Related papers: Alignment Based Kernel Learning with a Continuous …

Recent studies utilize multiple kernel learning to deal with incomplete-data problem. In this study, we introduce new methods that do not only complete multiple incomplete kernel matrices simultaneously, but also allow control of the…

When designing Convolutional Neural Networks (CNNs), one must select the size\break of the convolutional kernels before training. Recent works show CNNs benefit from different kernel sizes at different layers, but exploring all possible…

Kernel methods are of current interest in quantum machine learning due to similarities with quantum computing in how they process information in high-dimensional feature (Hilbert) spaces. Kernels are believed to offer particular advantages…

Kernel-based learning algorithms are widely used in machine learning for problems that make use of the similarity between object pairs. Such algorithms first embed all data points into an alternative space, where the inner product between…

Clustering samples according to an effective metric and/or vector space representation is a challenging unsupervised learning task with a wide spectrum of applications. Among several clustering algorithms, k-means and its kernelized version…

This survey is an introduction to positive definite kernels and the set of methods they have inspired in the machine learning literature, namely kernel methods. We first discuss some properties of positive definite kernels as well as…

Bursts of images exhibit significant self-similarity across both time and space. This motivates a representation of the kernels as linear combinations of a small set of basis elements. To this end, we introduce a novel basis prediction…

The use of kernels for nonlinear prediction is widespread in machine learning. They have been popularized in support vector machines and used in kernel ridge regression, amongst others. Kernel methods share three aspects. First, instead of…

Contrastive learning is an efficient approach to self-supervised representation learning. Although recent studies have made progress in the theoretical understanding of contrastive learning, the investigation of how to characterize the…

Recent advances in operator learning theory have improved our knowledge about learning maps between infinite dimensional spaces. However, for large-scale engineering problems such as concurrent multiscale simulation for mechanical…

Topological data analysis and its main method, persistent homology, provide a toolkit for computing topological information of high-dimensional and noisy data sets. Kernels for one-parameter persistent homology have been established to…

In this paper, we propose a multi-kernel classifier learning algorithm to optimize a given nonlinear and nonsmoonth multivariate classifier performance measure. Moreover, to solve the problem of kernel function selection and kernel…

Kernel methods are among the most popular techniques in machine learning. From a frequentist/discriminative perspective they play a central role in regularization theory as they provide a natural choice for the hypotheses space and the…

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…

Recent research on multiple kernel learning has lead to a number of approaches for combining kernels in regularized risk minimization. The proposed approaches include different formulations of objectives and varying regularization…

Empirical observation of high dimensional phenomena, such as the double descent behaviour, has attracted a lot of interest in understanding classical techniques such as kernel methods, and their implications to explain generalization…

Kernel methods are a cornerstone of classical machine learning. The idea of using quantum computers to compute kernels has recently attracted attention. Quantum embedding kernels (QEKs) constructed by embedding data into the Hilbert space…

We review machine learning methods employing positive definite kernels. These methods formulate learning and estimation problems in a reproducing kernel Hilbert space (RKHS) of functions defined on the data domain, expanded in terms of a…

Kernel-based methods enjoy powerful generalization capabilities in handling a variety of learning tasks. When such methods are provided with sufficient training data, broadly-applicable classes of nonlinear functions can be approximated…

Low-rank approximation of kernels is a fundamental mathematical problem with widespread algorithmic applications. Often the kernel is restricted to an algebraic variety, e.g., in problems involving sparse or low-rank data. We show that…