Related papers: Functional Singular Spectrum Analysis

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…

Constructing generative models for functional observations is an important task in statistical functional analysis. In general, functional data contains both phase (or x or horizontal) and amplitude (or y or vertical) variability. Tradi-…

The well-established practice of time series analysis involves estimating deterministic, non-stationary trend and seasonality components followed by learning the residual stochastic, stationary components. Recently, it has been shown that…

Many conventional statistical and machine learning methods face challenges when applied directly to high dimensional temporal observations. In recent decades, Functional Data Analysis (FDA) has gained widespread popularity as a framework…

Multivariate Functional Principal Component Analysis (MFPCA) is a valuable tool for exploring relationships and identifying shared patterns of variation in multivariate functional data. However, controlling the roughness of the extracted…

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…

Here, we address the problem of trend estimation for functional time series. Existing contributions either deal with detecting a functional trend or assuming a simple model. They consider neither the estimation of a general functional trend…

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…

The rise in data has led to the need for dimension reduction techniques, especially in the area of non-scalar variables, including time series, natural language processing, and computer vision. In this paper, we specifically investigate…

Cardiac Magnetic Resonance Imaging (MRI) is time-consuming and error-prone. To ease the patient's burden and to increase the efficiency and robustness of cardiac exams, interest in methods based on continuous steady-state acquisition and…

Multivariate time-series forecasting, as a typical problem in the field of time series prediction, has a wide range of applications in weather forecasting, traffic flow prediction, and other scenarios. However, existing works do not…

We present a novel method, Fractal Space-Curve Analysis (FSCA), which combines Space-Filling Curve (SFC) mapping for dimensionality reduction with fractal Detrended Fluctuation Analysis (DFA). The method is suitable for multidimensional…

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…

We propose nonparametric methods for functional linear regression which are designed for sparse longitudinal data, where both the predictor and response are functions of a covariate such as time. Predictor and response processes have smooth…

Functional principal component analysis has been shown to be invaluable for revealing variation modes of longitudinal outcomes, which serves as important building blocks for forecasting and model building. Decades of research have advanced…

Change detection has been a hotspot in remote sensing technology for a long time. With the increasing availability of multi-temporal remote sensing images, numerous change detection algorithms have been proposed. Among these methods, image…

Recent methods for long-tailed instance segmentation still struggle on rare object classes with few training data. We propose a simple yet effective method, Feature Augmentation and Sampling Adaptation (FASA), that addresses the data…

The frequency-domain properties of nonstationary functional time series often contain valuable information. These properties are characterized through its time-varying power spectrum. Practitioners seeking low-dimensional summary measures…

Time series analysis is crucial for understanding dynamics of complex systems. Recent advances in foundation models have led to task-agnostic Time Series Foundation Models (TSFMs) and Large Language Model-based Time Series Models (TSLLMs),…

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…