Related papers: Computing the multifractal spectrum from time seri…
The Fourier spectrum at a fractional period is often examined when extracting features from biological sequences and time series. It reflects the inner information structure of the sequences. A fractional period is not uncommon in time…
We propose new quantum algorithms for estimating spectral sums of positive semi-definite (PSD) matrices. The spectral sum of an PSD matrix $A$, for a function $f$, is defined as $ \text{Tr}[f(A)] = \sum_j f(\lambda_j)$, where $\lambda_j$…
I present the Automated Line Fitting Algorithm, ALFA, a new code which can fit emission line spectra of arbitrary wavelength coverage and resolution, fully automatically. In contrast to traditional emission line fitting methods which…
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…
Sequentially obtained dataset usually exhibits different behavior at different data resolutions/scales. Instead of inferring from data at each scale individually, it is often more informative to interpret the data as an ensemble of time…
In this paper, we study the nonlinear inverse problem of estimating the spectrum of a system matrix, that drives a finite-dimensional affine dynamical system, from partial observations of a single trajectory data. In the noiseless case, we…
Frequency domain methods form a ubiquitous part of the statistical toolbox for time series analysis. In recent years, considerable interest has been given to the development of new spectral methodology and tools capturing dynamics in the…
This paper introduces an algorithm-agnostic approach to feature-based time series clustering via amortized neural inference. By training neural networks to approximate the optimal partitioning rule from simulated data, the proposed…
New time-series analysis tools are needed in disciplines as diverse as astronomy, economics and meteorology. In particular, the increasing rate of data collection at multiple wavelengths requires new approaches able to handle these data.…
A useful approach for analysing multiple time series is via characterising their spectral density matrix as the frequency domain analog of the covariance matrix. When the dimension of the time series is large compared to their length,…
We propose graph-based predictable feature analysis (GPFA), a new method for unsupervised learning of predictable features from high-dimensional time series, where high predictability is understood very generically as low variance in the…
Accurate spectrum prediction is crucial for dynamic spectrum access (DSA) and resource allocation. However, due to the unique characteristics of spectrum data, existing methods based on the time or frequency domain often struggle to…
Motivated by electricity consumption metering, we extend existing nonnegative matrix factorization (NMF) algorithms to use linear measurements as observations, instead of matrix entries. The objective is to estimate multiple time series at…
We consider a dynamic method, based on synchronization and adaptive control, to estimate unknown parameters of a nonlinear dynamical system from a given scalar chaotic time series. We present an important extension of the method when time…
Context: Several approaches to estimate frequency, phase and amplitude errors in time series analyses were reported in the literature, but they are either time consuming to compute, grossly overestimating the error, or are based on…
Understanding the singular value spectrum of a matrix $A \in \mathbb{R}^{n \times n}$ is a fundamental task in countless applications. In matrix multiplication time, it is possible to perform a full SVD and directly compute the singular…
An algorithm is presented to update the multi-fractal spectrum of a time series in constant time when new data arrives. The discrete wavelet transform (DWT) of the time series is first updated for the new data value. This is done optimally…
Line spectral estimation theory aims to estimate the off-the-grid spectral components of a time signal with optimal precision. Recent results have shown that it is possible to recover signals having sparse line spectra from few temporal…
In this paper, we discuss the development of a sublinear sparse Fourier algorithm for high-dimensional data. In ``Adaptive Sublinear Time Fourier Algorithm" by D. Lawlor, Y. Wang and A. Christlieb (2013), an efficient algorithm with…
This paper is devoted to the error analysis of a time-spectral algorithm for fractional diffusion problems of order $\alpha$ ($0 < \alpha < 1$). The solution regularity in the Sobolev space is revisited, and new regularity results in the…