Related papers: Kernel PCA with the Nystr\"om method

Kernel-based modal statistical methods include mode estimation, regression, and clustering. Estimation accuracy of these methods depends on the kernel used as well as the bandwidth. We study effect of the selection of the kernel function to…

It is well known that kernel ridge regression (KRR) is a popular nonparametric regression estimator. Nonetheless, in the presence of a large data set with size $n\gg 1,$ the KRR estimator has the drawback to require an intensive…

Principal Component Analysis (PCA) is a well-known linear dimension-reduction technique designed for Euclidean data. In a wide spectrum of applied fields, however, it is common to observe multivariate circular data (also known as toroidal…

Principal component regression (PCR) is a popular technique for fixed-design error-in-variables regression, a generalization of the linear regression setting in which the observed covariates are corrupted with random noise. We provide the…

Spectral clustering techniques are valuable tools in signal processing and machine learning for partitioning complex data sets. The effectiveness of spectral clustering stems from constructing a non-linear embedding based on creating a…

This paper develops a simple method to construct confidence bands, centered at a principal component analysis (PCA) based estimator, for the slope function in a functional linear regression model with a scalar response variable and a…

Classical methods such as Principal Component Analysis (PCA) and Canonical Correlation Analysis (CCA) are ubiquitous in statistics. However, these techniques are only able to reveal linear relationships in data. Although nonlinear variants…

Principal component analysis (PCA) is a widely employed statistical tool used primarily for dimensionality reduction. However, it is known to be adversely affected by the presence of outlying observations in the sample, which is quite…

The GMM (generalized min-max) kernel was recently proposed (Li, 2016) as a measure of data similarity and was demonstrated effective in machine learning tasks. In order to use the GMM kernel for large-scale datasets, the prior work resorted…

This paper introduces a kernel discrepancy-based framework for rerandomization to enhance the precision of causal inference in controlled experiments. We demonstrate that the kernel discrepancy is the key part of the variance upper bound…

Principal Component Analysis (PCA) is one of the most important unsupervised methods to handle high-dimensional data. However, due to the high computational complexity of its eigen decomposition solution, it hard to apply PCA to the…

We consider the problem of learning a mixture of Random Utility Models (RUMs). Despite the success of RUMs in various domains and the versatility of mixture RUMs to capture the heterogeneity in preferences, there has been only limited…

Covariance matrix estimation and principal component analysis (PCA) are two cornerstones of multivariate analysis. Classic textbook solutions perform poorly when the dimension of the data is of a magnitude similar to the sample size, or…

This paper introduces the Nystr\"om PCG algorithm for solving a symmetric positive-definite linear system. The algorithm applies the randomized Nystr\"om method to form a low-rank approximation of the matrix, which leads to an efficient…

Low-rank matrix decomposition has gained great popularity recently in scaling up kernel methods to large amounts of data. However, some limitations could prevent them from working effectively in certain domains. For example, many existing…

The Column Subset Selection Problem (CSSP) and the Nystr\"om method are among the leading tools for constructing small low-rank approximations of large datasets in machine learning and scientific computing. A fundamental question in this…

In this article, we introduce a kernel-based consensual aggregation method for regression problems. We aim to exibly combine individual regression estimators $r_1, \ldots, r_M$ using a weighted average where the weights are dened based on…

Kernel methods are powerful and flexible approach to solve many problems in machine learning. Due to the pairwise evaluations in kernel methods, the complexity of kernel computation grows as the data size increases; thus the applicability…

Principal component analysis (PCA) is recognised as a quintessential data analysis technique when it comes to describing linear relationships between the features of a dataset. However, the well-known sensitivity of PCA to non-Gaussian…

Dimensionality reduction is a fundamental technique in machine learning and data analysis, enabling efficient representation and visualization of high-dimensional data. This paper explores five key methods: Principal Component Analysis…