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Register a new userA principled approach for weighted multilayer network aggregation
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Added by
Junyao Kuang
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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A multilayer network depicts different types of interactions among the same set of nodes. For example, protease networks consist of five to seven layers, where different layers represent distinct types of experimentally confirmed molecule interactions among proteins. In a multilayer protease network, the co-expression layer is obtained through the meta-analysis of transcriptomic data from various sources and platforms. While in some researches the co-expression layer is in turn represented as a multilayered network, a fundamental problem is how to obtain a single-layer network from the corresponding multilayered network. This process is called multilayer network aggregation. In this work, we propose a maximum a posteriori estimation-based algorithm for multilayer network aggregation. The method allows to aggregate a weighted multilayer network while conserving the core information of the layers. We evaluate the method through an unweighted friendship network and a multilayer gene co-expression network. We compare the aggregated gene co-expression network with a network obtained from conflated datasets and a network obtained from averaged weights. The Von Neumann entropy is adopted to compare the mixedness of the three networks, and, together with other network measurements, shows the effectiveness of the proposes method.
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People change their physical contacts as a preventive response to infectious disease propagations. Yet, only a few mathematical models consider the coupled dynamics of the disease propagation and the contact adaptation process. This paper presents a model where each agent has a default contact neighborhood set, and switches to a different contact set once she becomes alert about infection among her default contacts. Since each agent can adopt either of two possible neighborhood sets, the overall contact network switches among 2^N possible configurations. Notably, a two-layer network representation can fully model the underlying adaptive, state-dependent contact network. Contact adaptation influences the size of the disease prevalence and the epidemic threshold---a characteristic measure of a contact network robustness against epidemics---in a nonlinear fashion. Particularly, the epidemic threshold for the presented adaptive contact network belongs to the solution of a nonlinear Perron-Frobenius (NPF) problem, which does not depend on the contact adaptation rate monotonically. Furthermore, the network adaptation model predicts a counter-intuitive scenario where adaptively changing contacts may adversely lead to lower network robustness against epidemic spreading if the contact adaptation is not fast enough. An original result for a class of NPF problems facilitate the analytical developments in this paper.
In recent years, network embedding methods have garnered increasing attention because of their effectiveness in various information retrieval tasks. The goal is to learn low-dimensional representations of vertexes in an information network and simultaneously capture and preserve the network structure. Critical to the performance of a network embedding method is how the edges/vertexes of the network is sampled for the learning process. Many existing methods adopt a uniform sampling method to reduce learning complexity, but when the network is non-uniform (i.e. a weighted network) such uniform sampling incurs information loss. The goal of this paper is to present a generalized vertex sampling framework that works seamlessly with most existing network embedding methods to support weighted instead of uniform vertex/edge sampling. For efficiency, we propose a delicate sequential vertex-to-context graph data structure, such that sampling a training pair for learning takes only constant time. For scalability and memory efficiency, we design the graph data structure in a way that keeps space consumption low without requiring additional space. In addition to implementing existing network embedding methods, the proposed framework can be used to implement extensions that feature high-order proximity modeling and weighted relation modeling. Experiments conducted on three datasets, including a commercial large-scale one, verify the effectiveness and efficiency of the proposed weighted network embedding methods on a variety of tasks, including word similarity search, multi-label classification, and item recommendation.
Nuclear reaction rate ($lambda$) is a significant factor in the process of nucleosynthesis. A multi-layer directed-weighted nuclear reaction network in which the reaction rate as the weight, and neutron, proton, $^4$He and the remainder nuclei as the criterion for different reaction-layers is for the first time built based on all thermonuclear reactions in the JINA REACLIB database. Our results show that with the increase of the stellar temperature ($T_{9}$), the distribution of nuclear reaction rates on the $R$-layer network demonstrates a transition from unimodal to bimodal distributions. Nuclei on the $R$-layer in the region of $lambda = [1,2.5times10^{1}]$ have a more complicated out-going degree distribution than the one in the region of $lambda = [10^{11},10^{13}]$, and the number of involved nuclei at $T_{9} = 1$ is very different from the one at $T_{9} = 3$. The redundant nuclei in the region of $lambda = [1, 2.5times10^{1}]$ at $T_{9} = 3$ prefer $(gamma,p)$ and $({gamma,alpha})$ reactions to the ones at $T_{9}=1$, which produce nuclei around the $beta$ stable line. This work offers a novel way to the big-data analysis on nuclear reaction network at stellar temperatures.
Normalization is known to help the optimization of deep neural networks. Curiously, different architectures require specialized normalization methods. In this paper, we study what normalization is effective for Graph Neural Networks (GNNs). First, we adapt and evaluate the existing methods from other domains to GNNs. Faster convergence is achieved with InstanceNorm compared to BatchNorm and LayerNorm. We provide an explanation by showing that InstanceNorm serves as a preconditioner for GNNs, but such preconditioning effect is weaker with BatchNorm due to the heavy batch noise in graph datasets. Second, we show that the shift operation in InstanceNorm results in an expressiveness degradation of GNNs for highly regular graphs. We address this issue by proposing GraphNorm with a learnable shift. Empirically, GNNs with GraphNorm converge faster compared to GNNs using other normalization. GraphNorm also improves the generalization of GNNs, achieving better performance on graph classification benchmarks.
How might one test the hypothesis that graphs were sampled from the same distribution? Here, we compare two statistical tests that address this question. The first uses the observed subgraph densities themselves as estimates of those of the underlying distribution. The second test uses a new approach that converts these subgraph densities into estimates of the graph cumulants of the distribution. We demonstrate -- via theory, simulation, and application to real data -- the superior statistical power of using graph cumulants.
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