Related papers: Multivariate Functional Singular Spectrum Analysis…
Extensions of singular spectrum analysis (SSA) for processing of non-rectangular images and time series with gaps are considered. A circular version is suggested, which allows application of the method to the data given on a circle or on a…
We present a data-adaptive spectral method - Monte Carlo Singular Spectrum Analysis (MC-SSA) - and its modification to tackle astrophysical problems. Through numerical simulations we show the ability of the MC-SSA in dealing with…
Functional time series (FTS) data have become increasingly available in real-world applications. Research on such data typically focuses on two objectives: curve reconstruction and forecasting, both of which require efficient dimension…
A multifractal analysis is performed on a three-dimensional grayscale image associated with a complex system. First, a procedure for generating 3D synthetic images (2D image stacks) of a complex structure exhibiting multifractal behaviour…
Data mining, particularly the analysis of multivariate time series data, plays a crucial role in extracting insights from complex systems and supporting informed decision-making across diverse domains. However, assessing the similarity of…
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…
In Functional Data Analysis, data are commonly assumed to be smooth functions on a fixed interval of the real line. In this work, we introduce a comprehensive framework for the analysis of functional data, whose domain is a two-dimensional…
Detection of a signal in a noisy time series using Monte Carlo singular spectrum analysis (MC-SSA) is studied from the statistical viewpoint. The MC-SSA test consists of simultaneous testing of several hypotheses related to the presence of…
This paper introduces a robust estimation strategy for the spatial functional linear regression model using dimension reduction methods, specifically functional principal component analysis (FPCA) and functional partial least squares…
Multifractal time series analysis is a approach that shows the possible complexity of the system. Nowadays, one of the most popular and the best methods for determining multifractal characteristics is Multifractal Detrended Fluctuation…
Semi-structured networks (SSNs) merge the structures familiar from additive models with deep neural networks, allowing the modeling of interpretable partial feature effects while capturing higher-order non-linearities at the same time. A…
Multi-dimensional functional data arises in numerous modern scientific experimental and observational studies. In this paper we focus on longitudinal functional data, a structured form of multidimensional functional data. Operating within a…
We present a Bayesian approach for modeling multivariate, dependent functional data. To account for the three dominant structural features in the data--functional, time dependent, and multivariate components--we extend hierarchical dynamic…
For the purpose of monitoring the behavior of complex infrastructures (e.g. aircrafts, transport or energy networks), high-rate sensors are deployed to capture multivariate data, generally unlabeled, in quasi continuous-time to detect…
Functional Principal Component Analysis (FPCA) has become a widely-used dimension reduction tool for functional data analysis. When additional covariates are available, existing FPCA models integrate them either in the mean function or in…
In this paper, we propose the Fourier frequency vector (FFV), inherently, associated with multidimensional Fourier transform. With the help of FFV, we are able to provide physical meaning of so called negative frequencies in…
Recent progress in remote sensing image (RSI) super-resolution (SR) has exhibited remarkable performance using deep neural networks, e.g., Convolutional Neural Networks and Transformers. However, existing SR methods often suffer from either…
Motivated by the challenges of analyzing high-dimensional ($p \gg n$) sequencing data from longitudinal microbiome studies, where samples are collected at multiple time points from each subject, we propose supervised functional tensor…
Many scientific analyses require simultaneous comparison of multiple functionals of an unknown signal at once, calling for multidimensional confidence regions with guaranteed simultaneous frequentist under structural constraints (e.g.,…
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…