# Novel MIA-LSTM Deep Learning Hybrid Model with Data Preprocessing for Forecasting of PM2.5
## 2 Related Work
### Modern Methods Used for Forecasting  
For the time series data prediction problem, the existing work [37] that uses machine learning methods, such as ANN, does not remember the recurrent past data. However, it is very important to consider past data in time series forecasting. In recent times, time series data RNNs have gained a lot of attention; it is one of the classes of artificial neural networks (ANNs). The first architecture to reveal the hidden structure of data was the Elman RNN [38] where a simple RNN uses BPNN (back propagation through time). This RNN outperforms simple ANNs with feed-forward networks for data that are dynamic in nature [39]. Strength and limitations of forecasting techniques by in various research papers are summarized in Table 1.  
There are some limitations of RNNs too, as it is incapable of remembering long-term significant important data. Further, whenever there are long-term dependencies, BPNN experiences exploding and vanishing gradient problems. Long Short-Term Memory (LSTM), a further extension to RNN, provides the solution to the above problem. The state-of-the-art method of LSTM to predict the outbreak of COVID-19 infection is provided in [40], which obtains good prediction accuracy but also concluded that missing values in the data have put limitations in doing a thorough analysis. In this article, preprocessing was performed using a state-space vector using Taken's theorem, and outliers were treated. Hybrid methods utilizing LSTM are widely implemented for time series forecasting problems, such as stock prediction [41], which results in improved prediction accuracy [42]. Hybrid versions of LSTM, such as wavelet LSTM, are better in time series prediction compared to the traditional methods used [43]. Trending models for enhanced time series forecasting were proposed in the electrical domain where researchers concluded that a wavelet adaptive neuro-fuzzy inference system outperformed other competent models such as the group method of data handling, LSTM, bootstrap aggregation, sequential learning, and many ensemble learning methods [44]. Recently, many hybrid methods and ensemble learning methods have been applied for time series forecasting problems and provide encouraging results [45]. Out of the many ensemble learning models, random subspace and stacking ensemble models provide better results for prediction. Moreover, compared to LSTM, which takes higher computational power, the proposed ensemble models proved to be better. PM\({}_{2.5}\) concentrations can be forecasted in the future using state-of-the-art ensemble learning methods [46]. A deep learning model, i.e., multivariate LSTM, was used for air quality prediction during the pandemic for short-term and long-term prediction; the bidirectional LSTM outperformed other LSTM models. During this experimentation, missing values were replaced with simple median values, and no comments on outliers and anomalies were stated [47]. Air pollutant concentrations were predicted wth multivariate LSTM; the researchers found that meteorological features play a vital role in the prediction of CO concentrations for PM\({}_{2.5}\) prediction. Meteorological, pollutant, and traffic data were useful, but information regarding imputation and outliers in the preprocessing step was missing [48]. Statistical evidence shows that LSTM grouped by pollutant class (GP-LSTM) and LSTM with individual groups of pollutants as inputs (IGP-LSTM) outperform benchmark algorithms that have been observed. However, these models can still be improved, as LSTMs struggle to detect the presence of sudden high peaks since past information weights on the predictions [49]. In the prediction of air pollutant concentration, many researchers are continuously contributing to the literature by proposing many novel methods; recently, hybrid models have become popular and provide state-of-the-art solutions to prediction problems by extracting useful information from the raw data.