Related papers: The Block Neighborhood
Classical block designs are important combinatorial structures with a wide range of applications in Computer Science and Statistics. Here we give a new abstract description of block designs based on the arrow category construction. We show…
A generalization of modularity, called block modularity, is defined. This is a quality function which evaluates a label assignment against an arbitrary block pattern. Therefore, unlike standard modularity or its variants, arbitrary network…
Neighborhood is an important concept in covering based rough sets. That under what condition neighborhoods form a partition is a meaningful issue induced by this concept. Many scholars have paid attention to this issue and presented some…
We describe a framework for encoding cluster combinatorics using categorical methods. We give a definition of an abstract cluster structure, which captures the essence of cluster mutation at a tropical level and show that cluster algebras,…
A block in a linear order is an equivalence class when factored by the block relation B(x,y), satisfied by elements that are finitely far apart. We show that every computable linear order with dense condensation-type (i.e. a dense…
Community detection is a fundamental unsupervised learning problem for unlabeled networks which has a broad range of applications. Many community detection algorithms assume that the number of clusters $r$ is known apriori. In this paper,…
The most widely used techniques for community detection in networks, including methods based on modularity, statistical inference, and information theoretic arguments, all work by optimizing objective functions that measure the quality of…
In this paper, the class of random irregular block-hierarchical networks is defined and algorithms for generation and calculation of network properties are described. The algorithms presented for this class of networks are more efficient…
Recognizing number of communities and detecting community structures of complex network are discussed in this paper. As a visual and feasible algorithm, block model has been successfully applied to detect community structures in complex…
In this paper a relative number density parameter, called the neighborhood function, is introduced so that the crowded nature of the neighborhood of individual sources can be described. With this parameter one can determine the probability…
We present the Multi-Block DC (BDC) class, a rich class of structured nonconvex functions that admit a DC ("difference-of-convex") decomposition across parameter blocks. This multi-block class not only subsumes the usual DC programming, but…
Probabilistic Cellular Automata are a generalization of Cellular Automata. Despite their simple definition, they exhibit fascinating and complex behaviours. The stationary behaviour of these models changes when model parameters are varied,…
The labeled stochastic block model is a random graph model representing networks with community structure and interactions of multiple types. In its simplest form, it consists of two communities of approximately equal size, and the edges…
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…
Combinatorics, like computer science, often has to deal with large objects of unspecified (or unusable) structure. One powerful way to deal with such an arbitrary object is to decompose it into more usable components. In particular, it has…
We introduce an extension of the Difference of Convex Algorithm (DCA) in the form of a randomized block coordinate approach for problems with separable structure. For $n$ coordinate-blocks and $k$ iterations, our main result proves a…
Inspired by a work of Kapranov, we define the notion of Dolbeault complex of the formal neighborhood of a closed embedding of complex manifolds. This construction allows us to study coherent sheaves over the formal neighborhood via complex…
Set partitions and permutations with restrictions on the size of the blocks and cycles are important combinatorial sequences. Counting these objects lead to the sequences generalizing the classical Stirling and Bell numbers. The main focus…
Clusters or communities can provide a coarse-grained description of complex systems at multiple scales, but their detection remains challenging in practice. Community detection methods often define communities as dense subgraphs, or…
In recent years, the creation of block-structured dictionary has attracted a lot of interest. Learning such dictionaries involve two step process: block formation and dictionary update. Both these steps are important in producing an…