## 2 Research Framework  
In this paper, a deep learning-based CFST-LSTM model is proposed for air quality prediction. Deep learning, also known as deep structured learning or hierarchical learning, is a class of machine learning that uses multiple layers of non-linear processing units for feature selection and data modeling [20]. Due to its powerful learning ability, deep learning has been applied to a number of fields such as computer vision, speech recognition, language processing [21; 22], and has achieved state-of-the-art performance [23]. Development of deep learning can be traced back to the machine learning technology. Due to the intrinsic linear assumption of traditional statistical methods, scholars tried to adopt non-linear machine learning methods to better fit the non-linear mechanism of real-world data like air pollution. For example, [PERSON] et al. [24] identified pollution sources and predicted urban air quality using tree-ensemble machine learning methods. Their results demonstrated that the prediction accuracy of machine learning methods outperformed statistical methods. [PERSON] et al. [25] developed an online air quality prediction model based on support vector machine and achieved high prediction accuracy. Among various machine learning methods, artificial neural networks (ANNs) have been proved to have better prediction performance for air pollution compared with other models [26]. Typical ANNs usually contain three kinds of layers, including input layer, hidden layer, and output layer [27; 28]. Based on three-layer ANNs, scholars further found that as the architecture of a neural network becomes deeper and more complicated, its modeling performance becomes better. Therefore, deep learning is developed. Deep learning models are vaguely inspired by the information processing and communication patterns in biological nervous systems [20]. It normally contains multiple layers and the relationship between layers and neurons of each layer could be rather complicated. Commonly seen deep learning architectures include deep neural networks, deep belief networks, and recurrent neural networks. Among these networks, the recurrent neural network (RNN) is specially designed for time series data such as air pollution data modeling [29]. It can take the output of the last layer as the input of the current layer and therefore estimate the temporal mechanism of the data. Although RNN can pass on the information of the previous moment to the next moment, its modeling performance will become unsatisfactory for long-term data due to the vanishing or exploding gradient [30]. To overcome the limitation, a gated recurrent neural network named long short-term memory (LSTM) is proposed. It overcomes the vanishing/exploding gradient problem of RNN through several control gates and can learn from long-term dependencies. Its modeling performance for time series data has also been evaluated and proved by many studies [31; 32; 33; 34]. However, only a few of them have explored the implementation of LSTM on air quality prediction. Therefore, this paper adopts LSTM as the base prediction model for air pollutant concentrations and further proposes an extended LSTM model, namely correlation filtered spatial-temporal long short-term memory (CFST-LSTM). The research framework of this paper is shown in Figure 1. It consists of five parts. First is data collection. In this study, air quality datasets of California, the U.S., are collected for experiments. The collected data are then preprocessed to be more model-friendly. Missing data imputation and data normalization are conducted. After that, the CFST-LSTM model is constructed to forecast the PM2.5 concentrations. Its model structure and parameters are optimized and its modeling performance is compared with other commonly seen machine learning models and neural networks. Later, for each station in the study area, a CFST-LSTM model and an ordinary LSTM model are constructed to explore the model generalization.