FUNCTIONAL CLUSTERING ANALYSIS FOR TRAFFIC STATES FORECASTING

In the environment of rapid economic development, the number of various vehicles on urban roads is increasing year by year, and the incidence of traffic accidents is on the rise. In the field of traffic state prediction, few scholars discuss the functional data form of traffic data and consider how to study traffic problems based on this form. In addition, because the high-dimensional ecosystem formed by the behavior of traffic subjects, road network topology, and environment presents nonlinearity, randomness, and coupling, it is infeasible to use a model trained using a single sample to predict traffic state. The above problems increase the difficulty of accurately predicting traffic conditions.

Aiming at the traffic data types and temporal and the nonlinear problems of spatial characteristics, we propose a traffic prediction model based on functional clustering. Firstly, based on the smoothing method of the Fourier basis function, this paper makes an overall analysis of the road network data of two main roads in Shenzhen and selects the variable indicators of traffic road grouping evaluation. Secondly, by establishing a functional linear regression model, the multidimensional index set is transformed into a function varying with time, and then the coefficient matrix of each variable under all samples is obtained. Thirdly, the coefficient matrix is clustered by the K-means++ clustering model to obtain the category label of the variable under each sample. Then, the obtained category label matrix of different variables under each sample is clustered by quadratic Kmeans++, and the grouping of each road is obtained. Finally, combined with the classical time series model, the traffic speed of Shenzhen is predicted.

Through the comparative analysis of different indicators and dimensions under multiple models, the results show that the functional clustering prediction model proposed in this paper successfully identifies the roads with similar characteristics and improves the prediction accuracy of the average speed of vehicles passing through the road. By calculating the error volatility of 20 sections under different models, we verify that the functional clustering prediction model proposed in this paper is more robust than others. The model proposed in this paper can help the transportation administration effectively investigate and analyze the traffic operation status of the whole city, accurately find out the congested areas, and improve the traffic efficiency and the happiness index of people's lives through the implementation of directional road micro reconstruction.

在经济快速发展的大环境下，城市道路上各类车型的数量逐年增多，交通事故发生率呈上升趋势，人们迫切需要更加有效、精准的交通状态预测方法。对于交通状态预测的研究，很少有学者讨论交通数据具有的函数型数据形式以及考虑如何基于这种形式去研究交通问题。此外，由于交通主体行为、路网拓扑结构和环境三者所形成的高维生态系统呈现出非线性、随机性和耦合性，因此仅使用单一样本下交通数据的训练模型进行预测，预测的结果偏差较大。上述问题的出现加大了交通状态精准预测的困难性。

本文针对交通数据类型和时空特征的非线性问题，提出了一种函数型聚类的交通预测模型。首先，本文基于Fourier基函数的平滑方法对深圳市两条主干道的路网数据进行了整体分析并选择出交通道路分组评估的变量指标。其次，通过建立函数型线性回归模型，将多维指标集转换为随时间变化的函数，进而得到每个变量在所有样本下的系数矩阵。再次，通过K-means++聚类模型将系数矩阵聚类，得到每个样本下该变量的类别标签。然后，对已获得的关于每个样本下不同变量的类别标签矩阵进行二次K-means++聚类后，得到每条道路的分组。最后，结合经典的时间序列模型对深圳市交通速度进行预测。

通过对多个模型下不同指标、不同维度的对比分析，结果表明本文提出的函数型聚类预测模型成功识别了特征相似的道路，提高了车辆通过该道路平均速度的预测精度。通过计算不同模型下20个路段误差的波动性，我们验证了本文提出的函数型聚类预测模型比对比模型更加稳健。本文提出的模型可以帮助交通管理局对全市的交通运行状况进行有效排查分析，精确找出拥堵区域，通过实施定向道路微改造，从而提高通行效率，提升人民生活的幸福指数。

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