## 1 Introduction
However, the previous studies have a common limitation that they did not explicitly consider the traffic states and their changes, and this can deteriorate the imputation performances. Traffic data are inevitably affected significantly by the traffic state, e.g., free flow state vs. congested traffic state. The traffic flow data in the same traffic state are the results of being exposed to similar conditions. When the data are from different states, they show significantly different patterns. Especially congested state and transition state show more complex patterns than the free flow state. Because the phenomenon of the traffic congestion usually propagates up-stream with their associated traffic states, and it lasts for a relatively long time period, the data from neighboring detectors can be utilized for representing the traffic state of a missing target. Bottleneck activation and derived shockwaves are the most common examples. Thus, the spatial and temporal considerations of traffic states for identifying complex traffic conditions can improve imputation accuracies. Generally, previous studies have focused on the traffic state of a single spot, and therefore it cannot be applied for missing value imputations for the target area with the missing data. A section-based identification of traffic states that utilizes the neighboring detector's data (excluding the missing data at the target) is needed to improve the performance of missing value imputation. The objective of this study is to propose a new approach for the imputation of missing data by identifying section-based traffic state (SBTS) of a target location, and determining tempo-spatial dependencies customized for each SBTS, with data at different time periods from upstream/downstream traffic detectors in the vicinity of the target. A principal component analysis (PCA) can be used in two ways with relatively simple and light mathematical operations for practical implementations in the field. First, the angle between the first principal component (PC) and the standard vector is calculated. The angle can be used not only to classify the SBTS but it can also be used as an independent variable. Second, the PC loading is applied for variable selection to reflect the spatiotemporal dependencies among variables for each SBTS. The imputation models are developed for each SBTS using a regression model of the support vector machine (SVM). The performance of the SBTS separation of the proposed angle is compared with the average speed by using the speed-flow plot. The imputation performance of the proposed imputation method is compared with some relevant methods, such as linear interpolation, artificial neural network, and k-nearest neighborhood method, against the missing data rate of 10%, 20%, and 30%. The remainder of this study consists of four sections. The next section provides the theoretical background of the PCA and its application for determining SBTSs and missing value imputations. The SVM for the imputation model is also described. The third section describes the study data. The fourth section provides the result of the proposed model and evaluations. Then the conclusion section follows.