## 1 Introduction  
Over the first two decades of the twenty-first century, the use of mobile devices, such as smartphones with global positioning system (GPS) functions, has spread rapidly. Consequently, location data from these mobile devices via the GPS and the attribute data of users attached to these location data are now being collected on a grand scale, with the expectation that these data would be utilized for urban planning and the analysis of human activity, among other applications [1]. Location data and their associated data are regarded as the trajectories of mobile device users. There has been much research on classification and prediction models for user trajectories [2, 3, 4, 5]. This study mainly focuseson classifying user groups based on location data and their associated data, as obtained from mobile devices. Many studies have aimed at improving the accuracy of trajectory classification using location information consisting of spatiotemporal dimensions obtained from mobile terminals and associated semantic information [6; 7; 8; 9; 10; 11]. In particular, [PERSON] et al. proposed a MasterMovelet that characterizes trajectories with semantic dimensions using a series of uniform procedures [12]. However, whereas these studies assume that the semantic dimension is attached to the trajectory, the semantic information associated with the location data acquired from mobile devices is often missing. In this context, methods for trajectory similarity computation that do not require semantic dimensionality information other than spatial-temporal dimensionality have been proposed by [PERSON] et al. and [PERSON] et al. [13; 14]. In addition, [PERSON] et al. proposed a stacked denoising autoencoder (SDA) [15] based method for extracting trajectory features for transportation mode classification [16]. However, these methods do not assume that trajectories are sparse in the spatiotemporal dimension. Because irregular events obtain mobile terminal-based location information, the trajectories of such information could be sparser in spatial-temporal space. Many studies have focused on trajectory classification using dense or semantically rich data. However, location data generated by mobile devices often lack semantic information and exhibit spatial-temporal sparsity. This raises the challenge of effectively utilizing sparse trajectories for applications such as user group classification and mobility analysis. Addressing this issue is crucial for harnessing the potential of trajectory data in fields such as urban planning, marketing analysis, and public policy. In addition, increasing data integrity can significantly enhance the usability of location data for these applications. For these reasons, in our past work, we developed a sparse trajectory feature based on spatial-temporal information for classifying user age groups [17]; however, we conducted only a superficial analysis for limited binary classification and did not significantly examine feature availability. Furthermore, this past research focused solely on analyses based on the support vector classifier (SVC) [18; 19] model and did not include comparisons with other machine learning (ML) models and trajectory features based on existing methods. Therefore, this study provides a detailed analysis of whether user groups can be estimated using only a sparse spatial-temporal trajectory without considering prior knowledge and past historical data associated with mobile device users. In particular, we analyze the feature based on [17], which is extracted from users' location data using point-type dynamic population (PTDP) data [20] obtained from the GPS function of mobile devices. Moreover, we adopt multiple types of machine learning (ML) models that learn the features for six-class classification and conduct a detailed analysis. Additionally, by evaluating the user age group classification performance of the ML models, we verify the effectiveness of features based on sparse spatial-temporal trajectories in user age group estimation.