Related papers: Dynamic Functional Principal Component
Functional data often arise from measurements on fine time grids and are obtained by separating an almost continuous time record into natural consecutive intervals, for example, days. The functions thus obtained form a functional time…
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…
Nowadays many real-world datasets can be considered as functional, in the sense that the processes which generate them are continuous. A fundamental property of this type of data is that in theory they belong to an infinite-dimensional…
Regularized variants of Principal Components Analysis, especially Sparse PCA and Functional PCA, are among the most useful tools for the analysis of complex high-dimensional data. Many examples of massive data, have both sparse and…
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…
We introduce Adaptive Functional Principal Component Analysis, a novel method to capture directions of variation in functional data that exhibit sharp changes in smoothness. We first propose a new adaptive scatterplot smoothing technique…
A new procedure is proposed for the dimensional reduction of time series. Similarly to principal components, the procedure seeks a low-dimensional manifold that minimizes information loss. Unlike principal components, however, the new…
Principal Component Analysis (PCA) is a commonly used tool for dimension reduction in analyzing high dimensional data; Multilinear Principal Component Analysis (MPCA) has the potential to serve the similar function for analyzing tensor…
In a longitudinal metabolomics study, multiple metabolites are measured from several observations at many time points. Interest lies in reducing the dimensionality of such data and in highlighting influential metabolites which change over…
We consider estimation of large approximate factor models in high-dimensional panels of stationary time series using Principal Component Analysis (PCA). We review the key results establishing the necessary and sufficient conditions for…
Modelling a large bundle of curves arises in a broad spectrum of real applications. However, existing literature relies primarily on the critical assumption of independent curve observations. In this paper, we provide a general theory for…
Functional data analysis (FDA) is a statistical framework that allows for the analysis of curves, images, or functions on higher dimensional domains. The goals of FDA, such as descriptive analyses, classification, and regression, are…
The paper is concerned with asymptotic properties of the principal components analysis of functional data. The currently available results assume the existence of the fourth moment. We develop analogous results in a setting which does not…
A novel text data dimension reduction technique, called the tree-structured multi-linear principal component anal- ysis (TMPCA), is proposed in this work. Being different from traditional text dimension reduction methods that deal with the…
Principal Component Analysis (PCA) is a workhorse of modern data science. While PCA assumes the data conforms to Euclidean geometry, for specific data types, such as hierarchical and cyclic data structures, other spaces are more…
We address the problem of forecasting high-dimensional functional time series through a two-fold dimension reduction procedure. The difficulty of forecasting high-dimensional functional time series lies in the curse of dimensionality. In…
In the era of big data, reducing data dimensionality is critical in many areas of science. Widely used Principal Component Analysis (PCA) addresses this problem by computing a low dimensional data embedding that maximally explain variance…
We present a technique to perform dimensionality reduction on data that is subject to uncertainty. Our method is a generalization of traditional principal component analysis (PCA) to multivariate probability distributions. In comparison to…
In multivariate time series classification, although current sequence analysis models have excellent classification capabilities, they show significant shortcomings when dealing with long sequence multivariate data, such as prolonged…
Estimating intrinsic dimensionality of data is a classic problem in pattern recognition and statistics. Principal Component Analysis (PCA) is a powerful tool in discovering dimensionality of data sets with a linear structure; it, however,…