# An Integrated Fuzzy C-Means Method for Missing Data Imputation Using Taxi GPS Data
## 1 Introduction  
With the advent of the intelligent transportation era, various traffic sensors, including loop detectors, cameras, and GPS receivers, have been widely adopted to facilitate traffic control and management. Taking GPS as an example, as seen in Figure 1, it consists of three parts, including the space segment, the user segment, and the control segment. The user segment consists of GPS receivers and the user community. Currently, almost all taxis are required to be equipped with GPS receivers for location recording. Hence, a substantial amount of taxi mobile data from taxis is accurately recorded in the taxi GPS datasets. As seen in Table 1, the passengers' pick-up and drop-off locations, dates, etc., are easily obtained as they are recorded in the taxi GPS datasets. Currently, many applications have been made by analyzing taxi GPS data. For example, by utilizing taxi trajectory data, passengers' daily travel characteristics are mined [1]. Meanwhile, the real-time status of urban roads can be predicted as well [2]. Typically, the passengers' mobile data generated by the GPS reflect the dynamic states of the transportation network. Specifically, the dynamic states are the outcomes of different demands of commuters and travelers. Thus, another interesting topic focuses on taxi demand distribution learning [3]. By analyzing taxi demand, intelligent taxi dispatch can be achieved as well [4]. However, due to the malfunctions of hardware or software, the issue of missing data arises frequently. Consequently, it poses a challenge to transportation planning and management [5], passenger behavior analysis, and demand forecasting [6,7]. Thus, it is crucial to deal with the missing data issue. In general, there are various approaches that can be used to address the missing data. Ignoring, deleting, and zeroing are unsophisticated methods [8]. The common drawback of these methods is that valid information in the missing data is ignored. Furthermore, the lack of complete data would reduce the data quality and restrict data applications. Therefore, in order to obtain high-quality data, missing data should be generated by estimating effectively and efficiently [9]. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**PT** & **DT** & **PLO** & **PLA** & **DLO** & **DLA** & **TD** & **TDI** \\ \hline
2013-1-13 4:36 & 2013-1-13 4:46 & \(-\)73.9969 & 40.72006 & \(-\)73.9935 & 40.69304 & 600 & 3.12 \\
2013-1-13 4:37 & 2013-1-13 4:48 & \(-\)74.0003 & 40.73007 & \(-\)73.9874 & 40.76841 & 660 & 3.39 \\
2013-1-13 4:41 & 2013-1-13 4:45 & \(-\)73.9973 & 40.72098 & \(-\)74.0004 & 40.73238 & 240 & 1.16 \\ \(\cdots\) & \(\cdots\) & \(\cdots\) & \(\cdots\) & \(\cdots\) & \(\cdots\) & \(\cdots\) & \(\cdots\) \\ \hline \hline \multicolumn{10}{c}{PT means pick-up time; DT means drop-off time; PLO means pick-up longitude; PLA means pick-up latitude; DLO means drop-off longitude; DLA means drop-off latitude; TD means trip duration (seconds); TDI means trip distance (km).} \\ \end{tabular}
\end{table} 
Table 1: Samples of taxi GPS data. Figure 1: Working of GPS. In general, the imputation method mainly involves two types of approaches [10]. First, missing data are predicted by using the statistical method [11]. Specifically, some statistical features, including the mean and various indicators, are utilized to replace the missing values. Second, the missing values are estimated by machine learning techniques [12]. In particular, these techniques include fuzzy C-means (FCM) [13], support vector machine (SVM) [14], and random forest [15]. The core procedure is to generate several candidate values by using more than one model. Then, the missing data are replaced by the best candidate values, which are determined by some evaluation criteria. Motivated by recent works in the literature [16], this paper aims to establish a novel imputation method integrating the matrix-based method, the fuzzy C-means (FCM) method, and the genetic algorithm (GA).