Clustering assessment in weighted networks

We provide a systematic approach to validate the results of clustering methods on weighted networks, in particular for the cases where the existence of a community structure is unknown. Our validation of clustering comprises a set of criteria for assessing their significance and stability. To test for cluster significance, we introduce a set of community scoring functions adapted to weighted networks, and systematically compare their values to those of a suitable null model. For this we propose a switching model to produce randomized graphs with weighted edges while maintaining the degree distribution constant. To test for cluster stability, we introduce a non parametric bootstrap method combined with similarity metrics derived from information theory and combinatorics. In order to assess the effectiveness of our clustering quality evaluation methods, we test them on synthetically generated weighted networks with a ground truth community structure of varying strength based on the stochastic block model construction. When applying the proposed methods to these synthetic ground truth networks' clusters, as well as to other weighted networks with known community structure, these correctly identify the best performing algorithms, which suggests their adequacy for cases where the clustering structure is not known. We test our clustering validation methods on a varied collection of well known clustering algorithms applied to the synthetically generated networks and to several real world weighted networks. All our clustering validation methods are implemented in R, and will be released in the upcoming package clustAnalytics.

Network Re-Wiring During Allostery and Protein-Protein Interactions: A Graph Spectral Approach

The process of allostery is often guided by subtle changes in the non-covalent interactions between residues of a protein. These changes may be brought about by minor perturbations by natural processes like binding of a ligand or protein-protein interaction. The challenge lies in capturing minute changes at the residue interaction level and following their propagation at local as well as global distances. While macromolecular effects of the phenomenon of allostery are inferred from experiments, a computational microscope can elucidate atomistic-level details leading to such macromolecular effects. Network formalism has served as an attractive means to follow this path and has been pursued further for the past couple of decades. In this chapter some concepts and methods are summarized, and recent advances are discussed. Specifically, the changes in strength of interactions (edge weight) and their repercussion on the overall protein organization (residue clustering) are highlighted. In this review, we adopt a graph spectral method to probe these subtle changes in a quantitative manner. Further, the power of this method is demonstrated for capturing re-ordering of side-chain interactions in response to ligand binding, which culminates into formation of a protein-protein complex in β₂-adrenergic receptors.

EEG sleep stages identification based on weighted undirected complex networks

BACKGROUND AND OBJECTIVE

Sleep scoring is important in sleep research because any errors in the scoring of the patient's sleep electroencephalography (EEG) recordings can cause serious problems such as incorrect diagnosis, medication errors, and misinterpretations of patient's EEG recordings. The aim of this research is to develop a new automatic method for EEG sleep stages classification based on a statistical model and weighted brain networks.

METHODS

Each EEG segment is partitioned into a number of blocks using a sliding window technique. A set of statistical features are extracted from each block. As a result, a vector of features is obtained to represent each EEG segment. Then, the vector of features is mapped into a weighted undirected network. Different structural and spectral attributes of the networks are extracted and forwarded to a least square support vector machine (LS-SVM) classifier. At the same time the network's attributes are also thoroughly investigated. It is found that the network's characteristics vary with their sleep stages. Each sleep stage is best represented using the key features of their networks.

RESULTS

In this paper, the proposed method is evaluated using two datasets acquired from different channels of EEG (Pz-Oz and C3-A2) according to the R&K and the AASM without pre-processing the original EEG data. The obtained results by the LS-SVM are compared with those by Naïve, k-nearest and a multi-class-SVM. The proposed method is also compared with other benchmark sleep stages classification methods. The comparison results demonstrate that the proposed method has an advantage in scoring sleep stages based on single channel EEG signals.

CONCLUSIONS

An average accuracy of 96.74% is obtained with the C3-A2 channel according to the AASM standard, and 96% with the Pz-Oz channel based on the R&K standard.

Statistical methods for constructing disease comorbidity networks from longitudinal inpatient data

Tools from network science can be utilized to study relations between diseases. Different studies focus on different types of inter-disease linkages. One of them is the comorbidity patterns derived from large-scale longitudinal data of hospital discharge records. Researchers seek to describe comorbidity relations as a network to characterize pathways of disease progressions and to predict future risks. The first step in such studies is the construction of the network itself, which subsequent analyses rest upon. There are different ways to build such a network. In this paper, we provide an overview of several existing statistical approaches in network science applicable to weighted directed networks. We discuss the differences between the null models that these models assume and their applications. We apply these methods to the inpatient data of approximately one million people, spanning approximately 17 years, pertaining to the Montreal Census Metropolitan Area. We discuss the differences in the structure of the networks built by different methods, and different features of the comorbidity relations that they extract. We also present several example applications of these methods.

Significance-based community detection in weighted networks

Community detection is the process of grouping strongly connected nodes in a network. Many community detection methods for un-weighted networks have a theoretical basis in a null model. Communities discovered by these methods therefore have interpretations in terms of statistical significance. In this paper, we introduce a null for weighted networks called the continuous configuration model. First, we propose a community extraction algorithm for weighted networks which incorporates iterative hypothesis testing under the null. We prove a central limit theorem for edge-weight sums and asymptotic consistency of the algorithm under a weighted stochastic block model. We then incorporate the algorithm in a community detection method called CCME. To benchmark the method, we provide a simulation framework involving the null to plant "background" nodes in weighted networks with communities. We show that the empirical performance of CCME on these simulations is competitive with existing methods, particularly when overlapping communities and background nodes are present. To further validate the method, we present two real-world networks with potential background nodes and analyze them with CCME, yielding results that reveal macro-features of the corresponding systems.

Forbidden triads and creative success in jazz: the Miles Davis factor

This article argues for the importance of forbidden triads - open triads with high-weight edges - in predicting success in creative fields. Forbidden triads had been treated as a residual category beyond closed and open triads, yet I argue that these structures provide opportunities to combine socially evolved styles in new ways. Using data on the entire history of recorded jazz from 1896 to 2010, I show that observed collaborations have tolerated the openness of high weight triads more than expected, observed jazz sessions had more forbidden triads than expected, and the density of forbidden triads contributed to the success of recording sessions, measured by the number of record releases of session material. The article also shows that the sessions of Miles Davis had received an especially high boost from forbidden triads.

An efficient method for link prediction in weighted multiplex networks

Background

A great variety of artificial and natural systems can be abstracted into a set of entities interacting with each other. Such abstractions can very well represent the underlying dynamics of the system when modeled as the network of vertices coupled by edges. Prediction of dynamics in these structures based on topological attribute or dependency relations is an important task. Link Prediction in such complex networks is regarded useful in almost all types of networks as it can be used to extract missing information, identify spurious interactions, and evaluate network evolving mechanisms. Various similarity and likelihood-based indices have been employed to infer different topological and relation-based information to form a link prediction algorithm. These algorithms, however, are too specific to the domain and do not encapsulate the generic nature of the real-world information. In most natural and engineered systems, the entities are linked with multiple types of associations and relations which play a factor in the dynamics of the network. It forms multiple subsystems or multiple layers of networked information. These networks are regarded as Multiplex Networks.

Methods

This work presents an approach for link prediction in Multiplex networks where the associations are learned from the multiple layers of networks for link prediction purposes. Most of the real-world networks are represented as weighted networks. Weight prediction coupled with Link Prediction can be of great use. Link scores are received using various similarity measures and used to predict weights. This work further proposes and testifies a strategy for weight prediction.

Results and Conclusions

This work successfully proposes an algorithm for Weight Prediction using Link similarity measures on multiplex networks. The predicted weights show very less deviation from their actual weights. In comparison to other indices, the proposed method has a far low error rate and outperforms them concerning the metric performance NRMSE.

Weighting schemes in metabolic graphs for identifying biochemical routes

Metabolism forms an integral part of all cells and its study is important to understand the functioning of the system, to understand alterations that occur in disease state and hence for subsequent applications in drug discovery. Reconstruction of genome-scale metabolic graphs from genomics and other molecular or biochemical data is now feasible. Few methods have also been reported for inferring biochemical pathways from these networks. However, given the large scale and complex inter-connections in the networks, the problem of identifying biochemical routes is not trivial and some questions still remain open. In particular, how a given path is altered in perturbed conditions remains a difficult problem, warranting development of improved methods. Here we report a comparison of 6 different weighting schemes to derive node and edge weights for a metabolic graph, weights reflecting various kinetic, thermodynamic parameters as well as abundances inferred from transcriptome data. Using a network of 50 nodes and 107 edges of carbohydrate metabolism, we show that kinetic parameter derived weighting schemes [Formula: see text] fare best. However, these are limited by their extent of availability, highlighting the usefulness of omics data under such conditions. Interestingly, transcriptome derived weights yield paths with best scores, but are inadequate to discriminate the theoretical paths. The method is tested on a system of Escherichia coli stress response. The approach illustrated here is generic in nature and can be used in the analysis for metabolic network from any species and perhaps more importantly for comparing condition-specific networks.