相关论文: Functional principal component analysis estimator …

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…

Principal component analysis (PCA) is a standard dimensionality reduction technique used in various research and applied fields. From an algorithmic point of view, classical PCA can be formulated in terms of operations on a multivariate…

An improved mixture of probabilistic principal component analysis (PPCA) has been introduced for nonlinear data-driven process monitoring in this paper. To realize this purpose, the technique of a mixture of probabilistic principal…

Asymptotic inference using functional principal component regression (FPCR) has long been considered difficult, largely because, upon any scalar scaling, the FPCR estimator fails to satisfy a central limit theorem, leading to the prevailing…

Large-dimensional factor model has drawn much attention in the big-data era, in order to reduce the dimensionality and extract underlying features using a few latent common factors. Conventional methods for estimating the factor model…

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…

Dimensionality reduction is critical across various domains of science including neuroscience. Probabilistic Principal Component Analysis (PPCA) is a prominent dimensionality reduction method that provides a probabilistic approach unlike…

This study presents the development of multivariate functional Moran's I, along with a novel approach termed multivariate functional areal spatial principal component analysis (mfasPCA), specifically designed for analyzing functional areal…

In recent times, functional data analysis (FDA) has been successfully applied in the field of high dimensional data classification. In this paper, we present a novel classification framework using functional data and classwise Principal…

Principal component analysis (PCA) is traditionally implemented through a covariance or kernel matrix, leading-eigenvector extraction, and hard rank-$k$ projection. These steps can be computationally costly in high-dimensional and…

The problem of Non-Gaussian Component Analysis (NGCA) is about finding a maximal low-dimensional subspace $E$ in $\mathbb{R}^n$ so that data points projected onto $E$ follow a non-gaussian distribution. Although this is an appropriate model…

Fourier PCA is Principal Component Analysis of a matrix obtained from higher order derivatives of the logarithm of the Fourier transform of a distribution.We make this method algorithmic by developing a tensor decomposition method for a…

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…

In this paper, we propose a novel robust Principal Component Analysis (PCA) for high-dimensional data in the presence of various heterogeneities, especially the heavy-tailedness and outliers. A transformation motivated by the characteristic…

Sparse functional data frequently arise in real-world applications, posing significant challenges for accurate classification. To address this, we propose a novel classification method that integrates functional principal component analysis…

We propose a "small-uniform" statistic for the inference of the functional PCA estimator in a functional linear regression model. The literature has shown two extreme behaviors: on the one hand, the FPCA estimator does not converge in…

Functional data analysis offers a diverse toolkit of statistical methods tailored for analyzing samples of real-valued random functions. Recently, samples of time-varying random objects, such as time-varying networks, have been increasingly…

We propose a new high dimensional semiparametric principal component analysis (PCA) method, named Copula Component Analysis (COCA). The semiparametric model assumes that, after unspecified marginally monotone transformations, the…

Functional time series (FTS) data have become increasingly available in real-world applications. Research on such data typically focuses on two objectives: curve reconstruction and forecasting, both of which require efficient dimension…

In many applications, the variables that characterize a stochastic system are measured along a second dimension, such as time. This results in multivariate functional data and the interest is in describing the statistical dependences among…