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We present a tutorial on reduced-rank signal processing, design methods and algorithms for dimensionality reduction, and cover a number of important applications. A general framework based on linear algebra and linear estimation is employed…

Information Theory · Computer Science 2015-08-05 Rodrigo C. de Lamare

In the past few years, augmented reality (AR) and virtual reality (VR) technologies have experienced terrific improvements in both accessibility and hardware capabilities, encouraging the application of these devices across various domains.…

Human-Computer Interaction · Computer Science 2019-10-29 Marco Cavallo , Mishal Dholakia , Matous Havlena , Kenneth Ocheltree , Mark Podlaseck

Immersive environments have gradually become standard for visualizing and analyzing large or complex datasets that would otherwise be cumbersome, if not impossible, to explore through smaller scale computing devices. However, this type of…

Human-Computer Interaction · Computer Science 2019-03-12 Marco Cavallo , Mishal Dholakia , Matous Havlena , Kenneth Ocheltree , Mark Podlaseck

Dimensionality Reduction (DR) techniques are commonly used for the visual exploration and analysis of high-dimensional data due to their ability to project datasets of high-dimensional points onto the 2D plane. However, projecting datasets…

Machine Learning · Computer Science 2025-11-19 Jaume Ros , Alessio Arleo , Fernando Paulovich

We explore linear and non-linear dimensionality reduction techniques for statistical inference of parameters in cosmology. Given the importance of compressing the increasingly complex data vectors used in cosmology, we address questions…

Cosmology and Nongalactic Astrophysics · Physics 2025-02-12 Minsu Park , Marco Gatti , Bhuvnesh Jain

Dimension reduction is often the first step in statistical modeling or prediction of multivariate spatial data. However, most existing dimension reduction techniques do not account for the spatial correlation between observations and do not…

Methodology · Statistics 2025-05-27 Si Cheng , Magali N. Blanco , Timothy V. Larson , Lianne Sheppard , Adam Szpiro , Ali Shojaie

In the past few decades, researchers have proposed many discriminant analysis (DA) algorithms for the study of high-dimensional data in a variety of problems. Most DA algorithms for feature extraction are based on transformations that…

Computer Vision and Pattern Recognition · Computer Science 2012-06-12 Ali Shadvar

Interactive lenses are useful tools for supporting the analysis of data in different ways. Most existing lenses are designed for 2D visualization and are operated using standard mouse and keyboard interaction. On the other hand, research on…

Graphics · Computer Science 2020-09-08 Sven Kluge , Stefan Gladisch , Uwe Freiherr von Lukas , Oliver Staadt , Christian Tominski

Real-world data usually have high dimensionality and it is important to mitigate the curse of dimensionality. High-dimensional data are usually in a coherent structure and make the data in relatively small true degrees of freedom. There are…

Machine Learning · Computer Science 2021-03-12 Xiang Wang , Xiaoyong Li , Junxing Zhu , Zichen Xu , Kaijun Ren , Weiming Zhang , Xinwang Liu , Kui Yu

Multidimensional scaling allows visualizing high-dimensional data as 2D maps with the premise that insights in 2D reveal valid information in high-dimensions. However, the resulting projections suffer from artifacts such as bad local…

Human-Computer Interaction · Computer Science 2017-05-16 Nicolas Heulot , Jean-Daniel Fekete , Michael Aupetit

Multivariate signal processing is often based on dimensionality reduction techniques. We propose a new method, Dynamical Component Analysis (DyCA), leading to a classification of the underlying dynamics and - for a certain type of dynamics…

Signal Processing · Electrical Eng. & Systems 2019-03-19 Bastian Seifert , Katharina Korn , Steffen Hartmann , Christian Uhl

High-dimensional datasets are increasingly common across scientific and industrial domains, yet they remain difficult to cluster effectively due to the diminishing usefulness of distance metrics and the tendency of clusters to collapse or…

Machine Learning · Computer Science 2026-01-28 Mohammad Zare

Draco has been developed as an automated visualization recommendation system formalizing design knowledge as logical constraints in ASP (Answer-Set Programming). With an increasing set of constraints and incorporated design knowledge, even…

Graphics · Computer Science 2023-07-25 Johanna Schmidt , Bernhard Pointner , Silvia Miksch

The goal of supervised representation learning is to construct effective data representations for prediction. Among all the characteristics of an ideal nonparametric representation of high-dimensional complex data, sufficiency, low…

Machine Learning · Computer Science 2022-09-02 Jian Huang , Yuling Jiao , Xu Liao , Jin Liu , Zhou Yu

Optimizing application performance in today's hardware architecture landscape is an important, but increasingly complex task, often requiring detailed performance analyses. In particular, data movement and reuse play a crucial role in…

Software Engineering · Computer Science 2023-06-29 Philipp Schaad , Tal Ben-Nun , Torsten Hoefler

Understanding how helpful a visualization is from experimental results is difficult because the observed performance is confounded with aspects of the study design, such as how useful the information that is visualized is for the task. We…

Human-Computer Interaction · Computer Science 2023-08-21 Yifan Wu , Ziyang Guo , Michails Mamakos , Jason Hartline , Jessica Hullman

Dimensionality reduction is an important operation in information visualization, feature extraction, clustering, regression, and classification, especially for processing noisy high dimensional data. However, most existing approaches…

Machine Learning · Computer Science 2020-03-26 Zhenhua Shi , Dongrui Wu , Jian Huang , Yu-Kai Wang , Chin-Teng Lin

Dimensionality-reduction methods are a fundamental tool in the analysis of large data sets. These algorithms work on the assumption that the "intrinsic dimension" of the data is generally much smaller than the ambient dimension in which it…

Machine Learning · Computer Science 2018-10-30 Henry Kvinge , Elin Farnell , Michael Kirby , Chris Peterson

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…

Machine Learning · Statistics 2022-06-10 Yuta Hozumi , Rui Wang , Guo-Wei Wei

Referring expression comprehension aims to locate the object instance described by a natural language referring expression in an image. This task is compositional and inherently requires visual reasoning on top of the relationships among…

Computer Vision and Pattern Recognition · Computer Science 2019-09-19 Sibei Yang , Guanbin Li , Yizhou Yu