Related papers: Spectral Algorithms for Temporal Graph Cuts

Spectral Clustering is one of the most traditional methods to solve segmentation problems. Based on Normalized Cuts, it aims at partitioning an image using an objective function defined by a graph. Despite their mathematical attractiveness,…

Graphs are a natural representation of data from various contexts, such as social connections, the web, road networks, and many more. In the last decades, many of these networks have become enormous, requiring efficient algorithms to cut…

A common way of partitioning graphs is through minimum cuts. One drawback of classical minimum cut methods is that they tend to produce small groups, which is why more balanced variants such as normalized and ratio cuts have seen more…

Spectral graph theory is well known and widely used in computer vision. In this paper, we analyze image segmentation algorithms that are based on spectral graph theory, e.g., normalized cut, and show that there is a natural connection…

Modeling information that resides on vertices of large graphs is a key problem in several real-life applications, ranging from social networks to the Internet-of-things. Signal Processing on Graphs and, in particular, graph wavelets can…

Graphs are widely used in various fields of computer science. They have also found application in unrelated areas, leading to a diverse range of problems. These problems can be modeled as relationships between entities in various contexts,…

We propose a novel framework for learning time-varying graphs from spatiotemporal measurements. Given an appropriate prior on the temporal behavior of signals, our proposed method can estimate time-varying graphs from a small number of…

We study deterministic algorithms for computing graph cuts, with focus on two fundamental problems: balanced sparse cut and $k$-vertex connectivity for small $k$ ($k=O(\polylog n)$). Both problems can be solved in near-linear time with…

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…

Graphs naturally appear in several real-world contexts including social networks, the web network, and telecommunication networks. While the analysis and the understanding of graph structures have been a central area of study in algorithm…

Spectral clustering methods which are frequently used in clustering and community detection applications are sensitive to the specific graph constructions particularly when imbalanced clusters are present. We show that ratio cut (RCut) or…

Temporal graphs provide a useful model for many real-world networks. Unfortunately the majority of algorithmic problems we might consider on such graphs are intractable. There has been recent progress in defining structural parameters which…

Shortcut sets are a vital instrument for reducing the diameter of a static graph and, consequently, its shortest path complexity, which is relevant in numerous subfields of graph theory. We explore the notion of shortcut sets in temporal…

Several classical combinatorial problems have been considered and analysed on temporal graphs. Recently, a variant of Vertex Cover on temporal graphs, called MinTimelineCover, has been introduced to summarize timeline activities in social…

We consider the (exact, minimum) $k$-cut problem: given a graph and an integer $k$, delete a minimum-weight set of edges so that the remaining graph has at least $k$ connected components. This problem is a natural generalization of the…

Spectral clustering is sensitive to how graphs are constructed from data particularly when proximal and imbalanced clusters are present. We show that Ratio-Cut (RCut) or normalized cut (NCut) objectives are not tailored to imbalanced data…

We consider the classical Minimum Balanced Cut problem: given a graph $G$, compute a partition of its vertices into two subsets of roughly equal volume, while minimizing the number of edges connecting the subsets. We present the first {\em…

We describe a new sampling-based method to determine cuts in an undirected graph. For a graph (V, E), its cycle space is the family of all subsets of E that have even degree at each vertex. We prove that with high probability, sampling the…

Coresets have become an invaluable tool for solving $k$-means and kernel $k$-means clustering problems on large datasets with small numbers of clusters. On the other hand, spectral clustering works well on sparse graphs and has recently…

In this work we provide a new technique to design fast approximation algorithms for graph problems where the points of the graph lie in a metric space. Specifically, we present a sampling approach for such metric graphs that, using a…