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Kernel ridge regression (KRR) is a standard method for performing non-parametric regression over reproducing kernel Hilbert spaces. Given $n$ samples, the time and space complexity of computing the KRR estimate scale as $\mathcal{O}(n^3)$…
These notes provide a self-contained introduction to kernel methods and their geometric foundations in machine learning. Starting from the construction of Hilbert spaces, we develop the theory of positive definite kernels, reproducing…
Kernel power $k$-means (KPKM) leverages a family of means to mitigate local minima issues in kernel $k$-means. However, KPKM faces two key limitations: (1) the computational burden of the full kernel matrix restricts its use on extensive…
Kernel-based machine learning algorithms are based on mapping data from the original input feature space to a kernel feature space of higher dimensionality to solve a linear problem in that space. Over the last decade, kernel based…
The paper introduces a new efficient nonlinear one-class classifier formulated as the Rayleigh quotient criterion optimisation. The method, operating in a reproducing kernel Hilbert space, minimises the scatter of target distribution along…
Random features is one of the most popular techniques to speed up kernel methods in large-scale problems. Related works have been recognized by the NeurIPS Test-of-Time award in 2017 and the ICML Best Paper Finalist in 2019. The body of…
Three-dimensional object recognition has recently achieved great progress thanks to the development of effective point cloud-based learning frameworks, such as PointNet and its extensions. However, existing methods rely heavily on fully…
Kernel methods are powerful tools to capture nonlinear patterns behind data. They implicitly learn high (even infinite) dimensional nonlinear features in the Reproducing Kernel Hilbert Space (RKHS) while making the computation tractable by…
A simple yet effective architectural design of radial basis function neural networks (RBFNN) makes them amongst the most popular conventional neural networks. The current generation of radial basis function neural network is equipped with…
The method of "random Fourier features (RFF)" has become a popular tool for approximating the "radial basis function (RBF)" kernel. The variance of RFF is actually large. Interestingly, the variance can be substantially reduced by a simple…
Kernel ridge regression (KRR) is a widely used nonparametric method due to its strong theoretical guarantees and computational convenience. However, standard KRR does not distinguish between linear and nonlinear components in the signal,…
Kernel methods are powerful learning methodologies that allow to perform non-linear data analysis. Despite their popularity, they suffer from poor scalability in big data scenarios. Various approximation methods, including random feature…
Understanding the spectral properties of kernels offers a principled perspective on generalization and representation quality. While deep models achieve state-of-the-art accuracy in molecular property prediction, kernel methods remain…
Graph kernels have become an established and widely-used technique for solving classification tasks on graphs. This survey gives a comprehensive overview of techniques for kernel-based graph classification developed in the past 15 years. We…
Approximating kernel functions with random features (RFs)has been a successful application of random projections for nonparametric estimation. However, performing random projections presents computational challenges for large-scale…
In this abstract paper, we introduce a new kernel learning method by a nonparametric density estimator. The estimator consists of a group of k-centroids clusterings. Each clustering randomly selects data points with randomly selected…
The classical kernel ridge regression problem aims to find the best fit for the output $Y$ as a function of the input data $X\in \mathbb{R}^d$, with a fixed choice of regularization term imposed by a given choice of a reproducing kernel…
Despite their many appealing properties, kernel methods are heavily affected by the curse of dimensionality. For instance, in the case of inner product kernels in $\mathbb{R}^d$, the Reproducing Kernel Hilbert Space (RKHS) norm is often…
Permutation-valued features arise in a variety of applications, either in a direct way when preferences are elicited over a collection of items, or an indirect way in which numerical ratings are converted to a ranking. To date, there has…
This paper introduces a novel approach for multi-task regression that connects Kernel Machines (KMs) and Extreme Learning Machines (ELMs) through the exploitation of the Random Fourier Features (RFFs) approximation of the RBF kernel. In…