Co-Training Semi-Supervised Learning for Fine-Grained Air Quality Analysis

Abstract

Due to the limited number of air quality monitoring stations, the data collected are limited. Using supervised learning for air quality fine-grained analysis, that is used to predict the air quality index (AQI) of the locations without air quality monitoring stations, may lead to overfitting in that the models have superior performance on the training set but perform poorly on the validation and testing set. In order to avoid this problem in supervised learning, the most effective solution is to increase the amount of data, but in this study, this is not realistic. Fortunately, semi-supervised learning can obtain knowledge from unlabeled samples, thus solving the problem caused by insufficient training samples. Therefore, a co-training semi-supervised learning method combining the K-nearest neighbors (KNN) algorithm and deep neural network (DNN) is proposed, named KNN-DNN, which makes full use of unlabeled samples to improve the model performance for fine-grained air quality analysis. Temperature, humidity, the concentrations of pollutants and source type are used as input variables, and the KNN algorithm and DNN model are used as learners. For each learner, the labeled data are used as the initial training set to model the relationship between the input variables and the AQI. In the iterative process, by labeling the unlabeled samples, a pseudo-sample with the highest confidence is selected to expand the training set. The proposed model is evaluated on a real dataset collected by monitoring stations from 1 February to 30 April 2018 over a region between 118° E–118°53′ E and 39°45′ N–39°89′ N. Practical application shows that the proposed model has a significant effect on the fine-grained analysis of air quality. The coefficient of determination between the predicted value and the true value is 0.97, which is better than other models.

1. Introduction

Air quality is one of the main environmental issues in the world. Over the past few decades, rapid urbanization has brought economic maturity, but there is a decoupling trend between economic growth and pollution emission strategies [1]. Severe air pollution poses a persistent threat to humans. According to statistics, about 1 million people die each year from air pollution in China [2], and about 4.24 million people die prematurely each year globally due to air pollution [3]. In addition, air pollution can cause serious ecological damage, such as acid rain, climate change and global warming. The frequency of extreme weather events is increasing [4,5].

In such a situation, air quality is receiving more and more attention. In order to know the air quality at a specific time, the environmental protection department has set up monitoring stations with equipment that can automatically monitor air quality [6]. However, each station requires expensive construction costs and a large number of human resources to maintain them regularly, and the construction may be limited by urban land-use strategies [7,8]. As a result, the number of air quality monitoring stations is often limited, and the spatial distribution is highly uneven. Compared with the occupied area, the effective area covered by the monitoring station is limited. For example, Beijing covers an area of 16,410 km² but has only 36 monitoring stations; Taiwan covers an area of 36,193 km² but has only 78 monitoring stations. Therefore, it is necessary to design an adequate air quality fine-grained analysis model to predict the air quality at the location without monitoring stations.

At present, the methods applied to fine-grained analysis of air quality include numerical models and data-driven models. As the atmospheric environment has been increasingly explored, researchers have found ways to simulate the complex dispersion and transport processes of air pollutants using empirical assumptions, and various numerical models that can estimate the pollutant concentrations at any specified location have emerged [9]. Numerical models include physical models and chemistry transport models (CTMs). Physical models include the Gaussian plume model (GPM) [10], the convection–diffusion model, the urban street canyon model [11], computational fluid dynamics (CFD) [12,13], etc. Ghenai et al. [14] used the GPM to simulate the dispersion of PM₁₀ from point sources and area sources in the air around a 35-meter-high factory to obtain the average concentrations over the next 48 h. Rangel et al. [15] used the GPM to estimate the emissions and diffusion of CO, PM_2.5 and NO_X from burning sugarcane biomass in rural areas of Northeast Brazil. Yang et al. [16] modified the GPM to estimate the transport of ammonia and particulate matter from ventilation tunnel fans of poultry houses. Karim and Nolan [17] developed a CFD model to simulate the dispersion of motor vehicle pollution on motorways, mainly for NO₂ concentrations. Tonbon et al. [18] used a CFD model for the 3D simulation of CO in a real city. Kwak et al. [12] used CFD to simulate the concentration distribution of NO₂ and O₃ based on measured data from roadside air quality monitoring stations. Nie et al. [19] used CFD to simulate the dispersion and distribution of vehicle emissions as a guide for adjusting the location of pollutant monitoring devices and thereby improving air quality.

With the study of turbulence characteristics in the atmospheric boundary layer, researchers have carried out a lot of indoor numerical experiments and field observations, adding more complex meteorological models and nonlinear reaction mechanisms to the physical models. CTMs perform air quality prediction by simulating the chemical processes of emission, transport and mixing of pollutants in the atmosphere. Qiao et al. [20] used a source-oriented version of the Community Multiscale Air Quality (CMAQ) model to determine the source contributions to PM_2.5 during 2013 for 25 Chinese province capitals and municipalities. Koo et al. [21] used CAM_X to develop a PM₁₀ emission inventory, and a posteriori emissions to minimize the gap between the predicted and observed PM₁₀ concentrations were proposed. Manders et al. [22] studied the ability of CTM LOTOS-EUROS to predict PM₁₀ concentrations in the Netherlands. However, these numerical models are usually one or several mathematical formulas, and the setting of their parameters may not apply to all atmospheric environments, resulting in limited accuracy of the results.

Data-driven models such as random forest [23,24], combining a feedforward neural network with a recurrent neural network [25,26], K-nearest neighbor (KNN) [27], XGBoost [28], LightGBM [29,30], support vector machine (SVM) [31], deep neural network (DNN) [32], artificial neural network (ANN) [33], graph convolution network (GCN) [34,35], long and short-term memory (LSTM) [36,37], etc., are widely used. Compared with numerical models, data-driven models can automatically extract complex knowledge from data, model the changing trend of air quality and obtain unknown air quality information. Xu et al. [27] proposed a two-stage method for predicting the air quality index (AQI). In the first stage, ANN is used to predict the AQI at some locations to alleviate the problem of data sparseness. In the second stage, the tensor decomposition method is used to predict the complete AQI distribution for all locations. Based on causal analysis, Zhu et al. [38] selected the most relevant data, using back propagation neural networks to obtain the AQI in unobserved grids. Zhong et al. [26] considered the environmental similarity between regions with and without monitoring stations to select the stations most relevant to the target location. The attributes of candidate stations and target locations are input into the regressor composed of a feedforward neural network and LSTM for air quality fine-grained analysis. Hu et al. [32] estimated PM_2.5 distribution maps in real-time by spatial KNN and DNN based on data collected by air–ground wireless sensors and urban dynamic information captured online. Liu et al. [35] used GCN to construct the topology of the monitoring stations, introduced LSTM to dynamically capture the correlation between historical data and proposed a GC-LSTM to achieve real-time and future AQI prediction. Han et al. [36] proposed a multichannel attention model that models static and dynamic spatial correlations as independent channels to learn the effect of a station on the target location. Song et al. [39] proposed an FCN-based multipollutant spatio-temporal network to estimate grid-level concentrations of multiple air pollutant species based on fixed station measurements and multisource urban features. Qin et al. [24] proposed an environment-aware locally adaptive deep forest model to infer the fine-grained distribution of NO₂ at a resolution of 100 m and 1 h. Hsieh et al. [40] designed a hybrid predictor to predict the long-term AQI of cities without monitoring stations by using dynamic weighting and combining time-related and time-independent predictors. Chen et al. [41] proposed a cascade forest algorithm used to fit the relationship between multisource spatio-temporal characteristics and AQI. Dai et al. [28] built a model based on the GARCH family-XGBoost-MLP to capture the nonlinearity of PM_2.5 concentrations due to different meteorological changes and characteristics to describe the spatio-temporal volatility of PM_2.5.

There are also several hybrid methods for air quality fine-grained analysis. Ma et al. [42,43] quantitatively combined a convective diffusion model and a neural network for multitask learning, where the neural network learned the mapping of attributes to PM_2.5 concentrations and then fitted it to a convective diffusion model. Later, the ConvLSTM was chosen to model the pollution diffusion process, and an autoencoder-based algorithm for air pollution map recovery [44] was proposed, which directly simulates the emergence and diffusion of air pollution instead of modeling the mapping between observed data and unobserved samples. Xu et al. [45] proposed a model coupling Gaussian diffusion and GRU. Based on the diffusion law of pollutants, a multivariate Gaussian diffusion model was developed. Chen et al. [46] proposed a physically guided adaptive model to cope with the sparse coverage of mobile sensors, which adds to the physically guided model when the coverage is sparse and gives more importance to the data-driven model when the sensing coverage is dense. Hong et al. [47] proposed a hybrid model combining the CMAQ model and LSTM to predict PM_2.5 concentrations, improving the performance of large-area spatial distribution prediction at a relatively low cost.

However, the above models need a large number of labeled samples in order to be built. In contrast, the limited number of monitoring stations leads to a limited number of labeled samples, significantly reducing the performance of supervised learning methods. To avoid the problems, Lv et al. [48] proposed a multi-view transfer semi-supervised learning method for air quality estimation, which trains the initial models by leveraging the labeled data and refines the models using a semi-supervised regression algorithm by exploiting the unlabeled data from the target location. Zheng et al. [49] proposed a semi-supervised learning method named U-Air based on co-training [50] to infer the grade of fine-grained urban air quality. The enlightenment for us is that co-training semi-supervised learning can improve the prediction performance of the model by using unlabeled samples to enhance labeled data [51].

In this paper, the most important content focuses on predicting the accurate AQI for locations where monitoring stations are not deployed, which is a regression problem. Therefore, we proposed a new co-training semi-supervised learning method named KNN-DNN that trains two different regressors to model the relationship between the AQI and meteorological and pollutants factors, and constantly complements and improves each regressor. It can effectively enhance the real-time prediction of the AQI at the locations without monitoring stations, provide fine-grained distribution of the AQI and provide sufficient information for air quality prediction and pollutant prevention.

The contributions of this study are as follows:

1.

A co-training semi-supervised learning method combining KNN and DNN is proposed, which can use unlabeled data to improve the prediction accuracy. It avoids the overfitting of supervised learning methods caused by too few labeled samples in the fine-grained analysis of air quality;

2.

The method proposed in this paper combines two different types of learners, which can overcome the limitation of the co-training method combining two similar types of learners, and further improve the fine-grained analysis effect of air quality;

3.

The method proposed in this paper is evaluated on a real dataset to verify that the method is effective and superior to other models.

2. Materials and Methods

2.1. Study Area

Beijing–Tianjin–Hebei region is known as the gathering place of rapid development. Both sides of the region are surrounded by mountains, so air pollutants are difficult to drive away, and this region has experienced severe pollution events. The study area of this paper is between 118°–118°53′ east longitude and 39°45′–39°89′ north latitude, with a total area of 13,472 km². Here, heavy industry has developed, energy consumption is significant and air pollution is also severe.

Figure 1 shows all the air quality monitoring micro stations in the region, a total of 498, of which 6 are state-controlled stations and the rest are provincial-controlled micro-stations. It can be seen the number is limited, and the distribution is highly concentrated. This paper collected the hourly records of these monitoring stations from 1 February to 30 April 2018, with a total of 2136 moments.

2.2. Input Data

The data include the temperature, humidity, pollutant concentrations, source type and AQI of each monitoring station. Among them, AQI is used to describe the degree of air pollution quantitatively. The higher the AQI, indicating that the more serious the air pollution, the greater the harm. AQI is used as a label in the experiment, and the rest are related to the attributes that affect its changing trend. The impact of these attributes on AQI are discussed below.

1.

The changes in AQI are affected by meteorological factors.

Figure 2 shows the correlation between AQI and the two meteorological attributes of temperature and humidity. The horizontal axis represents the humidity, and the vertical axis represents the temperature. Each point in the graph reflects the AQI under specific temperature and humidity conditions. It can be seen that high humidity usually leads to poor air quality, and the effect of temperature on AQI is not apparent, but when the temperature is low and the humidity is high, the air quality is poor.

2.

Air pollutants’ concentrations are the most significant cause of AQI change.

In the correlation matrix shown in Figure 3, subgraphs per row/column represent the same specific air pollutant, including PM_2.5, PM₁₀, SO₂, NO₂, CO and O₃. The pollutant concentration unit is ug/m³, omitted in the graphs. Each subgraph represents the AQI under different pollutant concentrations. It can be seen that no matter which pollutant concentration increases, the air quality becomes worse, and the influence of PM_2.5 and PM₁₀ on AQI is especially obvious.

3.

AQI is directly related to the geographical environment.

On environments such as building sites, sand and gravel and other building materials easily produce dust, leading to poor air quality. We call the geographical environment of the air quality monitoring station the source type. Figure 4 shows the changing trend of the 24 h average AQI of different types of monitoring stations within the research time range of the study area. It can be seen that compared with other source types of monitoring stations, the AQI, which belongs to the locations of main pollution source and key enterprise, maintains a high level as a whole. This attribute is classified, so the single hot code method encodes it.

2.3. Method and Principles

2.3.1. DNN

DNN is a network model suitable for dealing with complex nonlinear relationships and has excellent regression performance. As shown in Figure 5, the DNN model is a hierarchical architecture. Each arrow in the network has its linear coefficient w and bias b. In fact, the local model, such as the perceptron, is composed of a linear relationship and an activation function σ(·). To represent the operation with matrices, the linear coefficient from the k-th neuron of layer l to the j-th neuron of layer l + 1 is defined as $w_{jk}^l$, and the bias of j-th neuron of layer l is defined as $b_j^l$, the activation value is expressed as $a_j^l$. All the linear coefficients of the l layer constitute the matrix W^l and all the biases constitute the vector b^l, then the output of layer l is:

$$a^l=\sigma (z^l)=\sigma (W^l{a}^{l-1}+b^l)$$

(1)

By analogy, we can obtain the final outputs. This process is called forward propagation of DNN, and the black solid line arrow in Figure 5 is the direction.

To obtain a DNN model with high accuracy through training, an appropriate loss function is needed to measure the output loss. By optimizing this function to minimize the loss, a series of corresponding linear coefficient matrices and bias vectors can be obtained to construct an excellent DNN. This process is called the backpropagation of DNN, and the dotted arrow in Figure 5 shows the direction.

2.3.2. KNN

The core idea of the KNN regression algorithm is: the label value of a sample to be predicted is the arithmetic mean of the label values of K samples with the smallest distance from this sample in the feature space. The algorithm flow is shown in Figure 6.

In the process of determining regression decision, KNN only determines the label value of the sample to be predicted according to the label values of the nearest sample or samples. The measure of proximity degree is the distance between the sample to be predicted and each sample, usually using Euclidean distance. The calculation formula is as follows:

$$d=\sqrt{{(x_1-x_2)}^2+{(y_1-y_2)}^2}$$

(2)

where (x₁, y₁) and (x₂, y₂) are the coordinates of two samples in 2D space.

2.3.3. Co-Training

Semi-supervised learning can integrate a small number of labeled samples and a large number of unlabeled samples to improve the learning performance of learners. The labeled sample refers to the sample with both attributes and label, while the unlabeled sample refers to the data with only attributes but no label. Co-training is one of the most well-known semi-supervised learning methods. It was first proposed by Blum et al. [50], and trains two classifiers on two different views, using the prediction of unlabeled examples of each classifier to enhance the training set of the other classifier. In other words, the standard co-training algorithm requires that the attributes are naturally divided into two views. Each view is sufficient for training and is conditionally independent of another view [52].

In practical applications, the requirement of multi-view is challenging to meet, so co-training is improved. The COREG algorithm proposed by Zhou and Li [53] is a single-view co-training method that uses two KNNs as regressors to distinguish between different K and p values. Liang et al. [54] implemented a single-view co-training algorithm using two ANN with different structures. Therefore, the single-view co-training method can make up for the problem that the data provide a challenge to meeting the requirements of multi-views by meeting the diversity of the learners.

The specific steps of single-view co-training are as follows:

• Train two different learners using training sets with labels to build a diverse learning framework that learns the relationship between sample labels and related attributes.
• Label the unlabeled samples and calculate the confidence of each sample.
• Select the unlabeled samples with the highest confidence for each learner, together with the predicted results, add them to the labeled sample set to achieve the purpose of expanding the labeled sample set.
• Train each learner with the expanded labeled sample set.
• Repeat steps 2, 3 and 4 until the preset termination goal is reached or the unlabeled sample set is empty, and two learners with excellent performance are obtained.

The validation set or sample to be predicted is input into two learners, and the average value of the prediction result are taken as the final result.

2.4. Co-Training Semi-Supervised Learning Method Combining KNN and DNN

2.4.1. Construction of a Framework

In the single-view co-training algorithm, if learners with the same type are combined, even if the initial parameters are different, the difference between the learners will continue to shrink with continuous training. Therefore, the prediction effect of each learning is difficult to improve significantly.

For this reason, this paper adopts a strategy of combining different types of learners and conducting co-training from a single view. A new co-training regression algorithm, a co-training semi-supervised learning method combining KNN and DNN named KNN-DNN, is proposed. This method can thoroughly incorporate the advantages of KNN and DNN in semi-supervised learning and overcome the ability limitation of the co-training semi-supervised learning method, which combines two learners with the same type.

Therefore, for the fine-grained analysis of air quality, this improved method can use unlabeled data to expand the training set. It can effectively avoid the overfitting problem caused by the limited number of labeled samples due to the limited number of air quality monitoring stations, thereby improving the model effect. The overall framework is shown in Figure 7. The original data are divided into three parts. The first part is the labeled sample set for the initialization of the learners in KNN-DNN; the second part is the unlabeled sample set, examples in it are used as candidates, which are labeled and added to the labeled sample set during the iterative process; the third part is the validation set: when the model is trained, it is input into the trained model to obtain the AQI of the target locations.

2.4.2. KNN-DNN

The implementation process of the KNN-DNN algorithm is as follows:

1.

The input dataset is divided into a labeled sample set $L=\{(x_1,y_1),(x_2,y_2),\dots ,(x_L,y_L)\}$ and an unlabeled sample set $U=\{x_1,x_2,\dots ,x_U\}$. The attributes and labels in L are used to train the initial learners KNN and DNN.

2.

Each learner receives a batch of randomly selected samples $u=\{x_1’,x_2’,\dots ,x_u’|x_i’\in U\}$ from U and predicts them. The confidence of each sample is calculated, and the sample with the highest confidence is taken as a pseudo-label sample. The predicted value y_i’, together with the attributes x_i’, are added to the training set of another learner.

3.

Through continuous iterative training, a large number of unlabeled samples are labeled and added to the labeled sample set, so they are fully applied.

It is worth noting that in specific training, in order to select the appropriate pseudo-label samples to join the training set of another learner, it is necessary to estimate the confidence of each sample in u. For example, in the classification problem, it can be estimated by calculating the probability that unlabeled samples are labeled to different categories. However, the air quality fine-grained analysis in this paper used to estimate AQI value is a regression problem, and the predicted value is infinite. No estimated probability can be used as with the one in classification.

Therefore, a critical problem in the process of constructing the KNN-DNN algorithm is how to scientifically calculate the confidence of the pseudo-label samples and select the sample with the highest confidence to enhance the performance of each learner. On regression problems such as fine-grained analysis of air quality, the samples that improve the performance of the learner most significantly should be the samples that reduce the error of the learner the most. Thus, calculate the error of the learners h₁ and h₂ trained by the original labeled sample first. Then calculate the error of the learners h_1′ and h_2′ trained by the original labeled set plus each pseudo-label sample. Finally, calculate the change in the error, the sample with the most error reduction is the most confident pseudo-label sample. For each learner, the confidence of each pseudo-labeled sample can be designed as follows:

$$\mathrm{\Delta }={\displaystyle \sum _{x_i\in u}({(y_i-h_k(x_i))}^2-{(y_i-h_k’(x_i))}^2)}$$

(3)

where k = 1, 2.

Algorithm 1 shows the KNN-DNN algorithm steps.

Algorithm 1. KNN-DNN.

Input: labeled sample set L and unlabeled sampled set U

Process: h1 = KNN(L1), h2 = DNN(L2) for k (number of iterations)

for each x’ in u y1 = h1 (x’), y2 = h2(x’) h1’ = KNN(L1∪(x’, y1)), h2’ = DNN(L2∪(x’, y2))     Calculate Δx1, Δx2 according to Formula (3) end for   if there exist Δx1 > 0   then select x’, which makes Δx1 maximum, as $x_1^{’}$, $y_1^{’}$ = h1($x_1^{’}$), u1 = ($x_1^{’}$, $y_1^{’}$), u = u − u1   else u1 = ∅   if there exist Δx1 > 0   then select x’, which makes Δx2 maximum, as $x_2^{’}$, $y_2^{’}$ = h2($x_2^{’}$), u2 = ($x_2^{’}$, $y_2^{’}$), u = u − u2   else u2 = ∅   L1 = L1 + u2, L2 = L2 + u1   if u not changed   then exit   else h1 = KNN(L1), h2 = DNN(L2)        Reselect u in U end for output: 1/2(h1(x) + h2(x))

3. Results

3.1. Evaluation Indicators

This paper predicts the AQI of the target location without monitoring equipment, which belongs to the regression problem. The root mean square error (RMSE), mean absolute error (MAE) and determination coefficient (R²) are used to evaluate the fine-grained prediction effect of each model. The smaller the RMSE and MAE are, the closer R² is to 1, and the better the effect of the model is.

3.2. Baseline Models and Parameter Settings

In the course of the experiment, the supervised learning methods and co-training semi-supervised learning methods were compared, respectively, which mainly included:

• Kriging: The AQI of the target location is estimated by the weighted values of all existing monitoring stations. The coefficient is not the reciprocal of the distance but a set of optimal coefficients that can satisfy the minimum difference between the estimated value and the real value at the target location;
• Liner Regression (LR): Use the curve to fit the relationship between the AQI of the existing monitoring stations and the relevant attributes. When the attributes of the target position are inputted, the AQI can be obtained according to the curve;
• Support Vector Regression (SVR): Use the hyperplane to fit the relationship between the AQI of the existing monitoring stations and the relevant attributes;
• XGBoost: A deep learning algorithm based on gradient boosting decision tree, which uses the second-order Taylor expansion to calculate the loss to overcome overfitting;
• CNN: A classical deep learning algorithm, which is based on local connection and parameter sharing, that automatically extracts features from the data;
• GCN: Construct the collected data into graphs according to the distribution of the monitoring stations, and then perform convolution operations;
• KNN: A single learner for supervised learning;
• DNN: A single learner for supervised learning;
• KNN-KNN: A co-training semi-supervised learning method combining the same type of learners, KNN1 and KNN2.

Because the real AQI data cannot be collected at the location without monitoring equipment, it can be used as an unlabeled sample in practical application. However, to verify the effectiveness of the models, in the experiment, for the co-training semi-supervised learning methods, the data of 100 monitoring stations among 498 monitoring stations were randomly selected as the training set, and 20 were randomly selected as the testing set. Data from other monitoring stations were stripped of labels and used as unlabeled samples.

The number of iterative rounds was set to 100. That is, in the training process, the data of up to 100 monitoring stations were selected for pseudo-labeling. After training, the unselected samples were used as the validation set to verify the effect of the trained model. To make a fair comparison, for the supervised learning model in the baseline models, the settings of the training set, testing set and validation set were the same as the semi-supervised learning methods.

Among the models, KNN has two key parameters, the nearest neighbor number K and the distance metric p of the vector space. In this paper, the cross-validation method was used to optimize these two values on the training set. Figure 8 shows that the fitting effect of KNN is the best when K = 3 and p = 2. That is, the Euclidean distance is used as the metric, and the number of neighbors is 3. The KNN learner in KNN-DNN also uses this parameter combination.

3.3. Analysis of Experimental Results

The proposed method KNN-DNN and the KNN-KNN were verified on the dataset. The relevant indicators of the prediction results of the two models and each learner were compared, as shown in

Table 1. Comparison of each learner in co-training semi-supervised learning models.

Title 1	RMSE	MAE	R2
KNN-KNN	3.12	2.30	0.84
KNN1	4.00	2.96	0.72
KNN2	3.25	2.47	0.82
KNN-DNN	1.51	1.30	0.97
KNN	2.05	1.54	0.94
DNN	1.61	1.41	0.97

.

As seen from Table 1, compared with the prediction results of its own two KNN learners, the KNN-KNN model decreased by 26% and 6% in RMSE, 16% and 8% in MAE and increased by 0.03 and 0 on R². Compared with the prediction results of its own KNN learner and the DNN learner, the DNN-KNN model decreased by 26% and 6% in RMSE, 16% and 8% in MAE index, and increased by 0.03 and 0 on R². It can be seen that in the process of co-training, by labeling the unlabeled samples and enriching the training set of each learner, the performance of each learner can be effectively improved. Therefore, a smaller error and higher fitting accuracy can be obtained.

In addition, the prediction result of the KNN-DNN model has a better performance on all three indicators than that of the KNN-KNN model, which decreases by 52% and 43% on RMSE and MAE, respectively, and increases by 0.15 on R². It can be seen that the co-training semi-supervised learning method combining two different types of learners can better fuse the respective advantages of both learners and break through the limitation of combining single-type learners.

The KNN-DNN model and all the baseline models mentioned in Section 3.2 were verified on the dataset. The relevant indicators of the prediction results of each model are shown in

Table 2. Comparison of different models.

Models	RMSE	MAE	R2
Kriging	15.56	13.23	0.12
LR	7.40	6.66	0.90
SVR	5.82	4.67	0.74
XGBoost	6.98	6.01	0.89
CNN	6.61	4.84	0.89
GCN	4.87	4.01	0.93
KNN	5.63	4.83	0.87
DNN	7.35	6.62	0.90
KNN-KNN	3.12	2.30	0.84
KNN-DNN	1.51	1.30	0.97

.

As can be seen from Table 2, compared with the prediction results of the Kriging, LR, SVR, XGBoost, CNN, GCN, KNN and DNN models, the prediction results of KNN-DNN decreased by 90%, 80%, 74%, 78%, 77%, 69%, 73% and 79%, respectively, on RMSE, 90%, 80%, 72%, 78, 73%, 68%, 73% and 80%, respectively, on MAE, and increased 0.85, 0.07, 0.23, 0.08, 0.08, 0.04, 0.10 and 0.07, respectively, on R². The prediction effect of the KNN-DNN model is better than that of each baseline model.

In summary, the co-training semi-supervised learning method continuously strengthens the view used to train the learners by using unlabeled samples, so that KNN-DNN achieves more competitive air quality fine-grained analysis performance than the existing methods when the number of samples is limited.

The trained KNN-DNN model was applied to the verification set, and the predicted value was compared with the true value, as shown in Figure 9. In theory, the predicted value should be equal to the real value; that is, the trend line is y = x, as shown by the solid line in Figure 9. The trend line obtained by the model is shown by the dotted line in the diagram, with an angle of about 4.4 inches, which is very close to the solid line.

4. Discussion

In this study, we adopt a single-view strategy and propose a co-training semi-supervised learning method that combines multi-type learners to achieve fine-grained analysis of air quality. It provides air quality information in areas that cannot be covered by current air quality monitoring systems. Through the evaluation, the proposed model performs well in all aspects and has better performance than other methods. Compared with supervised learning models such as KNN, DNN, CNN, GCN, XGBoost, etc., our advantage is to make full use of unlabeled samples to improve model performance by expanding the training set. When the number of air quality monitoring stations is limited, the superiority of our model is especially obvious. Compared with U-Air, our advantage is that we do not need to divide a dataset into two fully redundant views, reducing the requirements for the dataset. Compared with KNN-KNN, our advantage is that we increase the difference between the two learners and avoid the ability limitation of using the same type of learner in the co-training algorithm.

There are still some issues to be solved in this study. For example, the spread of air pollution has spatial and temporal correlation, so the distribution of the AQI also has spatial and temporal correlation. The proposed model uses data collected by the air quality monitoring stations to predict the AQI of locations without the deployment of the monitoring station at the current time. It is in real time, but it cannot predict the AQI in the future. In addition, the data we collected are not deep enough, which may lead to the lack of persuasion and generalization of the model.

In the future, we will collect more abundant and comprehensive data, such as topographical, human flow and traffic-related factors and so on so as to achieve a comprehensive understanding of the atmospheric environment and obtain a more rigorous and accurate air quality fine-grained analysis model. At the same time, we will improve the model structure and establish a model that can consider both the temporal and spatial propagation trends of the AQI. It will provide reasonable and effective prediction for the current and future air quality information in the area not covered by the monitoring system. It also facilitates residents to arrange outdoor activities reasonably, and policy makers to take pollution prevention measures in advance, so as to serve the sustainable development of the city.

5. Conclusions

In this paper, a co-training semi-supervised learning method combining KNN and DNN is proposed for fine-grained analysis of air quality. As two different types of learners, KNNs and DNN adopt a single-view co-training strategy. In each iteration, each learner selects a sample with the highest confidence for another learner among the unlabeled samples and constantly expands the training set to achieve the purpose of using unlabeled data to improve prediction performance.

By comparing the results with the co-training semi-supervised learning method of combining learners with the same type, the KNN-DNN proposed in this paper obtains a higher prediction accuracy and smaller error. The superiority and effectiveness of the combination of different types of learners in co-training is proven. More importantly, by comparing the prediction results of the interpolation method and supervised learning method with a single learner, KNN-DNN has the highest regression accuracy and the minimum error in the fine-grained analysis of air quality. It is proved that the co-training semi-supervised learning method effectively overcomes the problem of overfitting due to the limited number of air quality monitoring stations. It has a good application prospect in the fine-grained analysis of air quality.