Related papers: Sufficient Dimension Reduction via Random-Partitio…

Based on the theory of reproducing kernel Hilbert space (RKHS) and semiparametric method, we propose a new approach to nonlinear dimension reduction. The method extends the semiparametric method into a more generalized domain where both the…

In this paper, practically computable low-order approximations of potentially high-dimensional differential equations driven by geometric rough paths are proposed and investigated. In particular, equations are studied that cover the linear…

Kernel dimensionality reduction (KDR) algorithms find a low dimensional representation of the original data by optimizing kernel dependency measures that are capable of capturing nonlinear relationships. The standard strategy is to first…

This paper presents a novel adaptive-sparse polynomial dimensional decomposition (PDD) method for stochastic design optimization of complex systems. The method entails an adaptive-sparse PDD approximation of a high-dimensional stochastic…

Most of the existing methods for estimating the local intrinsic dimension of a data distribution do not scale well to high-dimensional data. Many of them rely on a non-parametric nearest neighbors approach which suffers from the curse of…

Most dimensionality reduction methods employ frequency domain representations obtained from matrix diagonalization and may not be efficient for large datasets with relatively high intrinsic dimensions. To address this challenge, Correlated…

Ridge regression is an indispensable tool in big data analysis. Yet its inherent bias poses a significant and longstanding challenge, compromising both statistical efficiency and scalability across various applications. To tackle this…

We first show that the commonly used dimensionality reduction (DR) methods such as t-SNE and LargeVis poorly capture the global structure of the data in the low dimensional embedding. We show this via a number of tests for the DR methods…

We introduce and develop a novel approach to outlier detection based on adaptation of random subspace learning. Our proposed method handles both high-dimension low-sample size and traditional low-dimensional high-sample size datasets.…

In an era where big and high-dimensional data is readily available, data scientists are inevitably faced with the challenge of reducing this data for expensive downstream computation or analysis. To this end, we present here a new method…

High-resolution radar range profile (RRP) is crucial for accurate target recognition and scene perception. To get a high-resolution RRP, many methods have been developed, such as multiple signal classification (MUSIC), orthogonal matching…

The covariate shift is a challenging problem in supervised learning that results from the discrepancy between the training and test distributions. An effective approach which recently drew a considerable attention in the research community…

Recently, Su and Cook proposed a dimension reduction technique called the inner envelope which can be substantially more efficient than the original envelope or existing dimension reduction techniques for multivariate regression. However,…

Recently there is a line of research work proposing to employ Spectral Clustering (SC) to segment (group){Throughout the paper, we use segmentation, clustering, and grouping, and their verb forms, interchangeably.} high-dimensional…

This paper addresses the challenge of dimension reduction (DR) in Bayesian inference of high-resolution two-or three-dimensional fields, where a priori parametrizations require a large number of terms. The underlying idea is common to…

The monitoring and management of high-volume feature-rich traffic in large networks offers significant challenges in storage, transmission and computational costs. The predominant approach to reducing these costs is based on performing a…

Mirror descent (MD) is a powerful first-order optimization technique that subsumes several optimization algorithms including gradient descent (GD). In this work, we develop a semi-definite programming (SDP) framework to analyze the…

Scenario reduction (SR) alleviates the computational complexity of scenario-based stochastic optimization with conditional value-at-risk (SBSO-CVaR) by identifying representative scenarios to depict the underlying uncertainty and tail…

Subspace clustering refers to the problem of clustering unlabeled high-dimensional data points into a union of low-dimensional linear subspaces, whose number, orientations, and dimensions are all unknown. In practice one may have access to…

Semidefinite programming (SDP) is a powerful tool for tackling a wide range of computationally hard problems such as clustering. Despite the high accuracy, semidefinite programs are often too slow in practice with poor scalability on large…