C³-GAN+: Complex-Condition-Controlled Generative Adversarial Networks with Enhanced Embedding

Given historical traffic distributions and associated urban conditions observed in a city, the conditional urban traffic estimation problem aims at estimating realistic future projections of the traffic under a set of new urban conditions, e.g., new bus routes, rainfall intensity, and travel demands. The problem is important in reducing traffic congestion, improving public transportation efficiency, and facilitating urban planning. However, solving this problem is challenging due to the strong spatial dependencies of traffic patterns and the complex relations between the traffic and urban conditions. Recently, we proposed a Complex-Condition-Controlled Generative Adversarial Network (\(\boldsymbol{C^{3}}\)-GAN), which tackles both of the challenges and solves the urban traffic estimation problem under various complex conditions by adding a fixed embedding network and an inference network on top of the standard conditional GAN model. The randomly chosen embedding network transforms the complex conditions to latent vectors, and the inference network enhances the connections between the embedded vectors and the traffic data. However, a randomly chosen embedding network cannot always successfully extract features of complex urban conditions, which indicates \(C^{3}\)-GAN is unable to uniquely map different urban conditions to proper latent distributions. Thus, \(C^{3}\)-GAN would fail in certain traffic estimation tasks. Besides, \(C^{3}\)-GAN is hard to train due to vanishing gradients and mode collapse problems. To address these issues, in this article, we extend our prior work by introducing a new deep generative model, namely, \(C^{3}\)-GAN\(+\), which significantly improves the estimation performance and model stability. \(C^{3}\)-GAN\(+\) has new objective, architecture, and training algorithm. The new objective applies Wasserstein loss to the conditional generation case to encourage stable training. Shared convolutional layers between the discriminator and the inference network help to capture spatial dependencies of traffic more efficiently, part of the shared convolutional layers are used to update the embedding network periodically aiming to encourage good representation and avoid model divergence. Extensive experiments on real-world datasets demonstrate that our \(C^{3}\)-GAN\(+\) produces high-quality traffic estimations and outperforms state-of-the-art baseline methods.