We investigate a series of learning kernel problems with polynomial combinations of base kernels, which will help us solve regression and classification problems. We also perform some numerical experiments of polynomial kernels with regression and classification tasks on different datasets.

Kernel approximation using random feature maps has recently gained a lot of interest. This is mainly due to their applications in reducing training and testing times of kernel based learning algorithms. In this work, we identify that previous approaches for polynomial kernel approximation create maps that can be rank deficient, and therefore may not utilize the capacity of the projected feature...

Click-evoked otoacoustic emissions (CEOAEs) and acoustical responses evoked by bandlimited Gaussian noise (noise-evoked otoacoustic emissions; NEOAEs) were measured in three normal-hearing subjects. For the NEOAEs the first- and second-order Wiener kernel and polynomial correlation functions up to the sixth order were calculated by cross correlating the noise stimulus and the emission response....

Support vector machine (SVM) was the first proposed kernel-based method. It uses a kernel function to transform data from input space into a high-dimensional feature space in which it searches for a separating hyperplane. SVM aims to maximise the generalisation ability that depends on the empirical risk and the complexity of the machine. SVM has been widely adopted in real-world applications in...

Face recognition techniques have gained much attention and research interests over the recent years due to their vast applications in security and authentication systems. Some of the popular approaches involve support vector machines (SVM), which can either be a binary or a multiclass classification problem, and subspace learning, where data is assumed to lie on some low dimensional manifold, s...

1 ENS Ca han, 61, avenue du Président Wilson, 94235 Ca han edex Fran e E-mail address: nbousque dptinfo.ensa han.fr 2 Université Montpellier II CNRS, LIRMM, 161 rue Ada 34392 Montpellier Cedex 5 Fran e E-mail address: daligault lirmm.fr E-mail address: thomasse lirmm.fr 3 Royal Holloway, University of London, Egham Hill, EGHAM, TW20 0EX UK E-mail address: anders s.rhul.a .uk Abstra t. The MULTI...

Sketching is a powerful dimensionality reduction tool for accelerating statistical learning algorithms. However, its applicability has been limited to a certain extent since the crucial ingredient, the so-called oblivious subspace embedding, can only be applied to data spaces with an explicit representation as the column span or row span of a matrix, while in many settings learning is done in a...

An H-free editing problem asks whether we can edit at most k edges to make a graph contain no induced copy of the fixed graph H. We obtain a polynomial kernel for this problem when H is a diamond. The incompressibility dichotomy for H being a 3-connected graph [4] and the classical complexity dichotomy [1] suggest that except for H being a complete/empty graph, Hfree editing problems admit poly...

We propose a new method which enables the training of a kernelized structured output model. The structured output learning can flexibly represent a problem, and thus is gaining popularity in natural language processing. Meanwhile the polynomial kernel method is effective in many natural language processing tasks, since it takes into account the combination of features. However, it is computatio...