# Representing and Inferring Massive Network Traffic Condition: A Case Study in Nashville, Tennessee
## 1 Introduction  
With the rapid development of intelligent transportation systems (ITSs) in the big data era, a huge amount of up-to-date data are being collected, archived, and analyzed from a variety of sources such as smart phones, probe vehicles, video cameras, and infrastructure-based detectors. Traditional detector loops and more advanced technologies, such as radar and microwave detectors, have been widely deployed in large metropolitan areas to monitor the traffic flow in a real-time manner. These systems deal with thousands of detector stations with high temporal resolution at 20 to 30 s per update, which poses great challenges for the efficiency and computational cost of analyzing ITS data. One of the main challenges is to assess the road network condition quickly and accurately for a given moment and efficiently infer and forecast meaningful spatial and temporal trends for the future, which can be useful for many ITS applications such as monitoring networks, planning traffic, and mitigating congestion [1, 2]. Previous research has aimed to model the road network by considering every road segment within it. However, this approach may not be practical for large traffic networksand real-time applications. Furthermore, missing data will significantly impair the effectiveness of this method. To address this issue, our focus is on creating low-dimensional network models that only require monitoring of a selected subset of road segments. To develop accurate low-dimensional models for large and diverse road networks, prior research has primarily focused on techniques such as principal component analysis (PCA) [3; 4; 5; 6; 7]. However, PCA models are difficult to interpret in terms of individual links in the network. [PERSON] et al. used PCA to analyze OD pair data in a small network [4; 5], while [PERSON] et al. applied various subspace methods to compress traffic speed data [8]. These studies demonstrated that subspace methods like PCA and DCT (discrete cosine transform) can effectively reduce the size of traffic data. However, they do not provide detailed insights into traffic patterns for specific roads and time periods. In addition, implementing PCA online still requires information from all detectors in the network because the principal component is basically a linear combination of all columns of the original data, which greatly reduces the efficiency of data processing. This is the reason why PCA is mostly used offline for dimension reduction purposes. In contrast, the CUR decomposition [9] considers selecting subsets from individual links and time instances, enabling us to directly extract underlying spatial and temporal patterns in large road networks. In 2013, [PERSON] et al. explored the use of the CUR matrix decomposition method for compressing and sensing traffic speed data. They compared this method to PCA and showed that the resulting low-dimensional models from CUR are much more easily interpretable. They also demonstrated how CUR can be used for compressed sensing of traffic data [2]. In 2015, [PERSON] et al. employed column-based (CX) low-dimensional models based on their previous research to improve the scalability of compressed sensing and prediction. The researchers broke down the compressed prediction error into different parts and examined how they related to each other, and their numerical findings demonstrate that this approach considerably lowers computational expenses with little effect on prediction accuracy [10]. The benefits of the CUR method are achieved with a trade-off of greater prediction errors as the compression ratio (the ratio of original number of columns to number of columns in a low-dimensional representation) increases. Nevertheless, there is significant room for improving the process of selecting columns based on statistical leverage [9] calculated from singular value decomposition (SVD) [11]. Another issue is that the author only tested a limited range of compression ratios from 2 to 10 [2; 10], which is not sufficient to depict the performance of the proposed method.