Support vector machines (SVMs) are the most well known nonlinear classifiers based on the Mercer kernel trick. They generally leads to very sparse solutions that ensure good generalization performance. Recently Mika et al. have proposed a new nonlinear technique based on the kernel trick and the Fisher criterion: the nonlinear kernel Fisher discriminant (KFD). Experiments show that KFD is compe...

The Kernel Principal Component Analysis (KPCA) has been effectively applied as an unsupervised non-linear feature extractor in many machine learning applications. However, with a time complexity of O(n3), the practicality of KPCA on large datasets is minimal. In this paper, we propose an approximate incremental KPCA algorithm which allows efficient processing of large datasets. We extend a line...

The kernel trick is a well known approach allowing to implicitly cast a linear method into a nonlinear one by replacing any dot product by a kernel function. However few vector quantization algorithms have been kernelized. Indeed, they usually imply to compute linear transformations (e.g. moving prototypes), what is not easily kernelizable. This paper introduces the Kernel-based Vector Quantiza...

The kernel trick is a well known approach allowing to implicitly cast a linear method into a nonlinear one by replacing any dot product by a kernel function. However few vector quantization algorithms have been kernelized. Indeed, they usually imply to compute linear transformations (e.g., moving prototypes), what is not easily kernelizable. This paper introduces the Kernel-based Vector Quantiz...

This brief note views to the Welch bound inequality using the idea of the kernel trick from the machine learning research area. From this angle, some novel insights of the inequality are obtained.

Pairwise learning corresponds to the supervised setting where goal is make predictions for pairs of objects. Prominent applications include predicting drug-target or protein-protein interactions, customer-product preferences. In this work, we present a comprehensive review pairwise kernels, that have been proposed incorporating prior knowledge about relationship between Specifically, consider s...

We employ so-called quantum kernel estimation to exploit complex dynamics of solid-state nuclear magnetic resonance for machine learning. propose map an input a feature space by input-dependent Hamiltonian evolution, and the is estimated interference evolution. Simple learning tasks, namely one-dimensional regression tasks two-dimensional classification are performed using proton spins which ex...

Kernel methods such as the support vector machine are one of the most successful algorithms in modern machine learning. Their advantage is that linear algorithms are extended to non-linear scenarios in a straightforward way by the use of the kernel trick. However, naive use of kernel methods is computationally expensive since the computational complexity typically scales cubically with respect ...

We consider the question of predicting nonlinear time series. Kernel Dynamical Modeling (KDM), a new method based on kernels, is proposed as an extension to linear dynamical models. The kernel trick is used twice: first, to learn the parameters of the model, and second, to compute preimages of the time series predicted in the feature space by means of Support Vector Regression. Our model shows ...