Weighted Graph-Based Signal Temporal Logic Inference Using Neural Networks

Extracting spatial-temporal knowledge from data is useful in many applications. It is important that the obtained knowledge is human-interpretable and amenable to formal analysis. In this letter, we propose a method that trains neural networks to learn spatial-temporal properties in the form of weighted graph-based signal temporal logic (w-GSTL) formulas. For learning w-GSTL formulas, we introduce a flexible w-GSTL formula structure in which the user's preference can be applied in the inferred w-GSTL formulas. In the proposed framework, each neuron of the neural networks corresponds to a subformula in a flexible w-GSTL formula structure. We initially train a neural network to learn the w-GSTL operators, and then train a second neural network to learn the parameters in a flexible w-GSTL formula structure. We use a COVID-19 dataset and a rain prediction dataset to evaluate the performance of the proposed framework and algorithms. We compare the performance of the proposed framework with three baseline classification methods including K-nearest neighbors, decision trees, support vector machine, and artificial neural networks. The classification accuracy obtained by the proposed framework is comparable with the baseline classification methods.