Related papers: Absence of a resolution limit in in-block nestedne…
Convergence analysis of block iterative solvers for Hermitian eigenvalue problems and the closely related research on properties of matrix-based signal filters are challenging, and attract increasing attention due to their recent…
Statistical analysis and node clustering in hypergraphs constitute an emerging topic suffering from a lack of standardization. In contrast to the case of graphs, the concept of nodes' community in hypergraphs is not unique and encompasses…
In this paper, a new cooperation structure for spectrum sensing in cognitive radio networks is proposed which outperforms the existing commonly-used ones in terms of energy efficiency. The efficiency is achieved in the proposed design by…
Many real networks feature the property of nestedness, i.e. the neighbours of nodes with a few connections are hierarchically nested within the neighbours of nodes with more connections. Despite the abstract simplicity of this notion,…
Many graph clustering quality functions suffer from a resolution limit, the inability to find small clusters in large graphs. So called resolution-limit-free quality functions do not have this limit. This property was previously introduced…
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…
In the high dimensional Stochastic Blockmodel for a random network, the number of clusters (or blocks) K grows with the number of nodes N. Two previous studies have examined the statistical estimation performance of spectral clustering and…
Largest theoretical contribution to Neural Networks comes from VC Dimension which characterizes the sample complexity of classification model in a probabilistic view and are widely used to study the generalization error. So far in the…
Correlation networks derived from multivariate data appear in many applications across the sciences. These networks are usually dense and require sparsification to detect meaningful structure. However, current methods for sparsifying…
Modular neural networks outperform nonmodular neural networks on tasks ranging from visual question answering to robotics. These performance improvements are thought to be due to modular networks' superior ability to model the compositional…
Rotation dynamics of eigenvectors of modular network adjacency matrices under random perturbations are presented. In the presence of $q$ communities, the number of eigenvectors corresponding to the $q$ largest eigenvalues form a "community"…
The explosion in the amount of data available for analysis often necessitates a transition from batch to incremental clustering methods, which process one element at a time and typically store only a small subset of the data. In this paper,…
There is no, nor will there ever be, single best clustering algorithm. Nevertheless, we would still like to be able to distinguish between methods that work well on certain task types and those that systematically underperform. Clustering…
Most methods proposed to uncover communities in complex networks rely on their structural properties. Here we introduce the stability of a network partition, a measure of its quality defined in terms of the statistical properties of a…
We prove the incompatibility of certain desirable properties of community partition quality functions. Our results generalize the impossibility result of [Kleinberg 2003] by considering sets of weaker properties. In particular, we use an…
Community structure discovery in complex networks is a quite challenging problem spanning many applications in various disciplines such as biology, social network and physics. Emerging from various approaches numerous algorithms have been…
Many complex networks show signs of modular structure, uncovered by community detection. Although many methods succeed in revealing various partitions, it remains difficult to detect at what scale some partition is significant. This problem…
The stochastic block model is widely used for detecting community structures in network data. How to test the goodness-of-fit of the model is one of the fundamental problems and has gained growing interests in recent years. In this article,…
Because networks can be used to represent many complex systems, they have attracted considerable attention in physics, computer science, sociology, and many other disciplines. One of the most important areas of network science is the…
\cite{bickel2009nonparametric} developed a general framework to establish consistency of community detection in stochastic block model (SBM). In most applications of this framework, the community label is discrete. For example, in…