Mining human-brain networks to discover patterns that can be used to discriminate between healthy individuals and patients affected by some neurological disorder, is a fundamental task in neuroscience. Learning simple and interpretable models is as important as mere classification accuracy. In this paper we introduce a novel approach for classifying brain networks based on extracting contrast subgraphs, i.e., a set of vertices whose induced subgraphs are dense in one class of graphs and sparse in the other. We formally define the problem and present an algorithmic solution for extracting contrast subgraphs. We then apply our method to a brain-network dataset consisting of children affected by Autism Spectrum Disorder and children Typically Developed. Our analysis confirms the interestingness of the discovered patterns, which match background knowledge in the neuroscience literature. Further analysis on other classification tasks confirm the simplicity, soundness, and high explainability of our proposal, which also exhibits superior classification accuracy, to more complex state-of-the-art methods.
Multilayer networks are a powerful paradigm to model complex systems, where multiple relations occur between the same entities. Despite the keen interest in a variety of tasks, algorithms, and analyses in this type of network, the problem of extracting dense subgraphs has remained largely unexplored so far.As a first step in this direction, in this work we study the problem of core decomposition of a multilayer network. Unlike the single-layer counterpart in which cores are all nested into one another and can be computed in linear time, the multilayer context is much more challenging as no total order exists among multilayer cores; rather, they form a lattice whose size is exponential in the number of layers. In this setting we devise three algorithms which differ in the way they visit the core lattice and in their pruning techniques. We assess time and space efficiency of the three algorithms on a large variety of real-world multilayer networks.We then move a step forward and study the problem of extracting the inner-most (also known as maximal) cores, i.e., the cores that are not dominated by any other core in terms of their core index in all the layers. Inner-most cores are typically orders of magnitude less than all the cores. Motivated by this, we devise an algorithm that effectively exploits the maximality property and extracts inner-most cores directly, without first computing a complete decomposition. This allows for a consistent speed up over a naïve method that simply filters out non-inner-most ones from all the cores.Finally, we showcase the multilayer core-decomposition tool in a variety of scenarios and problems. We start by considering the problem of densest-subgraph extraction in multilayer networks. We introduce a definition of multilayer densest subgraph that trades-off between high density and number of layers in which the high density holds, and exploit multilayer core decomposition to approximate this problem with quality guarantees. As further applications, we show how to utilize multilayer core decomposition to speed-up the extraction of frequent cross-graph quasi-cliques and to generalize the community-search problem to the multilayer setting.Dense structures in multilayer networks. Several recent works have dealt with the problem of extracting dense subgraphs from a set of multiple graphs sharing the same vertex set, which is a setting equivalent to the multilayer one we study in this work. Jethava and Beerenwinkel [49] define the densest common subgraph problem, i.e., find a subgraph maximizing the minimum average degree over all input graphs, and devise a linear-programming formulation and a greedy heuristic for it. Reinthal et al.[65] provide a Lagrangian relaxation of the Jethava and Beerenwinkel's linear program, which can be solved more efficiently. Semertzidis et al. [70] introduce three more variants of the problem, whose goal is to maximize the average average degree, the minimum minimum degree, and the average minimum degree, respectively. They show that the average-average varia...
Biological networks are often used to describe the relationships between relevant entities, in particular genes and proteins, and are a powerful tool for functional genomics. Many important biological problems can be investigated by comparing biological networks between different conditions, or networks obtained with different techniques. We show that contrast subgraphs, a recently introduced technique to identify the most important structural differences between two networks, provide a versatile tool for comparing gene and protein networks of diverse origin. We show in three concrete examples how contrast subgraphs can provide new insight in functional genomics by extracting the gene/protein modules whose connectivity is most altered between two conditions or experimental techniques.
Background Biological networks are often used to describe the relationships between relevant entities, particularly genes and proteins, and are a powerful tool for functional genomics. Many important biological problems can be investigated by comparing biological networks between different conditions or networks obtained with different techniques. Findings We show that contrast subgraphs, a recently introduced technique to identify the most important structural differences between 2 networks, provide a versatile tool for comparing gene and protein networks of diverse origin. We demonstrate the use of contrast subgraphs in the comparison of coexpression networks derived from different subtypes of breast cancer, coexpression networks derived from transcriptomic and proteomic data, and protein–protein interaction networks assayed in different cell lines. Conclusions These examples demonstrate how contrast subgraphs can provide new insight in functional genomics by extracting the gene/protein modules whose connectivity is most altered between 2 conditions or experimental techniques.
Despite the breakthrough achievements in understanding structural and functional connectivity alterations that underlie autism spectrum disorder (ASD), the exact nature and type of such alterations are not yet clear due to conflicting reports of hyper-connectivity, hypo-connectivity, and --in some cases-- combinations of both. In this work, we approach the debate about hyper- vs hypo-connectivity in ASD using a novel network comparison technique designed to capture mesoscopic-scale differential structures. In particular, we build on recent algorithmic advances in the sparsification of functional connectivity matrices, in the extraction of contrast subgraphs, and in the computation of statistically significant maximal frequent itemsets, and develop a method to identify mesoscale structural subgraphs that are maximally dense and different in terms of connectivity levels between the different sets of networks. We apply our method to analyse brain networks of typically developed individuals and ASD patients across different developmental phases and find a set of altered cortical-subcortical circuits between healthy subjects and patients affected by ASD. Specifically, our analysis highlights in ASD patients a significantly larger number of functional connections among regions of the occipital cortex and between the left precuneus and the superior parietal gyrus. At the same time, reduced connectivity characterised the superior frontal gyrus and the temporal lobe regions. More importantly, we can simultaneously detect regions of the brain that show hyper and hypo-connectivity in ASD in children and adolescents, recapitulating within a single framework multiple previous separate observations.
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