Recently, data from built-in sensors in smartphones have been readily available, and analyzing data for various types of health information from smartphone users has become a popular health care application area. Among relevant issues in the area, one of the most prominent topics is analyzing the characteristics of human movements. In this paper, we focus on characterizing the human movements of walking and running based on a novel machine learning approach. Since walking and running are human fundamental activities, analyzing their characteristics promptly and automatically during daily smartphone use is particularly valuable. In this paper, we propose a machine learning approach, referred to as ’two-stage latent dynamics modeling and filtering’ (TS-LDMF) method, where we combine a latent space modeling stage with a nonlinear filtering stage, for characterizing individual dynamic walking and running patterns by analyzing smartphone sensor data. For the task of characterizing movements, the proposed method makes use of encoding the high-dimensional sequential data from movements into random variables in a low-dimensional latent space. The use of random variables in the latent space, often called latent variables, is particularly useful, because it is capable of conveying compressed information concerning movements and efficiently handling the uncertainty originating from high-dimensional sequential observation. Our experimental results show that the proposed use of two-stage latent dynamics modeling and filtering yields promising results for characterizing individual dynamic walking and running patterns.