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Networks, which represent agents and interactions between them, arise in myriad applications throughout the sciences, engineering, and even the humanities. To understand large-scale structure in a network, a common task is to cluster a…
In the misspecified spectral algorithms problem, researchers usually assume the underground true function $f_{\rho}^{*} \in [\mathcal{H}]^{s}$, a less-smooth interpolation space of a reproducing kernel Hilbert space (RKHS) $\mathcal{H}$ for…
Mesoscopic pattern extraction (MPE) is the problem of finding a partition of the nodes of a complex network that maximizes some objective function. Many well-known network inference problems fall in this category, including, for instance,…
We present a solution to scale spectral algorithms for learning sequence functions. We are interested in the case where these functions are sparse (that is, for most sequences they return 0). Spectral algorithms reduce the learning problem…
There has been a recent interest in understanding the power of local algorithms for optimization and inference problems on sparse graphs. Gamarnik and Sudan (2014) showed that local algorithms are weaker than global algorithms for finding…
We consider the problem of exact community recovery in the Labeled Stochastic Block Model (LSBM) with $k$ communities, where each pair of vertices is associated with a label from the set $\{0,1, \dots, L\}$. A pair of vertices from…
One of the most widely used methods for community detection in networks is the maximization of the quality function known as modularity. Of the many maximization techniques that have been used in this context, some of the most conceptually…
Real-world networks usually have community structure, that is, nodes are grouped into densely connected communities. Community detection is one of the most popular and best-studied research topics in network science and has attracted…
In an era of unprecedented deluge of (mostly unstructured) data, graphs are proving more and more useful, across the sciences, as a flexible abstraction to capture complex relationships between complex objects. One of the main challenges…
Graph is a highly generic and diverse representation, suitable for almost any data processing problem. Spectral graph theory has been shown to provide powerful algorithms, backed by solid linear algebra theory. It thus can be extremely…
Neural node embeddings have recently emerged as a powerful representation for supervised learning tasks involving graph-structured data. We leverage this recent advance to develop a novel algorithm for unsupervised community discovery in…
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 analyze the performance of spectral clustering for community extraction in stochastic block models. We show that, under mild conditions, spectral clustering applied to the adjacency matrix of the network can consistently recover hidden…
Stochastic block models (SBMs) are a very commonly studied network model for community detection algorithms. In the standard form of an SBM, the $n$ vertices (or nodes) of a graph are generally divided into multiple pre-determined…
Spectral clustering has become one of the most popular algorithms in data clustering and community detection. We study the performance of classical two-step spectral clustering via the graph Laplacian to learn the stochastic block model.…
This paper is motivated by the reconstruction problem on the sparse stochastic block model. Mossel, et. al. proved that a reconstruction algorithm that recovers an optimal fraction of the communities in the symmetric, 2-community case. The…
Community detection in multi-layer networks is a crucial problem in network analysis. In this paper, we analyze the performance of two spectral clustering algorithms for community detection within the framework of the multi-layer…
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…
In this paper, we study the information theoretic bounds for exact recovery in sub-hypergraph models for community detection. We define a general model called the $m-$uniform sub-hypergraph stochastic block model ($m-$ShSBM). Under the…
In recent years, spectral clustering has become a standard method for data analysis used in a broad range of applications. In this paper we propose a new class of algorithms for multiway spectral clustering based on optimization of a…