Related papers: Cluster counting: The Hoshen-Kopelman algorithm vs…

We introduce a cluster growth process that provides a clear connection between equilibrium statistical mechanics and an explosive percolation model similar to the one recently proposed by Achlioptas et al. [Science 323, 1453 (2009)]. We…

Clustering is a widely used unsupervised learning method for finding structure in the data. However, the resulting clusters are typically presented without any guarantees on their robustness; slightly changing the used data sample or…

A scaling theory is used to derive the dependence of the average number <k> of spanning clusters at threshold on the lattice size L. This number should become independent of L for dimensions d<6, and vary as log L at d=6. The predictions…

Spectral clustering refers to a family of unsupervised learning algorithms that compute a spectral embedding of the original data based on the eigenvectors of a similarity graph. This non-linear transformation of the data is both the key of…

In recent years, a better understanding of the Monte Carlo method has provided us with many new techniques in different areas of statistical physics. Of particular interest are so called cluster methods, which exploit the considerable…

Bagging and boosting are proved to be the best methods of building multiple classifiers in classification combination problems. In the area of "flat clustering" problems, it is also recognized that multi-clustering methods based on boosting…

In the past few years powerful generalizations to the Euclidean k-means problem have been made, such as Bregman clustering [7], co-clustering (i.e., simultaneous clustering of rows and columns of an input matrix) [9,18], and tensor…

A new cluster algorithm based on invasion percolation is described. The algorithm samples the critical point of a spin system without a priori knowledge of the critical temperature and provides an efficient way to determine the critical…

Multi-view clustering has been widely used in recent years in comparison to single-view clustering, for clear reasons, as it offers more insights into the data, which has brought with it some challenges, such as how to combine these views…

Graph clustering is a fundamental problem that has been extensively studied both in theory and practice. The problem has been defined in several ways in literature and most of them have been proven to be NP-Hard. Due to their high practical…

Clustering is a fundamental analysis tool aiming at classifying data points into groups based on their similarity or distance. It has found successful applications in all natural and social sciences, including biology, physics, economics,…

Many fundamental statistical methods have become critical tools for scientific data analysis yet do not scale tractably to modern large datasets. This paper will describe very recent algorithms based on computational geometry which have…

We propose a novel graph clustering method guided by additional information on the underlying structure of the clusters (or communities). The problem is formulated as the matching of a graph to a template with smaller dimension, hence…

Finding a maximum clique in a given graph is one of the fundamental NP-hard problems. We compare two multi-core thread-parallel adaptations of a state-of-the-art branch and bound algorithm for the maximum clique problem, and provide a novel…

Cluster separation is a task typically tackled by widely used clustering techniques, such as k-means or DBSCAN. However, these algorithms are based on non-perceptual metrics, and our experiments demonstrate that their output does not…

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…

The non-stationary nature of data streams strongly challenges traditional machine learning techniques. Although some solutions have been proposed to extend traditional machine learning techniques for handling data streams, these approaches…

The main purpose of percolation theory is to model phase transitions in a variety of random systems, which is highly valuable in fields related to materials physics, biology, or otherwise unrelated areas like oil extraction or even quantum…

While spectral clustering algorithms for undirected graphs are well established and have been successfully applied to unsupervised machine learning problems ranging from image segmentation and genome sequencing to signal processing and…

Spectral clustering is a powerful method for finding structure in a dataset through the eigenvectors of a similarity matrix. It often outperforms traditional clustering algorithms such as $k$-means when the structure of the individual…