# Representing and Inferring Massive Network Traffic Condition: A Case Study in Nashville, Tennessee
## 1 Introduction
In addition to leverage-based column selection, [PERSON] et al. proposed [12] an algorithm to perform the approximation of the tensors based on the CX decomposition for matrices. [PERSON] and [PERSON] [13] proposed a road network compression method to improve the efficiency of data processing based on correlation analysis and CX decomposition, which is then integrated into a deep learning network to predict the short-term traffic flow. Apart from matrix decomposition, transformation techniques such as discrete Fourier transform (DFT) and discrete wavelet transform (DWT), which are commonly used for compressing signals and images, can be adapted for spatiotemporal data. In the context of road traffic data compression, methods involving DCT and SVD are utilized, leveraging Kronecker product and tensor decomposition [14]. Additionally, by organizing the data in a multidimensional format, algorithms based on DWT are integrated to achieve dimensionality reduction [15]. To harness the benefits provided by signal processing methods from other data types, the field of graph signal processing (GSP) [16] has been developed to conceptualize spatiotemporal data as a two-dimensional graph signal and establishes operations like linear filtering and linear prediction. Furthermore, [PERSON] et al. [1] adopted graph Fourier transform (GFT) and achieved less than one percent reconstruction error (RE) on California's Interstate 605 (I-605) freeway data. Although the GFT-based method outperformed other methods, the problems are twofold: (1) it is difficult to interpret in terms of individual detectors, and (2) the model is too complex, possessing a mathematical form which is unlikely to be deployed and understood by practitioners in real world situations. To summarize, previous studies have focused on the PCA approach, matrix decomposition methods, and signal transformation techniques to compress large datasets and represent the overall network condition using low-dimensional approximations. Three major research gaps were identified, as follows. First, the CUR decomposition method is widely used due to its strong interpretability, whereas the approach to selecting the optimal subset of columns remains to be improved. To this end, the clustering method is explored in this study to enhance the representing performance. Second, most previous studies failed to compare their method of selecting columns with a random sampling approach with equal probabilities. Finally, most studies only evaluated their algorithms in a limited range of compression ratios, but more interesting insights could be discovered if more cases, especially those under a high compression ratio, are tested. To address these issues, this paper aims to utilize a column-based CUR matrix decomposition technique integrated with a clustering method to represent the original traffic network as a smaller subset of original columns with acceptable errors. The experiment was conducted using radar detector outputs (speed) aggregated at 5 min resolution from Nashville, TN. A group of representative detectors are selected using the proposed weighted average method to establish a relationship with the original network by analyzing the historical data and calculating the relationship matrix offline. In addition, this study incorporates clustering analysis into CUR decomposition inspired by the methodology of computing stock indexes such as the S&P 500 and Nasdaq. Analogous to selecting stocks from different sectors to represent the whole market, a clustering analysis was first conducted, followed by the normal CUR decomposition within each cluster, and results from each cluster would be merged as the final outputs. In this regard, we also reviewed several papers applying clustering algorithms to tackle problems in the traffic domain. [PERSON] et al.