Entrograms and coarse graining of dynamics on complex networks

Using an information theoretic point of view, we investigate how a dynamics acting on a network can be coarse grained through the use of graph partitions. Specifically, we are interested in how aggregating the state space of a Markov process according to a partition impacts on the thus obtained lower-dimensional dynamics. We highlight that for a dynamics on a particular graph there may be multiple coarse grained descriptions that capture different, incomparable features of the original process. For instance, a coarse graining induced by one partition may be commensurate with a time-scale separation in the dynamics, while another coarse graining may correspond to a different lower-dimensional dynamics that preserves the Markov property of the original process. Taking inspiration from the literature of Computational Mechanics, we find that a convenient tool to summarise and visualise such dynamical properties of a coarse grained model (partition) is the entrogram. The entrogram gathers certain information-theoretic measures, which quantify how information flows across time steps. These information theoretic quantities include the entropy rate, as well as a measure for the memory contained in the process, i.e., how well the dynamics can be approximated by a first order Markov process. We use the entrogram to investigate how specific macro-scale connection patterns in the state-space transition graph of the original dynamics result in desirable properties of coarse grained descriptions. We thereby provide a fresh perspective on the interplay between structure and dynamics in networks, and the process of partitioning from an information theoretic perspective. We focus on networks that may be approximated by both a core-periphery or a clustered organization, and highlight that each of these coarse grained descriptions can capture different aspects of a Markov process acting on the network.Comment: 17 pages, 6 figue

Community structure in real-world networks from a non-parametrical synchronization-based dynamical approach

This work analyzes the problem of community structure in real-world networks based on the synchronization of nonidentical coupled chaotic R\"{o}ssler oscillators each one characterized by a defined natural frequency, and coupled according to a predefined network topology. The interaction scheme contemplates an uniformly increasing coupling force to simulate a society in which the association between the agents grows in time. To enhance the stability of the correlated states that could emerge from the synchronization process, we propose a parameterless mechanism that adapts the characteristic frequencies of coupled oscillators according to a dynamic connectivity matrix deduced from correlated data. We show that the characteristic frequency vector that results from the adaptation mechanism reveals the underlying community structure present in the network.Comment: 21 pages, 7 figures; Chaos, Solitons & Fractals (2012

Identification of network modules by optimization of ratio association

We introduce a novel method for identifying the modular structures of a network based on the maximization of an objective function: the ratio association. This cost function arises when the communities detection problem is described in the probabilistic autoencoder frame. An analogy with kernel k-means methods allows to develop an efficient optimization algorithm, based on the deterministic annealing scheme. The performance of the proposed method is shown on a real data set and on simulated networks

High Quality, Efficient Hierarchical Document Clustering Using Closed Interesting Itemsets

High dimensionality remains a significant challenge for document clustering. Recent approaches used frequent itemsets and closed frequent itemsets to reduce dimensionality, and to improve the efficiency of hierarchical document clustering. In this paper, we introduce the notion of "closed interesting" itemsets (i.e. closed itemsets with high interestingness). We provide heuristics such as "super item" to efficiently mine these itemsets and show that they provide significant dimensionality reduction over closed frequent itemsets. Using "closed interesting" itemsets, we propose a new hierarchical document clustering method that outperforms state of the art agglomerative, partitioning and frequent-itemset based methods both in terms of FScore and Entropy, without requiring dataset specific parameter tuning. We evaluate twenty interestingness measures on nine standard datasets and show that when used to generate "closed interesting" itemsets, and to select parent nodes, Mutual Information, Added Value, Yule's Q and Chi-Square offers best clustering performance, regardless of the characteristics of underlying dataset. We also show that our method is more scalable, and results in better run-time performance as compare to leading approaches. On a dual processor machine, our method scaled sub-linearly and was able to cluster 200K documents in about 40 seconds