A survey of clustering methods

In this paper, I describe a large variety of clustering methods within a single framework. This paper unifies work across different fields, from biology (numerical taxonomy) to machine learning (concept formation). An important objective for this paper is to show that one can benefit by a knowledge of research across different disciplines. After describing the task from a set of different viewpoints or paradigms, I begin by describing the similarity measures or evaluation functions that form the basis of any clustering technique. Next, I describe a number of different algorithms that use these measures, and I close with a brief discussion of ways to evaluate different approaches to clustering

Parallel Graph Partitioning for Complex Networks

Processing large complex networks like social networks or web graphs has recently attracted considerable interest. In order to do this in parallel, we need to partition them into pieces of about equal size. Unfortunately, previous parallel graph partitioners originally developed for more regular mesh-like networks do not work well for these networks. This paper addresses this problem by parallelizing and adapting the label propagation technique originally developed for graph clustering. By introducing size constraints, label propagation becomes applicable for both the coarsening and the refinement phase of multilevel graph partitioning. We obtain very high quality by applying a highly parallel evolutionary algorithm to the coarsened graph. The resulting system is both more scalable and achieves higher quality than state-of-the-art systems like ParMetis or PT-Scotch. For large complex networks the performance differences are very big. For example, our algorithm can partition a web graph with 3.3 billion edges in less than sixteen seconds using 512 cores of a high performance cluster while producing a high quality partition -- none of the competing systems can handle this graph on our system.Comment: Review article. Parallelization of our previous approach arXiv:1402.328

Recent Advances in Graph Partitioning

We survey recent trends in practical algorithms for balanced graph partitioning together with applications and future research directions

Maude: specification and programming in rewriting logic

Maude is a high-level language and a high-performance system supporting executable specification and declarative programming in rewriting logic. Since rewriting logic contains equational logic, Maude also supports equational specification and programming in its sublanguage of functional modules and theories. The underlying equational logic chosen for Maude is membership equational logic, that has sorts, subsorts, operator overloading, and partiality definable by membership and equality conditions. Rewriting logic is reflective, in the sense of being able to express its own metalevel at the object level. Reflection is systematically exploited in Maude endowing the language with powerful metaprogramming capabilities, including both user-definable module operations and declarative strategies to guide the deduction process. This paper explains and illustrates with examples the main concepts of Maude's language design, including its underlying logic, functional, system and object-oriented modules, as well as parameterized modules, theories, and views. We also explain how Maude supports reflection, metaprogramming and internal strategies. The paper outlines the principles underlying the Maude system implementation, including its semicompilation techniques. We conclude with some remarks about applications, work on a formal environment for Maude, and a mobile language extension of Maude

Resolution of ranking hierarchies in directed networks

Identifying hierarchies and rankings of nodes in directed graphs is fundamental in many applications such as social network analysis, biology, economics, and finance. A recently proposed method identifies the hierarchy by finding the ordered partition of nodes which minimises a score function, termed agony. This function penalises the links violating the hierarchy in a way depending on the strength of the violation. To investigate the resolution of ranking hierarchies we introduce an ensemble of random graphs, the Ranked Stochastic Block Model. We find that agony may fail to identify hierarchies when the structure is not strong enough and the size of the classes is small with respect to the whole network. We analytically characterise the resolution threshold and we show that an iterated version of agony can partly overcome this resolution limit.Comment: 27 pages, 9 figure