arXiv research

Optimizes graph spectral density learning for large networks.

This study bridges the gap between spatial and spectral GNNs.

Regularization improves spectral embedding by focusing on the largest blocks.

The goal of this paper is to show that there exists a simple, yet universal statistical logic of spectral graph analysis by recasting it into a nonparametric function estimation problem. The prescribed viewpoint appears to be good enough to accommodate most of the existing spectral graph techniques as a consequence of …

Graph convolutional networks fail to use eigenvectors beyond the first, unlike spectral embedding.

Spectral algorithms are graph partitioning algorithms that partition a node set of a graph into groups by using a spectral embedding map. Clustering techniques based on the algorithms are referred to as spectral clustering and are widely used in data analysis. To gain a better understanding of why spectral clustering i…

A new method boosts graph neural networks by preventing over-smoothing and over-squashing.

Spectral clustering (SC) is a popular clustering technique to find strongly connected communities on a graph. SC can be used in Graph Neural Networks (GNNs) to implement pooling operations that aggregate nodes belonging to the same cluster. However, the eigendecomposition of the Laplacian is expensive and, since cluste…

Develops mixed quantization for graph vector bundles.

New spectral clustering method using LASSO regularization for robust graph partitioning.

Developed a framework for designing filters in spectral GCNNs with improved performance.

Graph Laplacians and machine learning predict properties of finite graphs.

A novel 3D shape registration method using spectral graph embedding and probabilistic matching.

Spectral clustering has become one of the most widely used clustering techniques when the structure of the individual clusters is non-convex or highly anisotropic. Yet, despite its immense popularity, there exists fairly little theory about performance guarantees for spectral clustering. This issue is partly due to the…

Graph clustering is a basic technique in machine learning, and has widespread applications in different domains. While spectral techniques have been successfully applied for clustering undirected graphs, the performance of spectral clustering algorithms for directed graphs (digraphs) is not in general satisfactory: the…

New method clusters evolving networks using spatio-temporal graph Laplacian.

Graphon pooling preserves spectral properties in GNNs, reducing overfitting.

Spectral Method is a commonly used scheme to cluster data points lying close to Union of Subspaces by first constructing a Random Geometry Graph, called Subspace Clustering. This paper establishes a theory to analyze this method. Based on this theory, we demonstrate the efficiency of Subspace Clustering in fairly broad…

Regularization of the classical Laplacian matrices was empirically shown to improve spectral clustering in sparse networks. It was observed that small regularizations are preferable, but this point was left as a heuristic argument. In this paper we formally determine a proper regularization which is intimately related …

Spectral clustering is widely used to partition graphs into distinct modules or communities. Existing methods for spectral clustering use the eigenvalues and eigenvectors of the graph Laplacian, an operator that is closely associated with random walks on graphs. We propose a new spectral partitioning method that exploi…

Graph construction is a crucial step in spectral clustering (SC) and graph-based semi-supervised learning (SSL). Spectral methods applied on standard graphs such as full-RBF, $ε$-graphs and $k$-NN graphs can lead to poor performance in the presence of proximal and unbalanced data. This is because spectral methods based…

Spectral clustering for geometric graphs achieves strong consistency in community recovery.

Change detection in dynamic networks is an important problem in many areas, such as fraud detection, cyber intrusion detection and health care monitoring. It is a challenging problem because it involves a time sequence of graphs, each of which is usually very large and sparse with heterogeneous vertex degrees, resultin…

Partitioning a graph into groups of vertices such that those within each group are more densely connected than vertices assigned to different groups, known as graph clustering, is often used to gain insight into the organisation of large scale networks and for visualisation purposes. Whereas a large number of dedicated…

In this work, we are interested in generalizing convolutional neural networks (CNNs) from low-dimensional regular grids, where image, video and speech are represented, to high-dimensional irregular domains, such as social networks, brain connectomes or words' embedding, represented by graphs. We present a formulation o…

In this paper, we propose a scalable algorithm for spectral embedding. The latter is a standard tool for graph clustering. However, its computational bottleneck is the eigendecomposition of the graph Laplacian matrix, which prevents its application to large-scale graphs. Our contribution consists of reformulating spect…

Spectral analysis of neighborhood graphs is one of the most widely used techniques for exploratory data analysis, with applications ranging from machine learning to social sciences. In such applications, it is typical to first encode relationships between the data samples using an appropriate similarity function. Popul…

This paper analyzes various graph clustering methods and their applications.

Spectral clustering has become a popular technique due to its high performance in many contexts. It comprises three main steps: create a similarity graph between N objects to cluster, compute the first k eigenvectors of its Laplacian matrix to define a feature vector for each object, and run k-means on these features t…

Networks or graphs can easily represent a diverse set of data sources that are characterized by interacting units or actors. Social networks, representing people who communicate with each other, are one example. Communities or clusters of highly connected actors form an essential feature in the structure of several emp…

Graph embeddings, a class of dimensionality reduction techniques designed for relational data, have proven useful in exploring and modeling network structure. Most dimensionality reduction methods allow out-of-sample extensions, by which an embedding can be applied to observations not present in the training set. Appli…

DPSM clusters nodes in data and graph spaces via density propagation and subcluster merging.

A wide variety of application domains are concerned with data consisting of entities and their relationships or connections, formally represented as graphs. Within these diverse application areas, a common problem of interest is the detection of a subset of entities whose connectivity is anomalous with respect to the r…

Root Laplacian Eigenmaps help in spectral embedding of graphs.

This paper uses the relationship between graph conductance and spectral clustering to study (i) the failures of spectral clustering and (ii) the benefits of regularization. The explanation is simple. Sparse and stochastic graphs create a lot of small trees that are connected to the core of the graph by only one edge. G…

Introduces Spectral Graph Network combining spatial and spectral message passing.

Enhanced spectral clustering for geometric graphs improves clustering accuracy.

Spectral method for joint community detection and group synchronization.

Graph convolutional networks(GCNs) have become the most popular approaches for graph data in these days because of their powerful ability to extract features from graph. GCNs approaches are divided into two categories, spectral-based and spatial-based. As the earliest convolutional networks for graph data, spectral-bas…

Proves generic existence of spectral networks for many cases.

We study a spectral generalization of classical combinatorial graph spanners to the spectral setting. Given a set of vectors $V\subseteq \Re^d$, we say a set $U\subseteq V$ is an $α$-spectral spanner if for all $v\in V$ there is a probability distribution $μ_v$ supported on $U$ such that $$vv^\intercal \preceq α\cdot\m…

Laplacian Eigenvectors of the graph constructed from a data set are used in many spectral manifold learning algorithms such as diffusion maps and spectral clustering. Given a graph constructed from a random sample of a $d$-dimensional compact submanifold $M$ in $\mathbb{R}^D$, we establish the spectral convergence rate…

Proposes a Gaussian process for graph signals using adaptive spectral kernels.

Graph classification improved using spectral features and wavelet filters.

The paper bridges spectral and spatial graph convolutions, improving model capacity and transferability.

DeepWalk embeddings converge on SBM graphs, recovering cluster structure.

Paper revisits graph-CNNs using Laplace-Beltrami spectral filters and polynomials.

Learning meaningful graphs from data plays important roles in many data mining and machine learning tasks, such as data representation and analysis, dimension reduction, data clustering, and visualization, etc. In this work, for the first time, we present a highly-scalable spectral approach (GRASPEL) for learning large…