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Multilinear Principal Component Analysis (MPCA) is a widely utilized method for the dimension reduction of tensor data. However, the integration of MPCA into federated learning remains unexplored in existing research. To tackle this gap,…

Machine Learning · Computer Science 2024-04-30 Chengyu Zhou , Yuqi Su , Tangbin Xia , Xiaolei Fang

We introduce inferential methods for prediction based on functional random effects in generalized functional mixed effects models. This is similar to the inference for random effects in generalized linear mixed effects models (GLMMs), but…

Methodology · Statistics 2025-01-15 Xinkai Zhou , Erjia Cui , Joseph Sartini , Ciprian Crainiceanu

Functional principal component analysis (FPCA) could become invalid when data involve non-Gaussian features. Therefore, we aim to develop a general FPCA method to adapt to such non-Gaussian cases. A Kenall's $\tau$ function, which possesses…

Methodology · Statistics 2021-08-18 Rou Zhong , Shishi Liu , Haocheng Li , Jingxiao Zhang

Functional Principal Components Analysis (FPCA) provides a parsimonious, semi-parametric model for multivariate, sparsely-observed functional data. Frequentist FPCA approaches estimate principal components (PCs) from the data, then…

Methodology · Statistics 2026-05-11 Joseph Sartini , Scott Zeger , Ciprian Crainiceanu

In this paper, we address the problem of dimension reduction for time series of functional data $(X_t\colon t\in\mathbb{Z})$. Such {\it functional time series} frequently arise, e.g., when a continuous-time process is segmented into some…

Statistics Theory · Mathematics 2015-06-03 Siegfried Hörmann , Łukasz Kidziński , Marc Hallin

Functional principal component analysis (FPCA) has been widely used to capture major modes of variation and reduce dimensions in functional data analysis. However, standard FPCA based on the sample covariance estimator does not work well in…

Methodology · Statistics 2021-01-19 Guangxing Wang , Sisheng Liu , Fang Han , Chongzhi Di

This paper presents a novel approach to functional principal component analysis (FPCA) in Bayes spaces in the setting where densities are the object of analysis, but only few individual samples from each density are observed. We use the…

Methodology · Statistics 2023-09-21 Lisa Steyer , Sonja Greven

Understanding and predicting the electric consumption patterns in the short-, mid- and long-term, at the distribution and transmission level, is a fundamental asset for smart grids infrastructure planning, dynamic network reconfiguration,…

Systems and Control · Electrical Eng. & Systems 2020-02-27 Davide Beretta , Samuele Grillo , Davide Pigoli , Enea Bionda , Claudio Bossi , Carlo Tornelli

In this paper, we consider a new variant for principal component analysis (PCA), aiming to capture the grouping and/or sparse structures of factor loadings simultaneously. To achieve these goals, we employ a non-convex truncated…

Methodology · Statistics 2022-09-14 Haiyan Jiang , Shanshan Qin , Oscar Hernan Madrid Padilla

Functional principal components (FPC's) provide the most important and most extensively used tool for dimension reduction and inference for functional data. The selection of the number, d, of the FPC's to be used in a specific procedure has…

Statistics Theory · Mathematics 2013-02-26 Stefan Fremdt , Lajos Horváth , Piotr Kokoszka , Josef G. Steinebach

Principal component analysis (PCA) is a statistical technique commonly used in multivariate data analysis. However, PCA can be difficult to interpret and explain since the principal components (PCs) are linear combinations of the original…

Mathematical Software · Computer Science 2013-12-24 W. Liu , H. Zhang , D. Tao , Y. Wang , K. Lu

In this paper we review existing methods for robust functional principal component analysis (FPCA) and propose a new method for FPCA that can be applied to longitudinal data where only a few observations per trajectory are available. This…

Methodology · Statistics 2020-12-04 Graciela Boente , Matias Salibian-Barrera

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

We propose localized functional principal component analysis (LFPCA), looking for orthogonal basis functions with localized support regions that explain most of the variability of a random process. The LFPCA is formulated as a convex…

Methodology · Statistics 2015-01-21 Kehui Chen , Jing Lei

Functional data analysis is concerned with the analysis of infinite-dimensional data functions. Functional principal component analysis (FPCA) is a key method to obtain finite-dimensional summaries. Consistency of FPCA has been…

Methodology · Statistics 2026-04-24 Tim Kutta , Nina Dörnemann , Piotr Kokoszka

When measurements fall below or above a detection threshold, the resulting data are missing not at random (MNAR), posing challenges for statistical analysis. For example, in longitudinal biomarker studies, observations may be subject to…

Methodology · Statistics 2025-10-21 Haiyan Liu , Jeanine Houwing-Duistermaat

Data analysis often requires methods that are invariant with respect to specific transformations, such as rotations in case of images or shifts in case of images and time series. While principal component analysis (PCA) is a widely-used…

Machine Learning · Statistics 2024-01-30 Florian Heinrichs

With the advance of modern technology, more and more data are being recorded continuously during a time interval or intermittently at several discrete time points. They are both examples of "functional data", which have become a prevailing…

Methodology · Statistics 2015-07-21 Jane-Ling Wang , Jeng-Min Chiou , Hans-Georg Mueller

Analyzing longitudinal data in health studies is challenging due to sparse and error-prone measurements, strong within-individual correlation, missing data and various trajectory shapes. While mixed-effect models (MM) effectively address…

Methodology · Statistics 2024-07-11 Corentin Ségalas , Catherine Helmer , Robin Genuer , Cécile Proust-Lima

Principal component analysis (PCA) is a popular dimension reduction technique for vector data. Factored PCA (FPCA) is a probabilistic extension of PCA for matrix data, which can substantially reduce the number of parameters in PCA while…

Machine Learning · Statistics 2023-12-19 Xuan Ma , Jianhua Zhao , Yue Wang