Related papers: Statistical Guarantees for Local Spectral Clusteri…

Spectral clustering is popular among practitioners and theoreticians alike. While performance guarantees for spectral clustering are well understood, recent studies have focused on enforcing ``fairness'' in clusters, requiring them to be…

Network embedding has numerous practical applications and has received extensive attention in graph learning, which aims at mapping vertices into a low-dimensional and continuous dense vector space by preserving the underlying structural…

Spectral clustering is a fast and popular algorithm for finding clusters in networks. Recently, Chaudhuri et al. (2012) and Amini et al.(2012) proposed inspired variations on the algorithm that artificially inflate the node degrees for…

Spectral clustering is widely used in practice due to its flexibility, computational efficiency, and well-understood theoretical performance guarantees. Recently, spectral clustering has been studied to find balanced clusters under…

In the planted partition problem, the $n$ vertices of a random graph are partitioned into $k$ "clusters," and edges between vertices in the same cluster and different clusters are included with constant probability $p$ and $q$, respectively…

Spectral clustering algorithms typically require a priori selection of input parameters such as the number of clusters, a scaling parameter for the affinity measure, or ranges of these values for parameter tuning. Despite efforts for…

Probabilistic relaxations of graph cuts offer a differentiable alternative to spectral clustering, enabling end-to-end and online learning without eigendecompositions, yet prior work centered on RatioCut and lacked general guarantees and…

Graph clustering is an important technique to understand the relationships between the vertices in a big graph. In this paper, we propose a novel random-walk-based graph clustering method. The proposed method restricts the reach of the…

Spectral clustering is a popular and versatile clustering method based on a relaxation of the normalised graph cut objective. Despite its popularity, however, there is no single agreed upon method for tuning the important scaling parameter,…

Graph clustering is a fundamental problem that has been extensively studied both in theory and practice. The problem has been defined in several ways in literature and most of them have been proven to be NP-Hard. Due to their high practical…

Local Polynomial Regression (LPR) is a powerful tool for nonparametric smoothing, yet it traditionally suffers from a "Euclidean tautology": the variables used to define the local neighborhood are identical to those used in the polynomial…

We propose two spectral algorithms for partitioning nodes in directed graphs respectively with a cyclic and an acyclic pattern of connection between groups of nodes. Our methods are based on the computation of extremal eigenvalues of the…

This article explores and analyzes the unsupervised clustering of large partially observed graphs. We propose a scalable and provable randomized framework for clustering graphs generated from the stochastic block model. The clustering is…

We revisit the theoretical performances of Spectral Clustering, a classical algorithm for graph partitioning that relies on the eigenvectors of a matrix representation of the graph. Informally, we show that Spectral Clustering works well as…

Local Polynomial Regression (LPR) is a widely used nonparametric method for modeling complex relationships due to its flexibility and simplicity. It estimates a regression function by fitting low-degree polynomials to localized subsets of…

Markov networks are widely studied and used throughout multivariate statistics and computer science. In particular, the problem of learning the structure of Markov networks from data without invoking chordality assumptions in order to…

We present a simple spectral approach to the well-studied constrained clustering problem. It captures constrained clustering as a generalized eigenvalue problem with graph Laplacians. The algorithm works in nearly-linear time and provides…

Personalized PageRank (PPR) is a critical measure of the importance of a node t to a source node s in a graph. The Single-Source PPR (SSPPR) query computes the PPR's of all the nodes with respect to s on a directed graph $G$ with $n$ nodes…

Personalalized PageRank uses random walks to determine the importance or authority of nodes in a graph from the point of view of a given source node. Much past work has considered how to compute personalized PageRank from a given source…

Spectral algorithms are classic approaches to clustering and community detection in networks. However, for sparse networks the standard versions of these algorithms are suboptimal, in some cases completely failing to detect communities even…