# Improved Interpolation and Anomaly Detection for Personal PM\({}_{\mathbf{2.5}}\) Measurement
## 1 Introduction  
Korea has been experiencing severe environmental health problems caused by exposure to fine dust [1]. Thus, many stakeholders, including government officials, are trying hard to find solutions for the environmental issues. As part of these efforts, various artificial intelligence (AI)-based technologies are drawing attention as a way to predict future exposure levels as well as to reduce real-time exposure to PM\({}_{2.5}\) in our daily life. PM data is closely related to personalized health-care service and preventive medicine, which are research areas that have attracted much interest from many researchers today. The personalized healthcare service prompted us to develop predictive analytics technology, which requires the acquisition of data related to individual activity patterns [2, 3]. Such data can be seen as person-specific data that is different from the population-based data to be used for the existing broadcasting-type environmental information service aimed at a large audience [2, 4]. The pico-scale data is usually collected from each individual sensor device [4]. Unfortunately, such data are more likely to be incomplete than data collected from stationary sensors, because sensors attached to human subjects are affected significantly by the person's activity patterns, meteorological conditions, or the malfunction of the installed device or sensor itself. These kinds of incomplete data can lead to the provision of wrong services, because they may invoke wrong algorithmic decisions caused by the data. Such incomplete data typically include missing or abnormal data. In order to provide high-quality environmental information services, it is essential to conduct studies to deal with these two issues.  
Much research has been done on the two issues mentioned above. Most of such research tends to focus on detecting missing or anomalous data only as follows. Conventional techniques related to missing data imputation in time-series data include methods based on machine learning, suchas random forests [5], maximum likelihood estimation [6], expectation maximization [7], or nearest neighbors [8]. Technologies belonging to anomalous data detection include prediction-based [9], distance-based [10], probability-based [11], and linear models [11]. Researches dealing with both technologies include [12; 13] both using machine learning techniques. As we have seen, there are few studies that simultaneously address these two problems.  
Thus, in this study, we present our data-mining skills approach that deals with the two problems of missing and abnormal data included in the PM\({}_{2.5}\) data obtained from a personal portable sensor. Especially, we demonstrate that our kernel regression-based interpolation method and abnormal data detection method can be applied to our real personal PM\({}_{2.5}\) measurement data. We attempt to extend a well-known interpolation method incorporating a simple linear interpolation method to interpolate the bursty PM\({}_{2.5}\) data. The performance of the proposed method is provided in comparison to those of existing interpolation methods. In addition, details on the method are presented in the algorithmic method section of this paper.