Related papers: Constructing Linear-Sized Spectral Sparsification …
In this paper we focus on subsampling stationary random processes that reside on the vertices of undirected graphs. Second-order stationary graph signals are obtained by filtering white noise and they admit a well-defined power spectrum.…
Constructing a sparse spanning subgraph is a fundamental primitive in graph theory. In this paper, we study this problem in the Centralized Local model, where the goal is to decide whether an edge is part of the spanning subgraph by…
We study vertex sparsification for preserving cuts. Given a graph $G$ with a subset $|T|=k$ of its vertices called terminals, a \emph{quality-$q$ cut sparsifier} is a graph $G'$ that contains $T$, such that, for any partition $(T_1,T_2)$ of…
Suppose we are given an $n$-node, $m$-edge input graph $G$, and the goal is to compute a spanning subgraph $H$ on $O(n)$ edges. This can be achieved in linear $O(m + n)$ time via breadth-first search. But can we hope for \emph{sublinear}…
Reconstruction of undersampled periodic signals of unknown period is an important signal processing operation. It is especially difficult operation when the sequences of samples are short and no information on the inter-sequence time…
Some elements of the theory and algorithmics corresponding to the computation of semilinear sparse models for discrete-time signals are presented. In this study, we will focus on approximately eventually periodic discrete-time signals, that…
We revisit the asymptotic analysis of probabilistic construction of adjacency matrices of expander graphs proposed in [4]. With better bounds we derived a new reduced sample complexity for the number of nonzeros per column of these…
For an undirected/directed hypergraph $G=(V,E)$, its Laplacian $L_G\colon\mathbb{R}^V\to \mathbb{R}^V$ is defined such that its ``quadratic form'' $\boldsymbol{x}^\top L_G(\boldsymbol{x})$ captures the cut information of $G$. In particular,…
Constructing a similarity graph from a set $X$ of data points in $\mathbb{R}^d$ is the first step of many modern clustering algorithms. However, typical constructions of a similarity graph have high time complexity, and a quadratic space…
In practical machine learning systems, graph based data representation has been widely used in various learning paradigms, ranging from unsupervised clustering to supervised classification. Besides those applications with natural graph or…
The formation trajectory planning using complete graphs to model collaborative constraints becomes computationally intractable as the number of drones increases due to the curse of dimensionality. To tackle this issue, this paper presents a…
We consider the minimum cut problem in undirected, weighted graphs. We give a simple algorithm to find a minimum cut that $2$-respects (cuts two edges of) a spanning tree $T$ of a graph $G$. This procedure can be used in place of the…
Flow sparsification is a classic graph compression technique which, given a capacitated graph $G$ on $k$ terminals, aims to construct another capacitated graph $H$, called a flow sparsifier, that preserves, either exactly or approximately,…
We propose a convex and fast signal reconstruction method for block sparsity under arbitrary linear transform with unknown block structure. The proposed method is a generalization of the similar existing method and can reconstruct signals…
In this paper, we present and analyze a simple and robust spectral algorithm for the stochastic block model with $k$ blocks, for any $k$ fixed. Our algorithm works with graphs having constant edge density, under an optimal condition on the…
This paper explores sparsification methods as a form of regularization in Graph Neural Networks (GNNs) to address high memory usage and computational costs in large-scale graph applications. Using techniques from Network Science and Machine…
Given an order-$d$ tensor $\tensor A \in \R^{n \times n \times...\times n}$, we present a simple, element-wise sparsification algorithm that zeroes out all sufficiently small elements of $\tensor A$, keeps all sufficiently large elements of…
A cut sparsifier is a reweighted subgraph that maintains the weights of the cuts of the original graph up to a multiplicative factor of $(1\pm\epsilon)$. This paper considers computing cut sparsifiers of weighted graphs of size $O(n\log…
We study a new linear up to quadratic time algorithm for linear regression in the absence of strong assumptions on the underlying distributions of samples, and in the presence of outliers. The goal is to design a procedure which comes with…
Graph Neural Networks (GNNs) play a pivotal role in graph-based tasks for their proficiency in representation learning. Among the various GNN methods, spectral GNNs employing polynomial filters have shown promising performance on tasks…