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Spectral clustering is one of the most popular clustering methods. However, the high computational cost due to the involved eigen-decomposition procedure can immediately hinder its applications in large-scale tasks. In this paper we use…

The minimal spanning tree (MST) algorithm is a graph-theoretical cluster-finding method. We previously applied it to gamma-ray bidimensional images, showing that it is quite sensitive in finding faint sources. Possible sources are…

Spectral clustering is a leading and popular technique in unsupervised data analysis. Two of its major limitations are scalability and generalization of the spectral embedding (i.e., out-of-sample-extension). In this paper we introduce a…

This study investigates the problem of multi-view clustering, where multiple views contain consistent information and each view also includes complementary information. Exploration of all information is crucial for good multi-view…

Semantic segmentation is a crucial image understanding task, where each pixel of image is categorized into a corresponding label. Since the pixel-wise labeling for ground-truth is tedious and labor intensive, in practical applications, many…

Spectral-type subspace clustering algorithms have shown excellent performance in many subspace clustering applications. The existing spectral-type subspace clustering algorithms either focus on designing constraints for the reconstruction…

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…

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…

Graph Neural Networks (GNNs) have achieved remarkable success in learning node representations and have shown strong performance in tasks such as node classification. However, recent findings indicate that the presence of noise in…

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…

Spectral clustering has shown a superior performance in analyzing the cluster structure. However, its computational complexity limits its application in analyzing large-scale data. To address this problem, many low-rank matrix approximating…

The present paper is devoted to clustering geometric graphs. While the standard spectral clustering is often not effective for geometric graphs, we present an effective generalization, which we call higher-order spectral clustering. It…

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…

In recent years, Multi-View Clustering (MVC) has attracted increasing attention for its potential to reduce the annotation burden associated with large datasets. The aim of MVC is to exploit the inherent consistency and complementarity…

Spectral clustering is one of the most popular methods for community detection in graphs. A key step in spectral clustering algorithms is the eigen decomposition of the $n{\times}n$ graph Laplacian matrix to extract its $k$ leading…

Under the framework of spectral clustering, the key of subspace clustering is building a similarity graph which describes the neighborhood relations among data points. Some recent works build the graph using sparse, low-rank, and…

Spectral clustering is discussed from many perspectives, by extending it to rectangular arrays and discrepancy minimization too. Near optimal clusters are obtained with singular value decomposition and with the weighted $k$-means algorithm.…

We study the statistical and computational properties of a network Lasso method for local graph clustering. The clusters delivered by nLasso can be characterized elegantly via network flows between cluster boundary and seed nodes. While…

Spectral clustering is one of the most prominent clustering approaches. The distance-based similarity is the most widely used method for spectral clustering. However, people have already noticed that this is not suitable for multi-scale…

Anchor-based multi-view graph clustering (AMVGC) has received abundant attention owing to its high efficiency and the capability to capture complementary structural information across multiple views. Intuitively, a high-quality anchor graph…