## 1 Related Studies
### Semisupervised Learning for Mobile Fingerprinting  
In this section, the semisupervised learning methods for regression are presented, which are used to build the relationship between the Wi-Fi RSSI data sets and the locations. We then derive the contribution of the proposed mobile fingerprinting algorithm.  
Utilization of the unlabeled data has been studied in the semisupervised learning to improve the efficiency and accuracy of the indoor localization. In those works, semisupervised deep learning methods [18; 19; 30] have been recently developed. The mobile fingerprinting requires the light computation and should be implemented as fast as the mobile device or the server deals with huge amount of the unlabeled data. Therefore, rather than the heavily computational deep learning methods,the support vector machine (SVM)-based [31] semisupervised learning algorithms are applied in this paper, which solves a convex optimization problem.  
Semisupervised least square (SSL) [32] adds manifold regularization of unlabeled data into the standard Least Square SVR framework [33]. Because of its linearized setup, this algorithm is fast and useful for real-time application. Semisupervised colocalization (SSC) [34] builds an optimization framework consisting of a singular value decomposition, a manifold regularization, and a loss function. Because SSC estimates the locations of the APs as well as a target's location, it requires the known locations of the AP, whereas SVR-based semisupervised algorithms do not. Moreover, the large number of tuning parameters and the heavy computation may be a burden. Both SSL and SSC apply the unlabeled data only for making a manifold regularization, through the graph Laplacian. Further progressed utilization of unlabeled data occurs in transductive support vector machine (TSVM) [35] and Laplacian Embedded Regression Least Squares (LapERLS) [36]. TSVM attempts to find the labels of unlabeled data and obtain the decision function. Because finding a solution requires searching all candidate-labels of the unlabeled data, TSVM is not feasible in most applications.  
LapERLS introduces an intermediate variable as a substitute for the original labeled data. During the optimization process via Karush-Kuhn-Tucker (KKT) conditions, pseudolabels and a transformed kernel matrix are generated. Then, the pseudolabels and transformed kernel matrix are used as a substitution for the original labeled data and the original kernel matrix, respectively. This algorithm is useful for large-scale problems, due to the light computation necessary for obtaining the transformed kernel matrix, because the standard kernel matrix and Laplacian matrix are decoupled. However, LapERLS becomes inaccurate when only a small number of labeled training data points are used.  
We adopt the idea of pseudolabeling from LapERLS because the pseudolabels can compensate for the lack of labeled data. To improve the accuracy of the pseudolabels, we propose adding a temporal relation to unlabeled training data that are collected as time-series. A study [37] employing a Hodrick-Prescott (H-P) filter that captures a smoothed-curve representation for a time series from training data is helpful for assigning time-series pseudolabels. Consequently, our pseudolabeling is able to consider both the spatial and temporal aspect of the training data sets. Note that this pseudolabeling technique based on this semisupervised regression is used for the mobile fingerprinting, not for estimating the user's position.