Related papers: Functional Principal Component Analysis for Cointe…

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…

Principal component analysis (PCA) is a widely used unsupervised dimensionality reduction technique in machine learning, applied across various fields such as bioinformatics, computer vision and finance. However, when the response variables…

Principal Component Analysis (PCA) and its nonlinear extension Kernel PCA (KPCA) are widely used across science and industry for data analysis and dimensionality reduction. Modern deep learning tools have achieved great empirical success,…

In many longitudinal studies, a large number of variables are measured repeatedly over time, with substantial missing data. Existing methods, such as probabilistic principal component analysis (PPCA), are ill-equipped to handle such…

The advance of modern sensor technologies enables collection of multi-stream longitudinal data where multiple signals from different units are collected in real-time. In this article, we present a non-parametric approach to predict the…

I introduce Forecastable Component Analysis (ForeCA), a novel dimension reduction technique for temporally dependent signals. Based on a new forecastability measure, ForeCA finds an optimal transformation to separate a multivariate time…

Methods for supervised principal component analysis (SPCA) aim to incorporate label information into principal component analysis (PCA), so that the extracted features are more useful for a prediction task of interest. Prior work on SPCA…

In a fully-Bayesian Functional Principal Components Analysis (FPCA) the principal components are treated as unknown infinite-dimensional parameters. By projecting the functional principal components on a rich orthonormal spline basis, we…

This paper aims to develop new techniques to describe joint behavior of stocks, beyond regression and correlation. For example, we want to identify the clusters of the stocks that move together. Our work is based on applying Kernel…

We develop a robust Bayesian functional principal component analysis (RB-FPCA) method that utilizes the skew elliptical class of distributions to model functional data, which are observed over a continuous domain. This approach effectively…

As one of the newest members in the field of artificial immune systems (AIS), the Dendritic Cell Algorithm (DCA) is based on behavioural models of natural dendritic cells (DCs). Unlike other AIS, the DCA does not rely on training data,…

Principal Component Analysis (PCA) is known to be the most widely applied dimensionality reduction approach. A lot of improvements have been done on the traditional PCA, in order to obtain optimal results in the dimensionality reduction of…

Machine Learning models are prone to fail when test data are different from training data, a situation often encountered in real applications known as distribution shift. While still valid, the training-time knowledge becomes less…

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…

In this work, we develop a novel principal component analysis (PCA) for semimartingales by introducing a suitable spectral analysis for the quadratic variation operator. Motivated by high-dimensional complex systems typically found in…

We consider the problem of decomposing a large covariance matrix into the sum of a low-rank matrix and a diagonally dominant matrix, and we call this problem the "Diagonally-Dominant Principal Component Analysis (DD-PCA)". DD-PCA is an…

We use the methodology of singular spectrum analysis (SSA), principal component analysis (PCA), and multi-fractal detrended fluctuation analysis (MFDFA), for investigating characteristics of vibration time series data from a friction brake.…

We derive and study a significance test for determining if a panel of functional time series is separable. In the context of this paper, separability means that the covariance structure factors into the product of two functions, one…

Principal Component Analysis (PCA) is a fundamental data preprocessing tool in the world of machine learning. While PCA is often thought of as a dimensionality reduction method, the purpose of PCA is actually two-fold: dimension reduction…

Principal Component Analysis (PCA) is widely used for dimensionality reduction and data analysis. However, PCA results are adversely affected by outliers often observed in real-world data. Existing robust PCA methods are often…