Related papers: Principal Component Analysis using Frequency Compo…

Principal component analysis has been a main tool in multivariate analysis for estimating a low dimensional linear subspace that explains most of the variability in the data. However, in high-dimensional regimes, naive estimates of the…

We extend the principal component analysis (PCA) to second-order stationary vector time series in the sense that we seek for a contemporaneous linear transformation for a $p$-variate time series such that the transformed series is segmented…

We propose a novel principal component analysis in the graph frequency domain for dimension reduction of multivariate data residing on graphs. The proposed method not only effectively reduces the dimensionality of multivariate graph…

In this article, we introduce the mean independent component analysis for multivariate time series to reduce the parameter space. In particular, we seek for a contemporaneous linear transformation that detects univariate mean independent…

Time series analysis is crucial in fields like finance, economics, environmental science, and biomedical engineering, aiding in forecasting, pattern identification, and understanding underlying mechanisms. While traditional time-domain…

Analyzing time series in the frequency domain enables the development of powerful tools for investigating the second-order characteristics of multivariate processes. Parameters like the spectral density matrix and its inverse, the coherence…

A useful approach for analysing multiple time series is via characterising their spectral density matrix as the frequency domain analog of the covariance matrix. When the dimension of the time series is large compared to their length,…

Dimension reduction for high-dimensional compositional data plays an important role in many fields, where the principal component analysis of the basis covariance matrix is of scientific interest. In practice, however, the basis variables…

Compositional data, also referred to as simplicial data, naturally arise in many scientific domains such as geochemistry, microbiology, and economics. In such domains, obtaining sensible lower-dimensional representations and modes of…

We present a data-driven method for separating complex, multiscale systems into their constituent time-scale components using a recursive implementation of dynamic mode decomposition (DMD). Local linear models are built from windowed…

Interpretable classification of time series presents significant challenges in high dimensions. Traditional feature selection methods in the frequency domain often assume sparsity in spectral density matrices (SDMs) or their inverses, which…

Multivariate functional principal component analysis (MFPCA) is a powerful dimension reduction technique for analyzing multiple functional variables simultaneously. However, existing MFPCA methods assume that all functional observations are…

Principal component analysis is a versatile tool to reduce dimensionality which has wide applications in statistics and machine learning. It is particularly useful for modeling data in high-dimensional scenarios where the number of…

We assume a second-order source separation model where the observed multivariate time series is a linear mixture of latent, temporally uncorrelated time series with some components pure white noise. To avoid the modelling of noise, we…

Dimension reduction is often the first step in statistical modeling or prediction of multivariate spatial data. However, most existing dimension reduction techniques do not account for the spatial correlation between observations and do not…

Seasonal time series exhibit intricate long-term dependencies, posing a significant challenge for accurate future prediction. This paper introduces the Multi-scale Seasonal Decomposition Model (MSSD) for seasonal time-series forecasting.…

Singular spectrum analysis (SSA) as a nonparametric tool for decomposition of an observed time series into sum of interpretable components such as trend, oscillations and noise is considered. The separability of these series components by…

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…

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…