Evaluating graph resilience with tensor stack networks: a Keras implementation

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.