相关论文: Generalized Singular Spectrum Time Series Analysis

Slow feature analysis (SFA) is a new technique for extracting slowly varying features from a quickly varying signal. It is shown here that SFA can be applied to nonstationary time series to estimate a single underlying driving force with…

A method is presented for investigating the periodic signal content of time series in which a number of signals is present, such as arising from the observation of multiperiodic oscillating stars in observational asteroseismology. Standard…

In this work, we develop multivariate functional singular spectrum analysis (MFSSA) over different dimensional domains which is the functional extension of multivariate singular spectrum analysis (MSSA). In the following, we provide all of…

We first give an abstract framework to show the uniqueness of Ground State Solutions (GSS) for a large class of PDEs. To the best of our knowledge, all the existing results in the literature only addressed particular cases. Moreover, our…

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…

The generalised eigenfunction expansion method (GEM) and the singularity expansion method (SEM) are applied to solve the canonical problem of wave scattering on an infinite stretched string in the time domain. The GEM, which is shown to be…

Inverse medium problems involve the reconstruction of a spatially varying unknown medium from available observations by exploring a restricted search space of possible solutions. Standard grid-based representations are very general but all…

Sparse autoencoders (SAEs) have proven useful in disentangling the opaque activations of neural networks, primarily large language models, into sets of interpretable features. However, adapting them to domains beyond language, such as…

In a variety of contexts, we prove that singular continuous spectrum is generic in the sense that for certain natural complete metric spaces of operators, those with singular spectrum are a dense $G_\delta$.

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…

Multivariate time-series data are frequently observed in critical care settings and are typically characterized by sparsity (missing information) and irregular time intervals. Existing approaches for learning representations in this domain…

We study planar graphs with large negative curvature outside of a finite set and the spectral theory of Schr{\"o}dinger operators on these graphs. We obtain estimates on the first and second order term of the eigenvalue asymptotics.…

In this paper we study a general family of multivariable Gaussian stochastic processes. Each process is prescribed by a fixed Borel measure $\sigma$ on $\mathbb R^n$. The case when $\sigma$ is assumed absolutely continuous with respect to…

A key step in separating signal from noise in time series by means of singular spectrum analysis (SSA) is grouping. We present a multiple testing method for the grouping step in SSA. As separability criterion, we utilize the weighted…

Generalized prolate spheroidal functions (GPSFs) arise naturally in the study of bandlimited functions as the eigenfunctions of a certain truncated Fourier transform. In one dimension, the theory of GPSFs (typically referred to as prolate…

Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…

In this paper, we develop a representation-theoretic formulation of discrete-time linear systems. We show that such systems are naturally viewed as representations of time groups acting on vector spaces, thereby endowing the state space…

The steady-state approximation (hereafter abbreviated as SSA) consists in setting $dy/dt=0$, where $y$ denotes the concentration of a short-lived intermediate subject to first-order decay with a rate constant $k$. The sole reason for…

A set of regularly distributed transmission eigenvalues generates a density function. We use such a density function inversely determines the form of the indicator function. Using the entire function theory, we reduce an uniqueness problem…

A method for time-frequency analysis is given. The approach utilizes properties of Gaussian distribution, properties of Hermite polynomials and Fourier analysis. We begin by the definitions of a set of functions called harmonic Gaussian…