such an ensemble is through the notion of matrix. We present two basic reproducing kernels between matrices: namely trace and determinant kernel...

We propose a novel variant of conjugate gradient based on the Reproducing Kernel Hilbert Space (RKHS) inner product. An analysis of the algorithm suggests it enjoys better performance properties than standard iterative methods when applied to learning kernel machines. Experimental results for both classification and regression bear out the theoretical implications. We further address the domina...

Object classification according to their shape and size is of key importance in many scientific fields. This work focuses on the case where the size and shape of an object is characterized by a current. A current is a mathematical object which has been proved relevant to the modeling of geometrical data, like submanifolds, through integration of vector fields along them. As a consequence of the...

The aim of this paper is to present a unified framework in the setting Hilbert $$C^*$$ -modules for scalar- and vector-valued reproducing kernel spaces -valued spaces. We investigate conditionally negative definite kernels with values -algebra adjointable operators acting on -module. In addition, we show that there exists two-sided connection between positive -modules. Furthermore, explore some...

A mean function in a reproducing kernel Hilbert space (RKHS), or a kernel mean, is an important part of many algorithms ranging from kernel principal component analysis to Hilbert-space embedding of distributions. Given a finite sample, an empirical average is the standard estimate for the true kernel mean. We show that this estimator can be improved due to a well-known phenomenon in statistics...

It is a well known fact that transfer functions of scattering conservative systems and impedance conservative system are the analytic contractive function in the unit disk and functions with positive real part on the upper half plane, respectively. In this case, the interplay between the transfer functions is via the Moebius transformation. In the system representation the interplay is by the s...

We give two new global and algorithmic constructions of the reproducing kernel Hilbert space associated to a positive definite kernel. further present general setting using bilinear forms, we provide examples. Our results cover case measurable kernels, applications both stochastic analysis metric geometry number