Related papers: Functional Singular Spectrum Analysis
As high-dimensional and high-frequency data are being collected on a large scale, the development of new statistical models is being pushed forward. Functional data analysis provides the required statistical methods to deal with large-scale…
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…
The continuous advances in data collection and storage techniques allow us to observe and record real-life processes in great detail. Examples include financial transaction data, fMRI images, satellite photos, earths pollution distribution…
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 introduce Multivariate Circulant Singular Spectrum Analysis (M-CiSSA) to provide a comprehensive framework to analyze fluctuations, extracting the underlying components of a set of time series, disentangling their sources of variation…
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…
This study extends and evaluates the forecasting performance of the Singular Spectrum Analysis (SSA) technique using a general non-linear form for the re- current formula. In this study, we consider 24 series measuring the monthly…
Functional principal component analysis (FPCA) has been widely used to capture major modes of variation and reduce dimensions in functional data analysis. However, standard FPCA based on the sample covariance estimator does not work well in…
Singular spectrum analysis (SSA) is considered for decomposition of time series into identifiable components. The Basic SSA method is nonparametric and constructs an adaptive expansion based on singular value decomposition. The investigated…
We present a new method based on Functional Data Analysis (FDA) for detecting associations between one or more scalar covariates and a longitudinal response, while correcting for other variables. Our methods exploit the temporal structure…
In this paper we review existing methods for robust functional principal component analysis (FPCA) and propose a new method for FPCA that can be applied to longitudinal data where only a few observations per trajectory are available. This…
In recent times, functional data analysis (FDA) has been successfully applied in the field of high dimensional data classification. In this paper, we present a novel classification framework using functional data and classwise Principal…
Singular Spectrum Analysis (SSA) or Singular Value Decomposition (SVD) are often used to de-noise univariate time series or to study their spectral profile. Both techniques rely on the eigendecomposition of the cor- relation matrix…
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…
In this paper, we explore dimension reduction for functional time series. We propose a generalized dynamic functional principal component analysis (GDFPCA) which does not rely on spectral density estimation and demonstrates strong empirical…
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…
Functional principal component analysis (FPCA) is a key tool in the study of functional data, driving both exploratory analyses and feature construction for use in formal modeling and testing procedures. However, existing methods for FPCA…
Functional data analysis (FDA) is a statistical framework that allows for the analysis of curves, images, or functions on higher dimensional domains. The goals of FDA, such as descriptive analyses, classification, and regression, are…
Singular spectrum analysis (SSA) is a nonparametric and adaptive spectral decomposition of a time series. The singular value decomposition of the trajectory matrix and the anti-diagonal averaging leads to a time-series decomposition. In…
We introduce Contrastive Multivariate Singular Spectrum Analysis, a novel unsupervised method for dimensionality reduction and signal decomposition of time series data. By utilizing an appropriate background dataset, the method transforms a…