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In this paper, we introduce an algorithm for performing spectral clustering efficiently. Spectral clustering is a powerful clustering algorithm that suffers from high computational complexity, due to eigen decomposition. In this work, we…
Spectral clustering largely depends on the affinity graph, yet constructing a graph that preserves reliable local connectivity while adapting to heterogeneous data structures remains challenging. Existing granular-ball-based spectral…
Spectral clustering is sensitive to how graphs are constructed from data particularly when proximal and imbalanced clusters are present. We show that Ratio-Cut (RCut) or normalized cut (NCut) objectives are not tailored to imbalanced data…
One basic requirement of many studies is the necessity of classifying data. Clustering is a proposed method for summarizing networks. Clustering methods can be divided into two categories named model-based approaches and algorithmic…
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…
Existing clustering methods are based on a single granularity of information, such as the distance and density of each data. This most fine-grained based approach is usually inefficient and susceptible to noise. Inspired by adaptive process…
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…
Clustering techniques are very attractive for extracting and identifying patterns in datasets. However, their application to very large spatial datasets presents numerous challenges such as high-dimensionality data, heterogeneity, and high…
We address the problem of un-supervised soft-clustering called micro-clustering. The aim of the problem is to enumerate all groups composed of records strongly related to each other, while standard clustering methods separate records at…
Many methods have been developed for data clustering, such as k-means, expectation maximization and algorithms based on graph theory. In this latter case, graphs are generally constructed by taking into account the Euclidian distance as a…
Graph spectral techniques for measuring graph similarity, or for learning the cluster number, require kernel smoothing. The choice of kernel function and bandwidth are typically chosen in an ad-hoc manner and heavily affect the resulting…
In today's data-driven digital era, the amount as well as complexity, such as multi-view, non-Euclidean, and multi-relational, of the collected data are growing exponentially or even faster. Clustering, which unsupervisely extracts valid…
Clustering in image analysis is a central technique that allows to classify elements of an image. We describe a simple clustering technique that uses the method of similarity matrices. We expand upon recent results in spectral analysis for…
Clustering of high-dimensional data sets is a growing need in artificial intelligence, machine learning and pattern recognition. In this paper, we propose a new clustering method based on a combinatorial-topological approach applied to…
We study the connections between spectral clustering and the problems of maximum margin clustering, and estimation of the components of level sets of a density function. Specifically, we obtain bounds on the eigenvectors of graph Laplacian…
Efficient extraction of useful knowledge from these data is still a challenge, mainly when the data is distributed, heterogeneous and of different quality depending on its corresponding local infrastructure. To reduce the overhead cost,…
Cluster structure detection is a fundamental task for the analysis of graphs, in order to understand and to visualize their functional characteristics. Among the different cluster structure detection methods, spectral clustering is…
Constrained clustering has been well-studied for algorithms such as $K$-means and hierarchical clustering. However, how to satisfy many constraints in these algorithmic settings has been shown to be intractable. One alternative to encode…
The eigendeomposition of nearest-neighbor (NN) graph Laplacian matrices is the main computational bottleneck in spectral clustering. In this work, we introduce a highly-scalable, spectrum-preserving graph sparsification algorithm that…
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…