This work studies the classical spectral clustering algorithm which embeds the vertices of
some graph G=(V_G, E_G) into R^ k using k eigenvectors of some matrix of G, and applies k …

Clustering is an important topic in algorithms, and has a number of applications in machine
learning, computer vision, statistics, and several other research disciplines. Traditional …

Hierarchical clustering studies a recursive partition of a data set into clusters of successively
smaller size, and is a fundamental problem in data analysis. In this work we study the cost …

Given an underlying graph, we consider the following dynamics: Initially, each node locally
chooses a value in {-1,1\}, uniformly at random and independently of other nodes. Then, in …

Spectral clustering is a popular and effective algorithm designed to find $ k $ clusters in a
graph $ G $. In the classical spectral clustering algorithm, the vertices of $ G $ are …

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 …

Consider the following asynchronous, opportunistic communication model over a graph $ G
$: in each round, one edge is activated uniformly and independently at random and (only) its …

Graph sparsification is a powerful tool to approximate an arbitrary graph and has been used
in machine learning over graphs. As real-world networks are becoming very large and …

We investigate the behavior of a simple majority dynamics on networks of agents whose
interaction topology exhibits a community structure. By leveraging recent advancements in …

Attempts to discover knowledge through data are gradually becoming diversified to
understand complex aspects of social phenomena. Graph data analysis, which models and …