Related papers: Numerical Methods for Kernel Slicing
Kernel $k$-means clustering is a powerful tool for unsupervised learning of non-linearly separable data. Since the earliest attempts, researchers have noted that such algorithms often become trapped by local minima arising from…
Kernel methods have great promise for learning rich statistical representations of large modern datasets. However, compared to neural networks, kernel methods have been perceived as lacking in scalability and flexibility. We introduce a…
Kernel methods are fundamental tools in machine learning that allow detection of non-linear dependencies between data without explicitly constructing feature vectors in high dimensional spaces. A major disadvantage of kernel methods is…
Machine learning applied to computer vision and signal processing is achieving results comparable to the human brain on specific tasks due to the great improvements brought by the deep neural networks (DNN). The majority of state-of-the-art…
The use of kernel functions is a common technique to extract important features from data sets. A quantum computer can be used to estimate kernel entries as transition amplitudes of unitary circuits. Quantum kernels exist that, subject to…
The use of covariance kernels is ubiquitous in the field of spatial statistics. Kernels allow data to be mapped into high-dimensional feature spaces and can thus extend simple linear additive methods to nonlinear methods with higher order…
Support vector machines and kernel methods have recently gained considerable attention in chemoinformatics. They offer generally good performance for problems of supervised classification or regression, and provide a flexible and…
Spectral kernel methods are techniques for transforming data into a coordinate system that efficiently reveals the geometric structure - in particular, the "connectivity" - of the data. These methods depend on certain tuning parameters. We…
Kernel methods provide an elegant and principled approach to nonparametric learning, but so far could hardly be used in large scale problems, since na\"ive implementations scale poorly with data size. Recent advances have shown the benefits…
We present a geometric formulation of the Multiple Kernel Learning (MKL) problem. To do so, we reinterpret the problem of learning kernel weights as searching for a kernel that maximizes the minimum (kernel) distance between two convex…
Kernel machines have sustained continuous progress in the field of quantum chemistry. In particular, they have proven to be successful in the low-data regime of force field reconstruction. This is because many equivariances and invariances…
Quantum kernel methods, i.e., kernel methods with quantum kernels, offer distinct advantages as a hybrid quantum-classical approach to quantum machine learning (QML), including applicability to Noisy Intermediate-Scale Quantum (NISQ)…
We introduce a new numerical method for the computation of the inverse nonlinear Fourier transform and compare its computational complexity and accuracy to those of other methods available in the literature. For a given accuracy, the…
Support Vector Machines (SVMs) with various kernels have played dominant role in machine learning for many years, finding numerous applications. Although they have many attractive features interpretation of their solutions is quite…
The least-squares support vector machine is a frequently used kernel method for non-linear regression and classification tasks. Here we discuss several approximation algorithms for the least-squares support vector machine classifier. The…
We consider a particular approach to the regularization of the inverse problem of computerized tomography. This approach is based on notions pertaining to Fourier synthesis. It refines previous contributions, in which the preprocessing of…
The computational complexity of kernel methods has often been a major barrier for applying them to large-scale learning problems. We argue that this barrier can be effectively overcome. In particular, we develop methods to scale up kernel…
We present a new framework for online Least Squares algorithms for nonlinear modeling in RKH spaces (RKHS). Instead of implicitly mapping the data to a RKHS (e.g., kernel trick), we map the data to a finite dimensional Euclidean space,…
Kernel methods play an important role in machine learning applications due to their conceptual simplicity and superior performance on numerous machine learning tasks. Expressivity of a machine learning model, referring to the ability of the…
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…