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Clustering short text embeddings is a foundational task in natural language processing, yet remains challenging due to the need to specify the number of clusters in advance. We introduce a scalable spectral method that estimates the number…

Spectral clustering is a key research topic in the field of machine learning and data mining. Most of the existing spectral clustering algorithms are built upon Gaussian Laplacian matrices, which are sensitive to parameters. We propose a…

We present a method to estimate block membership of nodes in a random graph generated by a stochastic blockmodel. We use an embedding procedure motivated by the random dot product graph model, a particular example of the latent position…

As an indicator of the stability of spectral clustering of an undirected weighted graph into $k$ clusters, the $k$th spectral gap of the graph Laplacian is often considered. The $k$th spectral gap is characterized in this paper as an…

We build upon recent advances in graph signal processing to propose a faster spectral clustering algorithm. Indeed, classical spectral clustering is based on the computation of the first k eigenvectors of the similarity matrix' Laplacian,…

The k-nearest neighbors (kNN) algorithm is a cornerstone of non-parametric classification in artificial intelligence, yet its deployment in large-scale applications is persistently constrained by the computational trade-off between…

Spectral clustering is a popular algorithm that clusters points using the eigenvalues and eigenvectors of Laplacian matrices derived from the data. For years, spectral clustering has been working mysteriously. This paper explains spectral…

Graph Neural Network (GNN) on streaming graphs has gained increasing popularity. However, its practical deployment remains challenging, as the inference process relies on Runtime Embedding Computation (RTEC) to capture recent graph changes.…

The unsupervised learning of community structure, in particular the partitioning vertices into clusters or communities, is a canonical and well-studied problem in exploratory graph analysis. However, like most graph analyses the…

Graph-Laplacians and their spectral embeddings play an important role in multiple areas of machine learning. This paper is focused on graph-Laplacian dimension reduction for the spectral clustering of data as a primary application. Spectral…

We study random graphs with possibly different edge probabilities in the challenging sparse regime of bounded expected degrees. Unlike in the dense case, neither the graph adjacency matrix nor its Laplacian concentrate around their…

These are notes on the method of normalized graph cuts and its applications to graph clustering. I provide a fairly thorough treatment of this deeply original method due to Shi and Malik, including complete proofs. I include the necessary…

While a growing body of literature has been studying new Graph Neural Networks (GNNs) that work on both homophilic and heterophilic graphs, little has been done on adapting classical GNNs to less-homophilic graphs. Although the ability to…

Graph neural networks (GNNs) based methods have achieved impressive performance on node clustering task. However, they are designed on the homophilic assumption of graph and clustering on heterophilic graph is overlooked. Due to the lack of…

Graph clustering discovers groups or communities within networks. Deep learning methods such as autoencoders (AE) extract effective clustering and downstream representations but cannot incorporate rich structural information. While Graph…

Given a weighted undirected graph, a number of clusters $k$, and an exponent $z$, the goal in the $(k, z)$-clustering problem on graphs is to select $k$ vertices as centers that minimize the sum of the distances raised to the power $z$ of…

Classifying nodes in a graph is a common problem. The ideal classifier must adapt to any imbalances in the class distribution. It must also use information in the clustering structure of real-world graphs. Existing Graph Neural Networks…

Existing graph clustering networks heavily rely on a predefined yet fixed graph, which can lead to failures when the initial graph fails to accurately capture the data topology structure of the embedding space. In order to address this…

The prevalence of real-world multi-view data makes incomplete multi-view clustering (IMVC) a crucial research. The rapid development of Graph Neural Networks (GNNs) has established them as one of the mainstream approaches for multi-view…

Though graph representation learning (GRL) has made significant progress, it is still a challenge to extract and embed the rich topological structure and feature information in an adequate way. Most existing methods focus on local structure…