Abstract

In communication networks resilience or structural coherency, namely the ability to maintain total connectivity even after some data links are lost for an indefinite time, is a major design consideration. Evaluating resilience is a computationally challenging task since it often requires examining a prohibitively high number of connections or of node combinations, depending on the structural coherency definition. In order to study resilience, communication systems are treated in an abstract level as graphs where the existence of an edge depends heavily on the local connectivity properties between the two nodes. Once the graph is derived, its resilience is evaluated by a tensor stack network (TSN). TSN is an emerging deep learning classification methodology for big data which can be expressed either as stacked vectors or as matrices, such as images or oversampled data from multiple-input and multiple-output digital communication systems. As their collective name suggests, the architecture of TSNs is based on tensors, namely higher-dimensional vectors, which simulate the simultaneous training of a cluster of ordinary multilayer feedforward neural networks (FFNNs). In the TSN structure the FFNNs are also interconnected and, thus, at certain steps of the training process they learn from the errors of each other. An additional advantage of the TSN training process is that it is regularized, resulting in parsimonious classifiers. The TSNs are trained to evaluate how resilient a graph is, where the real structural strength is assessed through three established resiliency metrics, namely the Estrada index, the odd Estrada index, and the clustering coefficient. Although the approach of modelling the communication system exclusively in structural terms is function oblivious, it can be applied to virtually any type of communication network independently of the underlying technology. The classification achieved by four configurations of TSNs is evaluated through six metrics, including the F1 metric as well as the type I and type II errors, derived from the corresponding contingency tables. Moreover, the effects of sparsifying the synaptic weights resulting from the training process are explored for various thresholds. Results indicate that the proposed method achieves a very high accuracy, while it is considerably faster than the computation of each of the three resilience metrics. Concerning sparsification, after a threshold the accuracy drops, meaning that the TSNs cannot be further sparsified. Thus, their training is very efficient in that respect.

中文翻译：

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使用张量堆栈网络评估图弹性：Keras实现

摘要

在通信网络中，弹性或结构一致性是指即使在某些数据链路无限期丢失后仍保持总连接的能力，这是主要的设计考虑因素。评估弹性是一项计算难题，因为根据结构一致性定义，它通常需要检查数量过多的连接或节点组合。为了研究弹性，通信系统被抽象地视为图，其中边缘的存在在很大程度上取决于两个节点之间的本地连接性。推导图形后，将通过张量堆栈网络（TSN）评估其弹性。TSN是新兴的针对大数据的深度学习分类方法，可以将其表示为堆叠向量或矩阵，例如来自多输入和多输出数字通信系统的图像或超采样数据。就像它们的统称所暗示的那样，TSN的体系结构基于张量，即高维向量，它模拟了普通多层前馈神经网络（FFNN）簇的同时训练。在TSN结构中，FFNN也相互连接，因此，在训练过程的某些步骤中，它们从彼此的错误中学习。TSN训练过程的另一个优点是它是正规化的，从而导致简化的分类器。对TSN进行训练以评估图形的弹性，其中通过三个已建立的弹性指标（即Estrada索引，奇数Estrada索引和聚类系数）评估实际结构强度。尽管仅用结构术语对通信系统建模的方法是功能忽略的，但实际上它可以独立于基础技术而应用于任何类型的通信网络。通过六个度量标准（包括F1度量标准以及从相应的权变表得出的I型和II型错误）评估由TSN的四种配置实现的分类。此外，对于各种阈值，探索了使训练过程导致的突触权重稀疏的效果。结果表明，所提出的方法实现了很高的精度，同时比三个弹性指标中的每一个的计算都快得多。关于稀疏化，在阈值之后，准确性下降，这意味着TSN无法进一步稀疏化。从而，