Feature selection for optical network design via a new mutual information estimator

An efficient design of optical networks is a complex challenge that requires knowledge of the desired performance trends. Such knowledge would have a potential impact on an expert system to this end, for instance, would help identify reliable topological parameters to characterize the desired behavior of the network. Feature selection from information theory is widely explored in many areas of expert and intelligent systems, and it is a suitable technique to choose such parameters. In optical networks, many signals are carried along the same fiber, each one with its wavelength. A possible desired performance is the minimal usage of different wavelengths, which can be influenced by many topological parameters established in the network design. However, it is difficult to determine the dependence between topological parameters and the number of wavelengths, because this latter addresses an NP-hard problem. We perform a comprehensive literature review to find topological metrics that are easier to compute and apply feature selection using a new mutual information estimator. Based on coincidence detection, this estimator is lightweight and easy-to-use and allows measuring the relevance between discrete and continuous features, without discretization nor estimating probability density functions. For this purpose, tests are performed using 315 topological parameters from graph theory and complex networks, in 15 real-world optical networks and 2.2 million random topologies that mimic real-world ones. The topological parameters are ranked based on its mutual information values, obtaining a set of the most influential for explaining the wavelength requirements. Among these parameters, as a result, the method highlights the ones derived from the edge betweenness. Moreover, some parameters proposed by the literature do not perform as expected. The results of this study can serve as a basis for new expert systems to design and expansion of optical networks, driven by the most relevant topological parameters.