Related papers: Statistical Guarantees for Local Spectral Clusteri…

Spectral algorithms are graph partitioning algorithms that partition a node set of a graph into groups by using a spectral embedding map. Clustering techniques based on the algorithms are referred to as spectral clustering and are widely…

We propose and analyze two algorithms for maintaining approximate Personalized PageRank (PPR) vectors on a dynamic graph, where edges are added or deleted. Our algorithms are natural dynamic versions of two known local variations of power…

We study differentially private (DP) algorithms for recovering clusters in well-clustered graphs, which are graphs whose vertex set can be partitioned into a small number of sets, each inducing a subgraph of high inner conductance and small…

Local community detection consists of finding a group of nodes closely related to the seeds, a small set of nodes of interest. Such group of nodes are densely connected or have a high probability of being connected internally than their…

We analyse a mean-field model of Personalized PageRank on the Erdos-Renyi random graph containing a denser planted Erdos-Renyi subgraph. We investigate the regimes where the values of Personalized PageRank concentrate around the mean-field…

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…

Spectral clustering approaches have led to well-accepted algorithms for finding accurate clusters in a given dataset. However, their application to large-scale datasets has been hindered by computational complexity of eigenvalue…

In the context of clustering, we consider a generative model in a Euclidean ambient space with clusters of different shapes, dimensions, sizes and densities. In an asymptotic setting where the number of points becomes large, we obtain…

Among community detection methods, spectral clustering enjoys two desirable properties: computational efficiency and theoretical guarantees of consistency. Most studies of spectral clustering consider only the edges of a network as input to…

Graphs have become increasingly popular in modeling structures and interactions in a wide variety of problems during the last decade. Graph-based clustering and semi-supervised classification techniques have shown impressive performance.…

Clustering of data sets is a standard problem in many areas of science and engineering. The method of spectral clustering is based on embedding the data set using a kernel function, and using the top eigenvectors of the normalized Laplacian…

Local graph clustering and the closely related seed set expansion problem are primitives on graphs that are central to a wide range of analytic and learning tasks such as local clustering, community detection, nodes ranking and feature…

Spectral clustering is a widely used algorithm to find clusters in networks. Several researchers have studied the stability of spectral clustering under local differential privacy with the additional assumption that the underlying networks…

We present new results on community recovery based on the PageRank Nibble algorithm on a sparse directed stochastic block model (dSBM). Our results are based on a characterization of the local weak limit of the dSBM and the limiting…

Semantic segmentation with fine-grained pixel-level accuracy is a fundamental component of a variety of computer vision applications. However, despite the large improvements provided by recent advances in the architectures of convolutional…

PageRank is a well-known centrality measure for the web used in search engines, representing the importance of each web page. In this paper, we follow the line of recent research on the development of distributed algorithms for computation…

The present paper is devoted to clustering geometric graphs. While the standard spectral clustering is often not effective for geometric graphs, we present an effective generalization, which we call higher-order spectral clustering. It…

PageRank (PR) is a fundamental tool for assessing the relative importance of the nodes in a network. In this paper, we propose a measure, weighted PageRank (WPR), extended from the classical PR for weighted, directed networks with possible…

In this paper, we present the first differentially private clustering method for arbitrary-shaped node clusters in a graph. This algorithm takes as input only an approximate Minimum Spanning Tree (MST) $\mathcal{T}$ released under weight…

Unsupervised node clustering (or community detection) is a classical graph learning task. In this paper, we study algorithms, which exploit the geometry of the graph to identify densely connected substructures, which form clusters or…