## 1 Introduction  
Urban big data involves the daily life of citizens and the stable running of industries; it is characterized by large volume, complex sources, and heterogeneous structure [1]. How to make full use of urban big data to analyze city development issues and provide informational assistance for government departments has attracted great interest in recent years [2, 3]. In challenges of city management, traffic problems such as increasingly traffic congestion, frequently traffic accidents, severely environmental pollution, should be of the upmost concern [4]. The traffic flow prediction is an important part of urban traffic management and emergency response [5]. In the background of controlling and preventing epidemic diseases, traffic flow prediction can obtain travel indicators, judge crowd-gathering areas, analyze cross-regional movements. Traffic flow data are typical spatial-temporal data, which relate to various elements of the traffic network, including humans, vehicles, roads, and environmental information [6]. In the period of big data, city managers must dig deep into the potential value contained in traffic flow data. Traffic flow data contain multi-mode characteristics [7]. Most of the existing traffic flow prediction methods are based on three kinds of characteristics: temporal characteristics, spatial characteristics, and periodic characteristics [8, 9]. In recent years, the common traffic flow prediction methods fall into two categories: the model-driven methods and the data-driven methods [10]. The model-driven methods, also known as parametric methods, including Autoregressive (AR), Historical Average (HA), Autoregressive Integrated Moving Average (ARIMA), Seasonal ARIMA (SARIMA) [11, 12, 13, 14], etc. Generally, the model-driven methods only focus on temporal characteristics and need to satisfy predetermined theoretical assumptions, so the application of these methods is limited. The data-driven methods, also known as non-parametric methods, can be further divided into machine learning-based methods and deep learning-based methods [15, 16, 17, 18]. For example, machine learning methods, such as Support VectorRegression (SVR) and K-Nearest Neighbor (KNN), were employed for traffic flow prediction [19; 20]. Convolution Neural Networks (CNNs) are a classical type of deep learning method which can automatically capture spatial structural information and take spatial characteristics into account [21; 22; 23]. To settle spatial-temporal forecasting problems, some researchers proposed hybrid methods to improve the prediction accuracy, such as Convolutional LSTM Networks (ConvLSTMs) [24] and Spatio-Temporal Residual Network (ST-ResNet) [25]. However, hybrid methods increase the complexity of the prediction model. Moreover, all of the above methods cannot recover missing data. In the scenario of traffic flow prediction, missing data is inevitable due to equipment failure, bad weather and transmitting interference [26]. According to the report of the Texas Transportation Institute, the missing data of transportation system account for 16-93% in some states, with an average missing data rate of 67%. Therefore, how to recover the missing data is also an urgent problem in traffic flow prediction. To take full advantage of multi-mode characteristics, and recover missing data as much as possible, some researchers have applied tensor decomposition to traffic flow prediction [27; 28]. Using tensor to present traffic flow data can preserve the integrity of multi-mode characteristics. Tensor decomposition is an important part of multidimensional linear algebra theory, which can effectively mine potential characteristics contained in data. The common tensor decomposition methods include CP (CANDECOMP/PARAFAC) decomposition and Tucker decomposition. In this paper, we use a high-dimensional tensor to represent the traffic flow data, considering \"temporal-spatial-periodic\" multi-mode characteristics. Firstly, we recover the missing data of the traffic flow data.