Missing Traffic Flow Data Complement Based On The Non-negative Matrix Factorization With Dynamic Time Warping

Data in Intelligent Traffic System（ITS）often suffers from data missing.There are many missing values in traffic flow data collection in ITS,which leads to a decrease in the effectiveness of traffic flow data,leading to traffic flow predictions and vehicle path planning predictions.The lack of sufficient data makes it very difficult.At present,scholars at home and abroad pay close attention to an important research topic in the field of transportation,namely,the filling of missing values of traffic flow.Recent research on missing data filling mainly focuses on using data-driven or model-driven models to fill missing values.In most cases,the existing missing value filling methods do not make full use of spatio-temporal correlation.Non-negative Matrix Factorization（NMF）has achieved good results in many applications.In order to estimate missing values,the current research directly applies the NMF model to the filling of missing values,emphasizing the generality of the data and ignoring the subtle but important differences due to the sampling date,so the accuracy of filling the missing values is not high.In this paper,In order to solve the problem of missing values in traffic flow,this paper proposes a filling method based on NMF.The main tasks include:（1）Based on the similar time series exploration problem of dynamic time warping（DTW）model,a commonly used optimization algorithm for solving similar time series models called Lower Bounding Dynamic Time Warping（LBDTW）did a detailed discussion.Considering that the traffic flow data set has a large number of missing values,this paper improves the LBDTW algorithm so that it can be used to calculate the similarity between time series with missing data.（2）When filling the missing values of the traffic flow data matrix,the inhomogeneity of temporal and spatial correlation should be fully considered,and a method of filling missing values of traffic flow based on non-negative matrix factorization and dynamic time warping algorithm DKNMF is proposed.The specific process of the algorithm is described,and the performance of the algorithm is compared on a public traffic data set-PEMS and the traffic data set of Yunnan Province.The simulation results show that DKNMF is significantly better than NMF and some other commonly used filling algorithms.The innovations of this article are mainly the following two points:（1）This paper proposes an improved LBDTW algorithm to describe the similarity between traffic samples,fully considers the impact of missing values on LBDTW algorithm,and effectively expresses the correlation between traffic flow data.（2）This paper proposes the DKNMF algorithm based on the characteristics of traffic flow data,through the fusion of the improved LBDTW algorithm and the K-means algorithm,and applies the NMF algorithm to fill in the missing values.