The combination of the famed kernel trick and affine projection algorithms (APA) yields powerful nonlinear extensions, named collectively here KAPA. This paper is a follow-up study of the recently introduced kernel leastmean-square algorithm (KLMS). KAPA inherits the simplicity and online nature of KLMS while reducing its gradient noise, boosting performance. More interestingly, it provides a u...

The kernel method has become a useful trick and has been widely applied to various learning models to extend their nonlinear approximation and classification capabilities. Such extensions have also recently occurred to the Self-Organising Map (SOM). In this paper, two recently proposed kernel SOMs are reviewed, together with their link to an energy function. The Self-Organising Mixture Network ...

To efficiently deal with the face recognition problem, a novel face recognition algorithm based on enhancing kernel maximum margin projection(MMP) is proposed in this paper. The main contributions of this work are as follows. First, the nonlinear extension of MMP through kernel trick is adopted to capture the nonlinear structure of face images. Second, the kernel deformation technique is propos...

Neural networks have recently re-emerged as a powerful hypothesis class, yielding impressive empirical performance in multiple domains. However, their training is a non-convex optimization problem which poses exciting theoretical and practical challenges. Here we argue that by extending the class of neural nets, one can obtain a convex learning problem, whose practical solution relies on the ev...

Gaussian Mixture Model (GMM) is an efficient method for parametric clustering. However, traditional GMM can’t perform clustering well on data set with complex structure such as images. In this paper, kernel trick, successfully used by SVM and kernel PCA, is introduced into EM algorithm for solving parameter estimation of GMM, which is so called kernel GMM (kGMM). The basic idea of kernel GMM is...

In this work, we address the problem of protein-protein interaction network inference as a semi-supervised output kernel learning problem. Using the kernel trick in the output space allows one to reduce the problem of learning from pairs to learning a single variable function with values in a Hilbert space. We turn to the Reproducing Kernel Hilbert Space theory devoted to vectorvalued functions...

The “kernel trick” is well established as a means of constructing nonlinear algorithms from linear ones, by transferring the linear algorithms to a high dimensional feature space: specifically, a reproducing kernel Hilbert space (RKHS). Recently, it has become clear that a potentially more far reaching use of kernels is as a linear way of dealing with higher order statistics, by embedding proba...

This paper presents a robust matrix elastic net based canonical correlation analysis (RMEN-CCA) for multiple view unsupervised learning problems, which emphasizes the combination of CCA and the robust matrix elastic net (RMEN) used as coupled feature selection. The RMEN-CCA leverages the strength of the RMEN to distill naturally meaningful features without any prior assumption and to measure ef...

Kernels are now everywhere present in statistics as far as a dot product is at hand. However to the best of our knowledge kernels have not been used in mixture models. In the present work we show that they can be useful for classification purposes. They offer a flexibility in the modeling process through the kernel trick which enables capturing interesting features in some cases more easily tha...