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One key use of k-means clustering is to identify cluster prototypes which can serve as representative points for a dataset. However, a drawback of using k-means cluster centers as representative points is that such points distort the…
The community structure of complex networks reveals both their organization and hidden relationships among their constituents. Most community detection methods currently available are not deterministic, and their results typically depend on…
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…
Divide-and-conquer is a general strategy to deal with large scale problems. It is typically applied to generate ensemble instances, which potentially limits the problem size it can handle. Additionally, the data are often divided by random…
Spectral clustering uses the global information embedded in eigenvectors of an inter-item similarity matrix to correctly identify clusters of irregular shape, an ability lacking in commonly used approaches such as k-means and agglomerative…
Cluster analysis is the distribution of objects into different groups or more precisely the partitioning of a data set into subsets (clusters) so that the data in subsets share some common trait according to some distance measure. Unlike…
We present a technique for clustering categorical data by generating many dissimilarity matrices and averaging over them. We begin by demonstrating our technique on low dimensional categorical data and comparing it to several other…
This paper explores the critical role of data clustering in data science, emphasizing its methodologies, tools, and diverse applications. Traditional techniques, such as partitional and hierarchical clustering, are analyzed alongside…
Spectral clustering methods are widely used for detecting clusters in networks for community detection, while a small change on the graph Laplacian matrix could bring a dramatic improvement. In this paper, we propose a dual regularized…
We propose two spectral algorithms for partitioning nodes in directed graphs respectively with a cyclic and an acyclic pattern of connection between groups of nodes. Our methods are based on the computation of extremal eigenvalues of the…
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…
In this paper, we present a deep extension of Sparse Subspace Clustering, termed Deep Sparse Subspace Clustering (DSSC). Regularized by the unit sphere distribution assumption for the learned deep features, DSSC can infer a new data…
This work studies the classical spectral clustering algorithm which embeds the vertices of some graph $G=(V_G, E_G)$ into $\mathbb{R}^k$ using $k$ eigenvectors of some matrix of $G$, and applies $k$-means to partition $V_G$ into $k$…
An exponential-time exact algorithm is provided for the task of clustering n items of data into k clusters. Instead of seeking one partition, posterior probabilities are computed for summary statistics: the number of clusters, and pairwise…
We propose a Deep Variational Clustering (DVC) framework for unsupervised representation learning and clustering of large-scale medical images. DVC simultaneously learns the multivariate Gaussian posterior through the probabilistic…
The paper tackles the problem of clustering multiple networks, directed or not, that do not share the same set of vertices, into groups of networks with similar topology. A statistical model-based approach based on a finite mixture of…
The performance of spectral clustering relies on the fluctuations of the entries of the eigenvectors of a similarity matrix, which has been left uncharacterized until now. In this letter, it is shown that the signal $+$ noise structure of a…
We develop a novel clustering method for distributional data, where each data point is regarded as a probability distribution on the real line. For distributional data, it has been challenging to develop a clustering method that utilizes…
Scale invariance (fractality) is a prominent feature of the large-scale behavior of many stochastic systems. In this work, we construct an algorithm for the statistical identification of the Hurst distribution (in particular, the scaling…
The paper presents the algorithm for clustering a dataset by grouping the optimal, from the point of view of the BIC criterion, number of Gaussian clusters into the optimal, from the point of view of their statistical separability,…