In this paper, we developed the solution of roadside LiDAR object detection using a combination of two unsupervised learning algorithms. The 3D point clouds are firstly converted into spherical coordinates and filled into the elevation-azimuth matrix using a hash function. After that, the raw LiDAR data were rearranged into new data structures to store the information of range, azimuth, and intensity. Then, the Dynamic Mode Decomposition method is applied to decompose the LiDAR data into low-rank backgrounds and sparse foregrounds based on intensity channel pattern recognition. The Coarse Fine Triangle Algorithm (CFTA) automatically finds the dividing value to separate the moving targets from static background according to range information. After intensity and range background subtraction, the foreground moving objects will be detected using a density-based detector and encoded into the state-space model for tracking. The output of the proposed solution includes vehicle trajectories that can enable many mobility and safety applications. The method was validated at both path and point levels and outperformed the state-of-the-art. In contrast to the previous methods that process directly on the scattered and discrete point clouds, the dynamic classification method can establish the less sophisticated linear relationship of the 3D measurement data, which captures the spatial-temporal structure that we often desire.