Related papers: Localized Functional Principal Component Analysis

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…

We propose a new fast generalized functional principal components analysis (fast-GFPCA) algorithm for dimension reduction of non-Gaussian functional data. The method consists of: (1) binning the data within the functional domain; (2)…

Functional principal component analysis is one of the most commonly employed approaches in functional and longitudinal data analysis and we extend it to analyze functional/longitudinal data observed on a general $d$-dimensional domain. The…

Probabilistic Component Latent Analysis (PLCA) is a statistical modeling method for feature extraction from non-negative data. It has been fruitfully applied to various research fields of information retrieval. However, the EM-solved…

We propose a novel class of prior distributions for sequences of orthogonal functions, which are frequently required in various statistical models such as functional principal component analysis (FPCA). Our approach constructs priors…

Functional data analysis (FDA) methods have computational and theoretical appeals for some high dimensional data, but lack the scalability to modern large sample datasets. To tackle the challenge, we develop randomized algorithms for two…

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,…

Fair principal component analysis (FPCA), a ubiquitous dimensionality reduction technique in signal processing and machine learning, aims to find a low-dimensional representation for a high-dimensional dataset in view of fairness. The FPCA…

Classical multivariate principal component analysis has been extended to functional data and termed functional principal component analysis (FPCA). Most existing FPCA approaches do not accommodate covariate information, and it is the goal…

Functional principal component analysis (FPCA) based on the Karhunen--Lo\`{e}ve decomposition has been successfully applied in many applications, mainly for one sample problems. In this paper we consider common functional principal…

Functional principal component analysis (FPCA) has played an important role in the development of functional time series analysis. This note investigates how FPCA can be used to analyze cointegrated functional time series and proposes a…

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,…

Sparse functional data arise when measurements are observed infrequently and at irregular time points for each subject, often in the presence of measurement error. These characteristics introduce additional challenges for functional…

Robust Principal Component Analysis (RPCA) is a fundamental technique for decomposing data into low-rank and sparse components, which plays a critical role for applications such as image processing and anomaly detection. Traditional RPCA…

Sparse principal component analysis (PCA) is an important technique for dimensionality reduction of high-dimensional data. However, most existing sparse PCA algorithms are based on non-convex optimization, which provide little guarantee on…

Two existing approaches to functional principal components analysis (FPCA) are due to Rice and Silverman (1991) and Silverman (1996), both based on maximizing variance but introducing penalization in different ways. In this article we…

Sparse principal component analysis (SPCA) has emerged as a powerful technique for modern data analysis, providing improved interpretation of low-rank structures by identifying localized spatial structures in the data and disambiguating…

Sparse Principal Component Analysis (sPCA) is a cardinal technique for obtaining combinations of features, or principal components (PCs), that explain the variance of high-dimensional datasets in an interpretable manner. This involves…

Robust principal component analysis (RPCA) is a widely used technique for recovering low-rank structure from matrices with missing entries and sparse, possibly large-magnitude corruptions. Although numerous algorithms achieve accurate point…

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…