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Graph clustering under the framework of differential privacy, which aims to process graph-structured data while protecting individual privacy, has been receiving increasing attention. Despite significant achievements in current research,…

Consistency is a key property of all statistical procedures analyzing randomly sampled data. Surprisingly, despite decades of work, little is known about consistency of most clustering algorithms. In this paper we investigate consistency of…

In this paper, we propose a speed-up approach for subclass discriminant analysis and formulate a novel efficient multi-view solution to it. The speed-up approach is developed based on graph embedding and spectral regression approaches that…

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…

We present a parallelized bijective graph matching algorithm that leverages seeds and is designed to match very large graphs. Our algorithm combines spectral graph embedding with existing state-of-the-art seeded graph matching procedures.…

Learning a graph with a specific structure is essential for interpretability and identification of the relationships among data. It is well known that structured graph learning from observed samples is an NP-hard combinatorial problem. In…

This paper discusses clustering and latent semantic indexing (LSI) aspects of the singular value decomposition (SVD). The purpose of this paper is twofold. The first is to give an explanation on how and why the singular vectors can be used…

Spectral clustering is a technique that clusters elements using the top few eigenvectors of their (possibly normalized) similarity matrix. The quality of spectral clustering is closely tied to the convergence properties of these principal…

Graph clustering, or community detection, is the task of identifying groups of closely related objects in a large network. In this paper we introduce a new community-detection framework called LambdaCC that is based on a specially weighted…

Semi-supervised clustering is a basic problem in various applications. Most existing methods require knowledge of the ideal cluster number, which is often difficult to obtain in practice. Besides, satisfying the must-link constraints is…

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.…

In network data analysis, it is becoming common to work with a collection of graphs that exhibit \emph{heterogeneity}. For example, neuroimaging data from patient cohorts are increasingly available. A critical analytical task is to identify…

Spectral clustering is a popular tool in network data analysis, with applications in a variety of scientific application areas. However, many studies have shown that classical spectral clustering does not perform well on certain network…

In the first part of this paper, we survey results that are associated with three types of Laplacian matrices:difference, normalized, and signless. We derive eigenvalue and eigenvector formulaes for paths and cycles using circulant matrices…

Large-scale multi-layer networks with large numbers of nodes, edges, and layers arise across various domains, which poses a great computational challenge for the downstream analysis. In this paper, we develop an efficient randomized…

We present a space and time efficient practical parallel algorithm for approximating the diameter of massive weighted undirected graphs on distributed platforms supporting a MapReduce-like abstraction. The core of the algorithm is a…

(Hyper)Graph decomposition is a family of problems that aim to break down large (hyper)graphs into smaller sub(hyper)graphs for easier analysis. The importance of this lies in its ability to enable efficient computation on large and complex…

Web-based interactions can be frequently represented by an attributed graph, and node clustering in such graphs has received much attention lately. Multiple efforts have successfully applied Graph Convolutional Networks (GCN), though with…

Graph based clustering is one of the major clustering methods. Most of it work in three separate steps: similarity graph construction, clustering label relaxing and label discretization with k-means. Such common practice has three…

This paper shows that graph spectral embedding using the random walk Laplacian produces vector representations which are completely corrected for node degree. Under a generalised random dot product graph, the embedding provides uniformly…