Artificial neural networks (ANNs) are powerful tools for data analysis and are particularly suitable for modeling relationships between variables for best prediction of an outcome. While these models can be used to answer many important research questions, their utility has been critically limited because the interpretation of the "black box" model is difficult. Clinical investigators usually employ ANN models to predict the clinical outcomes or to make a diagnosis; the model however is difficult to interpret for clinicians. To address this important shortcoming of neural network modeling methods, we describe several methods to help subject-matter audiences (e.g., clinicians, medical policy makers) understand neural network models. Garson's algorithm describes the relative magnitude of the importance of a descriptor (predictor) in its connection with outcome variables by dissecting the model weights. The Lek's profile method explores the relationship of the outcome variable and a predictor of interest, while holding other predictors at constant values (e.g., minimum, 20th quartile, maximum). While Lek's profile was developed specifically for neural networks, partial dependence plot is a more generic version that visualize the relationship between an outcome and one or two predictors. Finally, the local interpretable model-agnostic explanations (LIME) method can show the predictions of any classification or regression, by approximating it locally with an interpretable model. R code for the implementations of these methods is shown by using example data fitted with a standard, feed-forward neural network model. We offer codes and step-by-step description on how to use these tools to facilitate better understanding of ANN.

How to identify influential nodes in social networks is of theoretical significance, which relates to how to prevent epidemic spreading or cascading failure, how to accelerate information diffusion, and so on. In this Letter, we make an attempt to find effective multiple spreaders in complex networks by generalizing the idea of the coloring problem in graph theory to complex networks. In our method, each node in a network is colored by one kind of color and nodes with the same color are sorted into an independent set. Then, for a given centrality index, the nodes with the highest centrality in an independent set are chosen as multiple spreaders. Comparing this approach with the traditional method, in which nodes with the highest centrality from the entire network perspective are chosen, we find that our method is more effective in accelerating the spreading process and maximizing the spreading coverage than the traditional method, no matter in network models or in real social networks. Meanwhile, the low computational complexity of the coloring algorithm guarantees the potential applications of our method.

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