# A Novel Spatiotemporal Analysis Framework for Air Pollution Episode Association in Puli, Taiwan
## 2 Literature Review  
### Air-Pollution Spatiotemporal Analysis  
The classic approaches for air-pollution spatiotemporal analysis fall into four categories. (1) Correlation and variance. The basic spatiotemporal relationship between PM\({}_{2.5}\) concentrations monitored at different sites along a time span can be realized by calculating the correlation coefficient (CC) and coefficient of variance (CV). [PERSON] et al. [12] profiled the spatiotemporal distribution of air pollution characteristics in Jiangsu Province, China, by investigating correlation and variance statistics such as the temporal and spatial air quality index (AQI) variations, the temporal correlation between AQI and meteorology,and the correlation between major pollutants. [PERSON] et al. [6] calculated CV among different sites within a city. A higher CV indicates a greater fluctuation in PM\({}_{2.5}\) concentrations in a city. The distribution of CV among ten community locations was analyzed. It is seen that more than one-fifth of the time in July and December, the CV exceeds 20%. The majority of cases appear on weekends, mainly due to traffic, restaurants, and temples. It conforms to the activities attended by the inbound tourists. The CC between microsites and the nearest supersite was evaluated in [6] to validate the consistency of pollution patterns at highly correlated sites. [PERSON] et al. [13] investigated the CC between PM\({}_{2.5}\) concentrations/variations and the urbanization level of the city. Their result manifests a positive/negative correlation between urbanization and PM\({}_{2.5}\) concentrations/variations. (2) Spatiotemporal regression. Regression has been widely applied to find the relationship between the response variable and independent variables. Several studies have attempted to find the regression expression between PM\({}_{2.5}\) concentrations and multiple independent variables (such as meteorological or socioeconomic data). To reduce the model computations, [PERSON] et al. [8] and [PERSON] et al. [9] applied spatial regression to neighboring monitoring sites and economic variables at a particular time period. [PERSON] et al. [13] applied quadratic spatial regression to disclose the contribution to PM\({}_{2.5}\) concentrations by urbanization, industrialization, and green land area. (3) Probabilistic approaches. To model the spatiotemporal variations of PM\({}_{2.5}\) concentrations, both parametric and non-parametric probability distributions have been employed. [PERSON] et al. [14] used a two-parameter gamma distribution to describe the probability density functions (PDFs) of the hourly surface PM\({}_{2.5}\) concentrations in each city over seasonal time frames. The two parameters are referred to as the shape parameter and the scale parameter, whose optimal values are determined by fitting the historical data. [PERSON] and [PERSON] [15] assumed a yearly-invariant spatiotemporal distribution of the PM\({}_{2.5}\)/PM\({}_{10}\) ratio at the same location during the same period of a year. Hence, the historical data of PM\({}_{2.5}\)/PM\({}_{10}\) ratios can be used to construct a non-parametric distribution for predicting PM\({}_{2.5}\) if the PM\({}_{10}\) observation is available. (4) Machine learning. Compared to the references using previously noted spatiotemporal analysis methods, the adoption of machine learning approaches has received more attention recently. [PERSON] et al. [11] considered the hourly PM\({}_{2.5}\) concentrations in each day as a 24-dimension vector and applied the agglomerative hierarchical clustering approach to partition the PM\({}_{2.5}\) time series into four groups. They identified that the first group contains those days with severe pollution, the second group corresponds to the dispersion period, the third group coincides with the pollution accumulation period, and the air is relatively clean during the days included in the last group. [PERSON] et al.