# Prediction of Air Pollution Concentration Based on mRMR and Echo State Network
## 1 Introduction  
With the rapid advancement of urbanization and industrialization, air quality has deteriorated severely, which has negatively affected the quality of the living environment and even hindered economic growth in some areas [1]. In particular, the inhalable particles produced by industrial pollution have small particle size, large diffusion area and strong activity, thus they can enter the human body through the respiratory tract, which has adverse effects on human health. Therefore, the prediction of air pollutants plays a crucial role in the early warning and control of environmental pollution [2]. Therefore, modeling and forecasting the air quality index (e.g., PM\({}_{2.5}\) concentration) has become an effective way to prevent and control air pollution, and it also provides a scientific basis for the development of effective measures [3]. The implementation of this idea can effectively reduce the health hazard of air pollution, thus achieving early warning and rational planning [4]. For a long time, many scholars have conducted in-depth research on air pollution. At the same time, a variety of predictive models have been proposed, such as autoregressive integrated moving average model [5], support vector machine [5], multiple linear regression model [6], neural networks [7; 8], and so on [9]. All of them have been applied to predict air pollution concentration. [PERSON] et al. [10] applied artificial neural network and adaptive neuro-fuzzy inference system to predict PM\({}_{2.5}\) concentration. [PERSON] et al. [11] proposed heterogeneous space-time artificial neural networks to deal with spatial heterogeneity, which has been applied to predict the concentration offine particles in Beijing-Tianjin-Hebei. [PERSON] et al. [12] proposed a deep recurrent neural network for time series prediction, which can accurately predict the PM\({}_{2.5}\) concentration. In order to solve the air pollution monitoring and prevention in Kunming and Yuxi, China, [PERSON] et al. [13] studied the method called co-integration flower-pollination-algorithm support vector machine for the prediction of PM\({}_{10}\) concentration time series. In order to study the attenuation effect of haze on solar radiation scattering, [PERSON] et al. [14] proposed a new SVM-based method that increases the accuracy of global solar radiation models by increasing variables of daily global solar radiation, sunshine hours, temperature, relative humidity, and air quality index. [PERSON] et al. [15] selected an optimal prediction model based on 10-fold cross-validation to estimate PM\({}_{2.5}\) concentrations during wildfires in Northern California in 2008, and reliably predicted major wildfire events. As can be seen, different types of predictive models can successfully solve different problems of air pollution time series prediction. Because the causes of air pollution are very complicated, analyzing the main pollutants and influence variables of air quality index will lay the foundation for the establishment of predictive models. Although the methods described earlier are effective, they do not analyze the validity of the input variables, so the models are likely to contain irrelevant or redundant information. In order to build an accurate predictive model, [PERSON] et al. [16] applied Pearson correlation coefficient to analyze the relationship between PM\({}_{2.5}\) and other variables and selected the appropriate input variables according to the correlation order. [PERSON] et al. [17] investigated cross-correlations between PM\({}_{2.5}\) and four meteorological factors based on multifractal detrended cross-correlation analysis method, which reveals the impact of meteorological variables on PM\({}_{2.5}\) concentration. [PERSON] et al. [18] proposed a novel graphical causality analysis approach and analyzed the impact of meteorological and traffic variables on air quality indexes. [PERSON] et al.