# Improved Interpolation and Anomaly Detection for Personal PM\({}_{\mathbf{2.5}}\) Measurement
## 4 Discussion  
This paper presented the results of research on two important technologies related to artificial intelligence environmental information services, such as PM\({}_{2.5}\) exposure level prediction, and providing alerts based on the prediction. Most environmental data inevitably contain both missing data and anomalies caused by various factors, such as sensor malfunctions, errors in transmission, or errors in storage. Such incomplete data can lead to the miscalculation of data-based analysis and so must be processed appropriately before we use them for data analysis. Most of the related studies have tended to deal with either interpolation or abnormal data problems only. However, it is desirable that interpolation and abnormal data should be handled together for viable data-based services. Therefore, we conducted the research on these two problems simultaneously. The first technique was interpolation, which can be regarded as a technique to cope with data lost from various sensors. Data tend to be missed mainly in time-series data, which is known to occur in three major forms: missing completely at random (MCAR), missing at random (MAR), and not missing at random (NMAR). In particular, the MAR type is an appropriate form of model for describing the data that are missing in most fine-dust time-series data [17]. This model assumes that the pattern of the time-series data can be described by a certain mathematical generative model and also attempts to take advantages of correlation information in multivariate environments to solve the missing-data problem [17]. In a stationary environment where sensors are fixed to certain objects, the generative model may be used to analyze the data. However, in a univariate case where data are collected from portable wearable devices, it is very challenging to estimate the missing data, because the number of  
Figure 9: Anomalies are detected and shown in red (**a**) outliers for the entire dataset (**b**) outliers shown enlarged for the part of the dataset between 2750 and 4000.  
attributes to use is very limited, and a large amount of data is likely to be missing [19]. In these cases, it is very difficult to apply a mathematical generation model to describe the data-distribution pattern or representative values for a specific activity. There are very few articles addressing the interpolation methods for univariate time-series data. Articles by [PERSON] studied the univariate algorithm in 2004, but do not consider time-series aspects [20]. Authors applied ARIMA (autoregressive integrated moving average) and SARIMA (seasonal autoregressive integrated moving average) models for the univariate model interpolation and provided comparison results [21]. A performance comparison is provided, using built-in interpolation methods in R [19]. Data loss in one instant or a short period of time can be easily interpolated with a simple error-recovery method such as linear interpolation. However, this simple interpolation method may be inadequate for a long bursty loss of sensor-provided data. When such long bursty data loss occurs, the interpolation method with the prediction technique may be more appropriate. In addition, anomalous-data detection technology should be applied to detect data that deviate from the characteristics of data distribution. The anomalies can be commonly found in various industries including the environmental and finance fields. Anomalous time-series data can be regarded as data that disturb the continuity of data based on temporal flow [11]. Most techniques to detect anomalies can be classified as supervised and unsupervised according to the presence or absence of data labels [22]. The supervised method is a technique for detecting abnormal data by means of a learning algorithm when the data are labeled. The unsupervised method can be used when there is no label in the data, and can be used more flexibly than the supervised method can be, because often data labels are not available.