Related papers: Partitioning Well-Clustered Graphs: Spectral Clust…
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…
Clustering is an important topic in algorithms, and has a number of applications in machine learning, computer vision, statistics, and several other research disciplines. Traditional objectives of graph clustering are to find clusters with…
Coresets have become an invaluable tool for solving $k$-means and kernel $k$-means clustering problems on large datasets with small numbers of clusters. On the other hand, spectral clustering works well on sparse graphs and has recently…
In addition to finding meaningful clusters, centroid-based clustering algorithms such as K-means or mean-shift should ideally find centroids that are valid patterns in the input space, representative of data in their cluster. This is…
We propose two related unsupervised clustering algorithms which, for input, take data assumed to be sampled from a uniform distribution supported on a metric space $X$, and output a clustering of the data based on the selection of a…
Graph clustering has many important applications in computing, but due to growing sizes of graphs, even traditionally fast clustering methods such as spectral partitioning can be computationally expensive for real-world graphs of interest.…
In this paper we introduce a new clustering technique called Regularity Clustering. This new technique is based on the practical variants of the two constructive versions of the Regularity Lemma, a very useful tool in graph theory. The…
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…
Cut-based directed graph (digraph) clustering often focuses on finding dense within-cluster or sparse between-cluster connections, similar to cut-based undirected graph clustering methods. In contrast, for flow-based clusterings the edges…
Graph clustering, aiming to partition nodes of a graph into various groups via an unsupervised approach, is an attractive topic in recent years. To improve the representative ability, several graph auto-encoder (GAE) models, which are based…
Dimensionality reduction, cluster analysis, and sparse representation are basic components in machine learning. However, their relationships have not yet been fully investigated. In this paper, we find that the spectral graph theory…
We consider the problem of learning from a similarity matrix (such as spectral clustering and lowd imensional embedding), when computing pairwise similarities are costly, and only a limited number of entries can be observed. We provide a…
One of the fundamental problems in network analysis is detecting community structure in multi-layer networks, of which each layer represents one type of edge information among the nodes. We propose integrative spectral clustering approaches…
This paper focuses on scalability and robustness of spectral clustering for extremely large-scale datasets with limited resources. Two novel algorithms are proposed, namely, ultra-scalable spectral clustering (U-SPEC) and ultra-scalable…
Spectral clustering uses a graph Laplacian spectral embedding to enhance the cluster structure of some data sets. When the embedding is one dimensional, it can be used to sort the items (spectral ordering). A number of empirical results…
We propose a novel robust decentralized graph clustering algorithm that is provably equivalent to the popular spectral clustering approach. Our proposed method uses the existing wave equation clustering algorithm that is based on…
We introduce a new subclass of chordal graphs that generalizes split graphs, which we call well-partitioned chordal graphs. Split graphs are graphs that admit a partition of the vertex set into cliques that can be arranged in a star…
Local clustering aims to identify specific substructures within a large graph without any additional structural information of the graph. These substructures are typically small compared to the overall graph, enabling the problem to be…
Our problem of interest is to cluster vertices of a graph by identifying underlying community structure. Among various vertex clustering approaches, spectral clustering is one of the most popular methods because it is easy to implement…
We consider the problem of estimating the number of clusters (k) in a dataset. We propose a non-parametric approach to the problem that utilizes similarity graphs to construct a robust statistic that effectively captures similarity…