Related papers: On Sparse Graph Fourier Transform
In this paper a deterministic sparse Fourier transform algorithm is presented which breaks the quadratic-in-sparsity runtime bottleneck for a large class of periodic functions exhibiting structured frequency support. These functions…
Graph filtering is a fundamental tool in graph signal processing. Polynomial graph filters (PGFs), defined as polynomials of a fundamental graph operator, can be implemented in the vertex domain, and usually have a lower complexity than…
We address the problem of prediction of multivariate data process using an underlying graph model. We develop a method that learns a sparse partial correlation graph in a tuning-free and computationally efficient manner. Specifically, the…
Graph signal processing (GSP) provides a powerful framework for analyzing signals arising in a variety of domains. In many applications of GSP, multiple network structures are available, each of which captures different aspects of the same…
We present a new deterministic algorithm for the sparse Fourier transform problem, in which we seek to identify k << N significant Fourier coefficients from a signal of bandwidth N. Previous deterministic algorithms exhibit quadratic…
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…
We introduce the computational problem of graphlet transform of a sparse large graph. Graphlets are fundamental topology elements of all graphs/networks. They can be used as coding elements to encode graph-topological information at…
In this paper, we present a novel generalization of the graph Fourier transform (GFT). Our approach is based on separately considering the definitions of signal energy and signal variation, leading to several possible orthonormal GFTs. Our…
Graph Neural Networks (GNN) exhibit superior performance in graph representation learning, but their inference cost can be high, due to an aggregation operation that can require a memory fetch for a very large number of nodes. This…
Given a time series vector, how can we efficiently compute a specified part of Fourier coefficients? Fast Fourier transform (FFT) is a widely used algorithm that computes the discrete Fourier transform in many machine learning applications.…
Modern compression systems use linear transformations in their encoding and decoding processes, with transforms providing compact signal representations. While multiple data-dependent transforms for image/video coding can adapt to diverse…
Graph inference plays an essential role in machine learning, pattern recognition, and classification. Signal processing based approaches in literature generally assume some variational property of the observed data on the graph. We make a…
In this paper we consider Sparse Fourier Transform (SFT) algorithms for approximately computing the best $s$-term approximation of the Discrete Fourier Transform (DFT) $\mathbf{\hat{f}} \in \mathbb{C}^N$ of any given input vector…
The FFT algorithm that implements the discrete Fourier transform is considered one of the top ten algorithms of the $20$th century. Its main strengths are the low computational cost of $\mathcal{O}(n \log n$) and its stability. It is one of…
The problem of computing the Fourier Transform of a signal whose spectrum is dominated by a small number $k$ of frequencies quickly and using a small number of samples of the signal in time domain (the Sparse FFT problem) has received…
In this paper a sublinear time algorithm is presented for the reconstruction of functions that can be represented by just few out of a potentially large candidate set of Fourier basis functions in high spatial dimensions, a so-called…
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…
Graph spectral representations are fundamental in graph signal processing, offering a rigorous framework for analyzing and processing graph-structured data. The graph fractional Fourier transform (GFRFT) extends the classical graph Fourier…
Graph fractional Fourier transform (GFRFT) is an extension of graph Fourier transform (GFT) that provides an additional fractional analysis tool for graph signal processing (GSP) by generalizing temporal-vertex domain Fourier analysis to…
Fast Fourier Transform (FFT) is one of the most important tools in digital signal processing. FFT costs O(N \log N) for transforming a signal of length N. Recently, Sparse Fourier Transform (SFT) has emerged as a critical issue addressing…