Related papers: Scalable Constrained Clustering: A Generalized Spe…

Clustering is the problem of separating a set of objects into groups (called clusters) so that objects within the same cluster are more similar to each other than to those in different clusters. Spectral clustering is a now well-known…

Fairness of decision-making algorithms is an increasingly important issue. In this paper, we focus on spectral clustering with group fairness constraints, where every demographic group is represented in each cluster proportionally as in the…

Observational data usually comes with a multimodal nature, which means that it can be naturally represented by a multi-layer graph whose layers share the same set of vertices (users) with different edges (pairwise relationships). In this…

Spectral clustering approaches have led to well-accepted algorithms for finding accurate clusters in a given dataset. However, their application to large-scale datasets has been hindered by computational complexity of eigenvalue…

Spectral clustering is a widely studied problem, yet its complexity is prohibitive for dynamic graphs of even modest size. We claim that it is possible to reuse information of past cluster assignments to expedite computation. Our approach…

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…

Spectral clustering is widely used in practice due to its flexibility, computational efficiency, and well-understood theoretical performance guarantees. Recently, spectral clustering has been studied to find balanced clusters under…

Spectral clustering has found extensive use in many areas. Most traditional spectral clustering algorithms work in three separate steps: similarity graph construction; continuous labels learning; discretizing the learned labels by k-means…

Large graphs commonly appear in social networks, knowledge graphs, recommender systems, life sciences, and decision making problems. Summarizing large graphs by their high level properties is helpful in solving problems in these settings.…

Nonlinear reformulations of the spectral clustering method have gained a lot of recent attention due to their increased numerical benefits and their solid mathematical background. We present a novel direct multiway spectral clustering…

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…

Spectral clustering is one of the most popular clustering methods. However, how to balance the efficiency and effectiveness of the large-scale spectral clustering with limited computing resources has not been properly solved for a long…

In this paper we generalize the spectral concentration problem as formulated by Slepian, Pollak and Landau in the 1960s. We show that a generalized version with arbitrary space and Fourier masks is well-posed, and we prove some new results…

We propose a spectral clustering method based on local principal components analysis (PCA). After performing local PCA in selected neighborhoods, the algorithm builds a nearest neighbor graph weighted according to a discrepancy between the…

Spectral clustering is a standard approach to label nodes on a graph by studying the (largest or lowest) eigenvalues of a symmetric real matrix such as e.g. the adjacency or the Laplacian. Recently, it has been argued that using instead a…

Spectral clustering is one of the most effective clustering approaches that capture hidden cluster structures in the data. However, it does not scale well to large-scale problems due to its quadratic complexity in constructing similarity…

Graph clustering involves the task of dividing nodes into clusters, so that the edge density is higher within clusters as opposed to across clusters. A natural, classic and popular statistical setting for evaluating solutions to this…

Spectral clustering is a popular method for effectively clustering nonlinearly separable data. However, computational limitations, memory requirements, and the inability to perform incremental learning challenge its widespread application.…

We introduce a new method for performing clustering with the aim of fitting clusters with different scatters and weights. It is designed by allowing to handle a proportion $\alpha$ of contaminating data to guarantee the robustness of the…

In this paper we generalise the results on eigenvalues and eigenvectors of unnormalized (combinatorial) Laplacian of two-dimensional grid presented by Edwards:2013 first to a grid graph of any dimension, and second also to other types of…