Related papers: Supervising Nystr\"om Methods via Negative Margin …
Kernel-based models such as kernel ridge regression and Gaussian processes are ubiquitous in machine learning applications for regression and optimization. It is well known that a major downside for kernel-based models is the high…
The Nystr\"om method is one of the most popular techniques for improving the scalability of kernel methods. However, it has not yet been derived for kernel PCA in line with classical PCA. In this paper we derive kernel PCA with the…
Use of nonlinear feature maps via kernel approximation has led to success in many online learning tasks. As a popular kernel approximation method, Nystr\"{o}m approximation, has been well investigated, and various landmark points selection…
The Nystrom method is a popular technique that uses a small number of landmark points to compute a fixed-rank approximation of large kernel matrices that arise in machine learning problems. In practice, to ensure high quality…
Kernel methods provide a principled approach to nonparametric learning. While their basic implementations scale poorly to large problems, recent advances showed that approximate solvers can efficiently handle massive datasets. A shortcoming…
This paper studies a Nystr\"om type subsampling approach to large kernel learning methods in the misspecified case, where the target function is not assumed to belong to the reproducing kernel Hilbert space generated by the underlying…
We propose a continuous optimization algorithm for the Column Subset Selection Problem (CSSP) and Nystr\"om approximation. The CSSP and Nystr\"om method construct low-rank approximations of matrices based on a predetermined subset of…
We study a relaxed version of the column-sampling problem for the Nystr\"om approximation of kernel matrices, where approximations are defined from multisets of landmark points in the ambient space; such multisets are referred to as…
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…
Kernel methods provide a theoretically grounded framework for non-linear and non-parametric learning, with strong analytic foundations and statistical guarantees. Yet, their scalability has long been limited by prohibitive time and memory…
We study the problem of column selection in large-scale kernel canonical correlation analysis (KCCA) using the Nystr\"om approximation, where one approximates two positive semi-definite kernel matrices using "landmark" points from the…
Support vector machine (SVM), is a popular kernel method for data classification that demonstrated its efficiency for a large range of practical applications. The method suffers, however, from some weaknesses including; time processing,…
We provide the first mathematically complete derivation of the Nystr\"om method for low-rank approximation of indefinite kernels and propose an efficient method for finding an approximate eigendecomposition of such kernel matrices. Building…
Kernel mean embeddings are a powerful tool to represent probability distributions over arbitrary spaces as single points in a Hilbert space. Yet, the cost of computing and storing such embeddings prohibits their direct use in large-scale…
Subgradient algorithms for training support vector machines have been quite successful for solving large-scale and online learning problems. However, they have been restricted to linear kernels and strongly convex formulations. This paper…
We investigate an extension of classical empirical risk minimization, where the hypothesis space consists of a random subspace within a given Hilbert space. Specifically, we examine the Nystr\"om method where the subspaces are defined by a…
Kernel methods are powerful tools in various data analysis tasks. Yet, in many cases, their time and space complexity render them impractical for large datasets. Various kernel approximation methods were proposed to overcome this issue,…
We consider the problem of metric learning for multi-view data and present a novel method for learning within-view as well as between-view metrics in vector-valued kernel spaces, as a way to capture multi-modal structure of the data. We…
In recent years, the spectral analysis of appropriately defined kernel matrices has emerged as a principled way to extract the low-dimensional structure often prevalent in high-dimensional data. Here we provide an introduction to spectral…
Kernel-based methods for support vector machines (SVM) have shown highly advantageous performance in various applications. However, they may incur prohibitive computational costs for large-scale sample datasets. Therefore, data reduction…