Related papers: Principal Component Analysis using Frequency Compo…

This paper develops change-point methods for the spectrum of a locally stationary time series. We focus on series with a bounded spectral density that change smoothly under the null hypothesis but exhibits change-points or becomes less…

In this paper, we propose a fast, well-performing, and consistent method for segmenting a piecewise-stationary, linear time series with an unknown number of breakpoints. The time series model we use is the nonparametric Locally Stationary…

The collective mode spectrum of a symmetry-breaking state, such as a superconductor, provides crucial insight into the nature of the order parameter. In this context, we present a microscopic weak-coupling theory for the collective modes of…

In areas of application, including actuarial science and demography, it is increasingly common to consider a time series of curves; an example of this is age-specific mortality rates observed over a period of years. Given that age can be…

Principal component analysis is a statistical method, which lowers the number of important variables in a data set. The use of this method for the bursts' spectra and afterglows is discussed in this paper. The analysis indicates that three…

Current approaches for time series forecasting, whether in the time or frequency domain, predominantly use deep learning models based on linear layers or transformers. They often encode time series data in a black-box manner and rely on…

A common class of methods for analyzing of multivariate time series, stationary and nonstationary, decomposes the observed series into latent sources. Methods such as principal compoment analysis (PCA), independent component analysis (ICA)…

Multivariate time series forecasting is crucial across various industries, where accurate extraction of complex periodic and trend components can significantly enhance prediction performance. However, existing models often struggle to…

Many real-world time series exhibit strong periodic structures arising from physical laws, human routines, or seasonal cycles. However, modern deep forecasting models often fail to capture these recurring patterns due to spectral bias and a…

The diagonal elements of the time correlation matrix are used to probe closed quantum systems that are measured at random times. This enables us to extract two distinct parts of the quantum evolution, a recurrent part and an exponentially…

In scientific applications, multivariate observations often come in tandem with temporal or spatial covariates, with which the underlying signals vary smoothly. The standard approaches such as principal component analysis and factor…

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.…

We consider the sparse principal component analysis for high-dimensional stationary processes. The standard principal component analysis performs poorly when the dimension of the process is large. We establish the oracle inequalities for…

The first order behavior of multivariate heavy-tailed random vectors above large radial thresholds is ruled by a limit measure in a regular variation framework. For a high dimensional vector, a reasonable assumption is that the support of…

Fourier PCA is Principal Component Analysis of a matrix obtained from higher order derivatives of the logarithm of the Fourier transform of a distribution.We make this method algorithmic by developing a tensor decomposition method for a…

Multi-view data provides complementary information on the same set of observations, with multi-omics and multimodal sensor data being common examples. Analyzing such data typically requires distinguishing between shared (joint) and unique…

Modern time series are usually composed of multiple oscillatory components, with time-varying frequency and amplitude contaminated by noise. The signal processing mission is further challenged if each component has an oscillatory pattern,…

This paper proposes a frequency domain approach to test the hypothesis that a complex-valued vector time series is proper, i.e., for testing whether the vector time series is uncorrelated with its complex conjugate. If the hypothesis is…

Sparse principal component analysis (sparse PCA) is a widely used technique for dimensionality reduction in multivariate analysis, addressing two key limitations of standard PCA. First, sparse PCA can be implemented in high-dimensional low…

The decomposition of a time series is an essential task that helps to understand its very nature. It facilitates the analysis and forecasting of complex time series expressing various hidden components such as the trend, seasonal…