Related papers: Diverse Landmark Sampling from Determinantal Point…

Kernel methods have achieved very good performance on large scale regression and classification problems, by using the Nystr\"om method and preconditioning techniques. The Nystr\"om approximation -- based on a subset of landmarks -- gives a…

Selecting diverse and important items, called landmarks, from a large set is a problem of interest in machine learning. As a specific example, in order to deal with large training sets, kernel methods often rely on low rank matrix Nystr\"om…

The Nystr\"om method has long been popular for scaling up kernel methods. Its theoretical guarantees and empirical performance rely critically on the quality of the landmarks selected. We study landmark selection for Nystr\"om using…

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…

Scalable kernel methods, including kernel ridge regression, often rely on low-rank matrix approximations using the Nystrom method, which involves selecting landmark points from large data sets. The existing approaches to selecting landmarks…

The Nystrom method has been popular for generating the low-rank approximation of kernel matrices that arise in many machine learning problems. The approximation quality of the Nystrom method depends crucially on the number of selected…

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…

We study the problem of determining the configuration of $n$ points by using their distances to $m$ nodes, referred to as anchor nodes. One sampling scheme is Nystrom sampling, which assumes known distances between the anchors and between…

A Point Distribution Model (PDM) is the basis of a Statistical Shape Model (SSM) that relies on a set of landmark points to represent a shape and characterize the shape variation. In this work, we present a self-supervised approach to…

Subspace clustering methods based on expressing each data point as a linear combination of all other points in a dataset are popular unsupervised learning techniques. However, existing methods incur high computational complexity on…

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…

We adapt a manifold sampling algorithm for the nonsmooth, nonconvex formulations of learning that arise when imposing robustness to outliers present in the training data. We demonstrate the approach on objectives based on trimmed loss.…

This paper addresses the problem of estimating the positions of points from distance measurements corrupted by sparse outliers. Specifically, we consider a setting with two types of nodes: anchor nodes, for which exact distances to each…

As a pivotal branch of machine learning, manifold learning uncovers the intrinsic low-dimensional structure within complex nonlinear manifolds in high-dimensional space for visualization, classification, clustering, and gaining key…

Many applications in machine learning or signal processing involve nonsmooth optimization problems. This nonsmoothness brings a low-dimensional structure to the optimal solutions. In this paper, we propose a randomized proximal gradient…

Sampling from very large spatial populations is challenging. The solutions suggested in recent literature on this subject often require that the randomly selected units are well distributed across the study region by using complex…

Although significant progress achieved, multi-label classification is still challenging due to the complexity of correlations among different labels. Furthermore, modeling the relationships between input and some (dull) classes further…

A strategy to assist visualization and analysis of large and complex data sets is dimensionality reduction, with which one maps each data point into a low-dimensional manifold. However, various dimensionality reduction techniques are…

Analyzing high-dimensional data with manifold learning algorithms often requires searching for the nearest neighbors of all observations. This presents a computational bottleneck in statistical manifold learning when observations of…

In the setting of nonparametric regression, we propose and study a combination of stochastic gradient methods with Nystr\"om subsampling, allowing multiple passes over the data and mini-batches. Generalization error bounds for the studied…