Related papers: A short-graph Fourier transform via personalized P…
A graph short-time Fourier transform is defined using the eigenvectors of the graph Laplacian and a graph heat kernel as a window parametrized by a non-negative time parameter $t$. We show that the corresponding Gabor-like system forms a…
Multivariate time series forecasting is a pivotal task in several domains, including financial planning, medical diagnostics, and climate science. This paper presents the Neural Fourier Transform (NFT) algorithm, which combines…
We propose a variant of the Rapidly Exploring Random Tree Star (RRT$^{\star}$) algorithm to synthesize trajectories satisfying a given spatio-temporal specification expressed in a fragment of Signal Temporal Logic (STL) for linear systems.…
Digital Transforms have important applications on subjects such as channel coding, cryptography and digital signal processing. In this paper, two Fourier Transforms are considered, the discrete time Fourier transform (DTFT) and the finite…
Truncated Fourier Transforms (TFTs), first introduced by Van der Hoeven, refer to a family of algorithms that attempt to smooth "jumps" in complexity exhibited by FFT algorithms. We present an in-place TFT whose time complexity, measured in…
Implementing linear transformations is a key task in the decentralized signal processing framework, which performs learning tasks on data sets distributed over multi-node networks. That kind of network can be represented by a graph.…
An emerging way of tackling the dimensionality issues arising in the modeling of a multivariate process is to assume that the inherent data structure can be captured by a graph. Nevertheless, though state-of-the-art graph-based methods have…
With the wide application of spectral and algebraic theory in discrete signal processing techniques in the field of graph signal processing, an increasing number of signal processing methods have been proposed, such as the graph Fourier…
Computing the Sparse Fast Fourier Transform(sFFT) of a K-sparse signal of size N has emerged as a critical topic for a long time. The sFFT algorithms decrease the runtime and sampling complexity by taking advantage of the signal inherent…
Time series forecasting is a long-standing problem in statistics and machine learning. One of the key challenges is processing sequences with long-range dependencies. To that end, a recent line of work applied the short-time Fourier…
We propose novel two-channel filter banks for signals on graphs. Our designs can be applied to arbitrary graphs, given a positive semi definite variation operator, while using arbitrary vertex partitions for downsampling. The proposed…
Basic operations in graph signal processing consist in processing signals indexed on graphs either by filtering them, to extract specific part out of them, or by changing their domain of representation, using some transformation or…
Short term Load Forecasting (STLF) plays an important role in traditional and modern power systems. Most STLF models predominantly exploit temporal dependencies from historical data to predict future consumption. Nowadays, with the…
Time-frequency (TF) representation of non-stationary signals typically requires the effective concentration of energy distribution along the instantaneous frequency (IF) ridge, which exhibits intrinsic sparsity. Inspired by the sparse…
Using projections on the (generalized) eigenvectors associated to matrices that characterize the topological structure, several authors have constructed generalizations of the Fourier transform on graphs. By exploring mappings of the…
Multimodal time series forecasting is crucial in real-world applications, where decisions depend on both numerical data and contextual signals. The core challenge is to effectively combine temporal numerical patterns with the context…
It recently has been found that methods of the statistical theories of spectra can be a useful tool in the analysis of spectra far from levels of Hamiltonian systems. Several examples originate from areas, such as quantitative linguistics…
Spectral analysis in conjunction with discrete data in one and more dimensions can become a challenging task, because the methods are sometimes difficult to understand. This paper intends to provide an overview about the usage of the…
Many real-world relational systems, such as social networks and biological systems, contain dynamic interactions. When learning dynamic graph representation, it is essential to employ sequential temporal information and geometric structure.…
In this paper, we combine ideas from two different scientific traditions: 1) graph transformation systems (GTSs) stemming from the theory of formal languages and concurrency, and 2) mean field approximations (MFAs), a collection of…