Related papers: Principal Component Analysis for Functional Data o…
Local field potentials (LFPs) are signals that measure electrical activity in localized cortical regions from implanted tetrodes in the human or animal brain. The LFP signals are curves observed at multiple tetrodes which are implanted…
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…
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…
This paper focuses on the analysis of spatially correlated functional data. The between-curve correlation is modeled by correlating functional principal component scores of the functional data. We propose a Spatial Principal Analysis by…
Over the years, Principal Component Analysis (PCA) has served as the baseline approach for dimensionality reduction in gene expression data analysis. It primary objective is to identify a subset of disease-causing genes from a vast pool of…
Phylogenetic PCA (p-PCA) is a version of PCA for observations that are leaf nodes of a phylogenetic tree. P-PCA accounts for the fact that such observations are not independent, due to shared evolutionary history. The method works on…
This paper investigates the generalization of Principal Component Analysis (PCA) to Riemannian manifolds. We first propose a new and general type of family of subspaces in manifolds that we call barycentric subspaces. They are implicitly…
Robust Principal Component Analysis (RPCA) aims at recovering a low-rank subspace from grossly corrupted high-dimensional (often visual) data and is a cornerstone in many machine learning and computer vision applications. Even though RPCA…
The principal component analysis (PCA) is a staple statistical and unsupervised machine learning technique in finance. The application of PCA in a financial setting is associated with several technical difficulties, such as numerical…
This paper presents a new framework for manifold learning based on a sequence of principal polynomials that capture the possibly nonlinear nature of the data. The proposed Principal Polynomial Analysis (PPA) generalizes PCA by modeling the…
Phylogenetic analysis of DNA or other data commonly gives rise to a collection or sample of inferred evolutionary trees. Principal Components Analysis (PCA) cannot be applied directly to collections of trees since the space of evolutionary…
A general asymptotic framework is developed for studying consis- tency properties of principal component analysis (PCA). Our frame- work includes several previously studied domains of asymptotics as special cases and allows one to…
Principal Component Analysis (PCA) finds the best linear representation of data, and is an indispensable tool in many learning and inference tasks. Classically, principal components of a dataset are interpreted as the directions that…
We present a new straightforward principal component analysis (PCA) method based on the diagonalization of the weighted variance-covariance matrix through two spectral decomposition methods: power iteration and Rayleigh quotient iteration.…
Data integration, or the strategic analysis of multiple sources of data simultaneously, can often lead to discoveries that may be hidden in individualistic analyses of a single data source. We develop a new unsupervised data integration…
This paper addresses the challenge of spectral-spatial feature extraction for hyperspectral image classification by introducing a novel tensor-based framework. The proposed approach incorporates circular convolution into a tensor structure…
We propose a supervised principal component regression method for relating functional responses with high dimensional predictors. Unlike the conventional principal component analysis, the proposed method builds on a newly defined expected…
Principal component analysis (PCA) is perhaps the most widely used method for data dimensionality reduction. A key question in PCA is deciding how many factors to retain. This manuscript describes a new approach to automatically selecting…
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…
Principal Component Analysis (PCA) is a highly useful topic within an introductory Linear Algebra course, especially since it can be used to incorporate a number of applied projects. This method represents an essential application and…