Spatiotemporal traffic data imputation is of great significance in intelligent transportation systems and data-driven decision-making processes. To make an accurate reconstruction from partially observed traffic data, we assert the importance of characterizing both global and local trends in traffic time series. In the literature, substantial prior works have demonstrated the effectiveness of utilizing low-rankness property of traffic data by matrix/tensor completion models. In this study, we first introduce a Laplacian kernel to temporal regularization for characterizing local trends in traffic time series, which can be formulated in the form of circular convolution. Then, we develop a low-rank Laplacian convolutional representation (LCR) model by putting the nuclear norm of a circulant matrix and the Laplacian temporal regularization together, which is proved to meet a unified framework that takes a fast Fourier transform (FFT) solution in a relatively low time complexity. Through extensive experiments on some traffic datasets, we demonstrate the superiority of LCR for imputing traffic time series of various time series behaviors (e.g., data noises and strong/weak periodicity). The proposed LCR model is an efficient and effective solution to large-scale traffic data imputation over the existing baseline models. Despite the LCR's application to time series data, the key modeling idea lies in bridging the low-rank models and the Laplacian regularization through FFT, which is also applicable to image inpainting. The adapted datasets and Python implementation are publicly available at https://github.com/xinychen/transdim.
翻译:在智能交通系统和数据驱动的决策过程中,随机流量数据估算非常重要。 为了根据部分观测的交通数据进行准确的重建,我们强调在交通时间序列中将全球和地方趋势定性的重要性。 在文献中,大量先前的工程已经证明,通过矩阵/天体完成模型利用交通数据中低级别特性是有效的。在本研究中,我们首先引入一个拉巴西内核圈,以描述交通时间序列中当地趋势的特征,这种趋势可以循环变换的形式形成。然后,我们开发了一个低等级的拉普拉西亚曲线代表模型(LCR),方法是将一个循环矩阵和拉普拉普西时间序列的核规范结合起来。在文献中,大量以前的工作证明,能够满足一个统一框架,以相对较低的时间复杂性快速的Fourier变换(FFT)解决方案。通过对一些交通数据集进行广泛的实验,我们展示了LCR的优势,可以将各种时间序列的交通时间序列(例如,数据噪音和坚固/湿度的循环周期)的低级别代表模式,而拟议的LCRCR模型则是一个高效的标准化数据模型,在现有的数据库中,在现有的数据库中,在使用。