Principal component analysis (PCA) is a widely used tool for data analysis and dimension reduction in applications throughout science and engineering. However, the principal components (PCs) can sometimes be difficult to interpret, because they are linear combinations of all the original variables. To facilitate interpretation, sparse PCA produces modified PCs with sparse loadings, i.e. loading...

Sparse principal component analysis addresses the problem of finding a linear combination of the variables in a given dataset with a sparse coefficients vector that maximizes the variability of the data. This model enhances the ability to interpret the principal components and is applicable in a wide variety of fields including genetics and finance, just to name a few. We suggest a necessary co...

Principal component analysis (PCA) is a widely used tool in medical image analysis for data reduction, model building, and data understanding and exploration. While PCA is a holistic approach where each new variable is a linear combination of all original variables, sparse PCA (SPCA) aims at producing easily interpreted models through sparse loadings, i.e. each new variable is a linear combinat...

We study sparse principal component analysis (sparse PCA) for high dimensional multivariate vector autoregressive (VAR) time series. By treating the transition matrix as a nuisance parameter, we show that sparse PCA can be directly applied on analyzing multivariate time series as if the data are i.i.d. generated. Under a double asymptotic framework in which both the length of the sample period ...

We consider nonparametric estimation of the mean and covariance functions for functional/longitudinal data. Strong uniform convergence rates are developed for estimators that are local-linear smoothers. Our results are obtained in a unified framework in which the number of observations within each curve/cluster can be of any rate relative to the sample size. We show that the convergence rates f...

Sparse principal component analysis combines the idea of sparsity with principal component analysis (PCA). There are two kinds of sparse PCA; sparse loading PCA (slPCA) which keeps all the variables but zeroes out some of their loadings; and sparse variable PCA (svPCA) which removes whole variables by simultaneously zeroing out all the loadings on some variables. In this paper we propose a mode...

We develop nonparametric methods, and theory, for analysing data on a random p-vector Y represented as a linear form in a p-vector X, say Y = AX, where the components of X are nonnegative and uncorrelated. Problems of this nature are motivated by a wide range of applications in which physical considerations deny the possibility that X can have negative components. Our approach to inference is f...

—We propose an image denoising method that exploits nonlocal image modeling, principal component analysis (PCA), and local shape-adaptive anisotropic estimation. The nonlocal modeling is exploited by grouping similar image patches in 3-D groups. The denoising is performed by shrinkage of the spectrum of a 3-D transform applied on such groups. The effectiveness of the shrinkage depends on the ab...

Recently, a successful extension of Principal Component Analysis for structured input, such as sequences, trees, and graphs, has been proposed. This allows the embedding of discrete structures into vectorial spaces, where all the classical pattern recognition and machine learning methods can be applied. The proposed approach is based on eigenanalysis of extended vectorial representations of the...