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Principal component analysis (PCA) is a widely used method for data processing, such as for dimension reduction and visualization. Standard PCA is known to be sensitive to outliers, and thus, various robust PCA methods have been proposed.…

Machine Learning · Statistics 2020-08-11 Keishi Sando , Hideitsu Hino

Estimation and inference with modern longitudinal data from wearable devices, which consist of biological signals at high-frequency time points, is burdened by massive computational costs. We propose a distributed estimation and inference…

Methodology · Statistics 2023-09-13 Cole Manschot , Emily C. Hector

When generating social policies and pricing annuity at national and subnational levels, it is essential both to forecast mortality accurately and ensure that forecasts at the subnational level add up to the forecasts at the national level.…

Applications · Statistics 2020-09-22 Han Lin Shang

Principal Components Analysis is a widely used technique for dimension reduction and characterization of variability in multivariate populations. Our interest lies in studying when and why the rotation to principal components can be used…

Machine Learning · Statistics 2014-10-01 Daniel A Díaz-Pachón , Jean-Eudes Dazard , J. Sunil Rao

Traditional principal component analysis (PCA) is well known in high-dimensional data analysis, but it requires to express data by a matrix with observations to be continuous. To overcome the limitations, a new method called flexible PCA…

Methodology · Statistics 2021-08-17 Tonglin Zhang , Baijian Yang , Qianqian Song , Jing Su

In some real world applications, such as spectrometry, functional models achieve better predictive performances if they work on the derivatives of order m of their inputs rather than on the original functions. As a consequence, the use of…

Statistics Theory · Mathematics 2011-05-04 Fabrice Rossi , Nathalie Villa-Vialaneix

Principal component analysis is a useful dimension reduction and data visualization method. However, in high dimension, low sample size asymptotic contexts, where the sample size is fixed and the dimension goes to infinity,a paradox has…

Applications · Statistics 2012-11-21 Dan Shen , Haipeng Shen , Hongtu Zhu , J. S. Marron

Recently popularized randomized methods for principal component analysis (PCA) efficiently and reliably produce nearly optimal accuracy --- even on parallel processors --- unlike the classical (deterministic) alternatives. We adapt one of…

Computation · Statistics 2011-12-23 Nathan Halko , Per-Gunnar Martinsson , Yoel Shkolnisky , Mark Tygert

We present a federated, asynchronous, and $(\varepsilon, \delta)$-differentially private algorithm for PCA in the memory-limited setting. Our algorithm incrementally computes local model updates using a streaming procedure and adaptively…

Machine Learning · Computer Science 2020-10-26 Andreas Grammenos , Rodrigo Mendoza-Smith , Jon Crowcroft , Cecilia Mascolo

Nonparametric estimation of the mean and covariance functions is ubiquitous in functional data analysis and local linear smoothing techniques are most frequently used. Zhang and Wang (2016) explored different types of asymptotic properties…

Statistics Theory · Mathematics 2025-01-28 Shaojun Guo , Dong Li , Xinghao Qiao , Yizhu Wang

The process generates substantial amounts of data with highly complex structures, leading to the development of numerous nonlinear statistical methods. However, most of these methods rely on computations involving large-scale dense kernel…

Machine Learning · Statistics 2025-03-18 Ke Chen , Dandan Jiang

Principal Component Analysis (PCA) is the most widely used tool for linear dimensionality reduction and clustering. Still it is highly sensitive to outliers and does not scale well with respect to the number of data samples. Robust PCA…

Computer Vision and Pattern Recognition · Computer Science 2015-04-24 Nauman Shahid , Vassilis Kalofolias , Xavier Bresson , Michael Bronstein , Pierre Vandergheynst

We consider the problem of minimizing an objective function that depends on an orthonormal matrix. This situation is encountered when looking for common principal components, for example, and the Flury method is a popular approach. However,…

Computation · Statistics 2017-10-09 Ryan P. Browne , Paul D. McNicholas

We propose a new reconstruction operator that aims to recover the missing parts of a function given the observed parts. This new operator belongs to a new, very large class of functional operators which includes the classical regression…

Statistics Theory · Mathematics 2019-05-14 Alois Kneip , Dominik Liebl

Recently, deep learning has been widely applied in functional data analysis (FDA) with notable empirical success. However, the infinite dimensionality of functional data necessitates an effective dimension reduction approach for functional…

Machine Learning · Statistics 2025-05-13 Zhongjie Shi , Jun Fan , Linhao Song , Ding-Xuan Zhou , Johan A. K. Suykens

With the development of new remote sensing technology, large or even massive spatial datasets covering the globe become available. Statistical analysis of such data is challenging. This article proposes a semiparametric approach to model…

Methodology · Statistics 2019-10-24 Pulong Ma , Emily L. Kang

We present an implementation of all-electron density-functional theory for massively parallel GPGPU-based platforms, using localized atom-centered basis functions and real-space integration grids. Special attention is paid to domain…

Computational Physics · Physics 2020-07-24 William Huhn , Björn Lange , Victor Wen-zhe Yu , Mina Yoon , Volker Blum

Principal component analysis (PCA) frequently suffers from the disturbance of outliers and thus a spectrum of robust extensions and variations of PCA have been developed. However, existing extensions of PCA treat all samples equally even…

Machine Learning · Computer Science 2021-03-23 Rui Zhang , Hongyuan Zhang , Xuelong Li

The literature on high-dimensional functional data focuses on either the dependence over time or the correlation among functional variables. In this paper, we propose a factor-guided functional principal component analysis (FaFPCA) method…

Methodology · Statistics 2022-11-23 Shoudao Wen , Huazhen Lin

Principal Component Analysis is a novel way of of dimensionality reduction. This problem essentially boils down to finding the top k eigen vectors of the data covariance matrix. A considerable amount of literature is found on algorithms…

Machine Learning · Computer Science 2019-01-08 Jian Vora