Traffic-data recovery plays an important role in traffic prediction, congestion judgment, road network planning and other fields. Complete and accurate traffic data help to find the laws contained in the data more efficiently and effectively. However, existing methods still have problems to cope with the case when large amounts of traffic data are missed. As a generalization of vector algebra, geometric algebra has more powerful representation and processing capability for high-dimensional data. In this article, we are thus inspired to propose the geometric-algebra-based generative adversarial network to repair the missing traffic data by learning the correlation of multidimensional traffic parameters. The generator of the proposed model consists of a geometric algebra convolution module, an attention module and a deconvolution module. Global and local data mean squared errors are simultaneously applied to form the loss function of the generator. The discriminator is composed of a multichannel convolutional neural network which can continuously optimize the adversarial training process. Real traffic data from two elevated highways are used for experimental verification. Experimental results demonstrate that our method can effectively repair missing traffic data in a robust way and has better performance when compared with the state-of-the-art methods.

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