Related papers: Local Differential Privacy-Preserving Spectral Clu…
Blowfish privacy is a recent generalisation of differential privacy that enables improved utility while maintaining privacy policies with semantic guarantees, a factor that has driven the popularity of differential privacy in computer…
This paper develops a framework for privatizing the spectrum of the graph Laplacian of an undirected graph using differential privacy. We consider two privacy formulations. The first obfuscates the presence of edges in the graph and the…
Graph neural networks (GNNs) have gained an increasing amount of popularity due to their superior capability in learning node embeddings for various graph inference tasks, but training them can raise privacy concerns. To address this, we…
Symmetric edge polytopes are lattice polytopes associated with finite simple graphs that are of interest in both theory and applications. We investigate the facet structure of symmetric edge polytopes for various models of random graphs.…
We propose a spectral clustering method based on local principal components analysis (PCA). After performing local PCA in selected neighborhoods, the algorithm builds a nearest neighbor graph weighted according to a discrepancy between the…
Graph embeddings have emerged as a powerful tool for understanding the structure of graphs. Unlike classical spectral methods, recent methods such as DeepWalk, Node2Vec, etc. are based on solving nonlinear optimization problems on the…
For data represented by networks, the community structure of the underlying graph is of great interest. A classical clustering problem is to uncover the overall ``best'' partition of nodes in communities. Here, a more elaborate description…
The community structure of complex networks reveals both their organization and hidden relationships among their constituents. Most community detection methods currently available are not deterministic, and their results typically depend on…
Given the widespread popularity of spectral clustering (SC) for partitioning graph data, we study a version of constrained SC in which we try to incorporate the fairness notion proposed by Chierichetti et al. (2017). According to this…
Spectral clustering has been widely used for community detection in network sciences. While its empirical successes are well-documented, a clear theoretical understanding, particularly for sparse networks where degrees are much smaller than…
We consider the problem of spectral clustering under group fairness constraints, where samples from each sensitive group are approximately proportionally represented in each cluster. Traditional fair spectral clustering (FSC) methods…
Spectral clustering and its extensions usually consist of two steps: (1) constructing a graph and computing the relaxed solution; (2) discretizing relaxed solutions. Although the former has been extensively investigated, the discretization…
Reproduction numbers are widely used for the estimation and prediction of epidemic spreading processes over networks. However, conventional reproduction numbers of an overall network do not indicate where an epidemic is spreading.…
The theoretical analysis of spectral clustering mainly focuses on consistency, while there is relatively little research on its generalization performance. In this paper, we study the excess risk bounds of the popular spectral clustering…
We propose a node clustering method for time-varying graphs based on the assumption that the cluster labels are changed smoothly over time. Clustering is one of the fundamental tasks in many science and engineering fields including signal…
Bipartite graphs, formed by two vertex layers, arise as a natural fit for modeling the relationships between two groups of entities. In bipartite graphs, common neighborhood computation between two vertices on the same vertex layer is a…
This paper establishes the consistency of spectral approaches to data clustering. We consider clustering of point clouds obtained as samples of a ground-truth measure. A graph representing the point cloud is obtained by assigning weights to…
Large graphs commonly appear in social networks, knowledge graphs, recommender systems, life sciences, and decision making problems. Summarizing large graphs by their high level properties is helpful in solving problems in these settings.…
The eigendeomposition of nearest-neighbor (NN) graph Laplacian matrices is the main computational bottleneck in spectral clustering. In this work, we introduce a highly-scalable, spectrum-preserving graph sparsification algorithm that…
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,…