Developing an autonomous driving system which can generate human-like actions requires the ability to utilize the basic driving skills learned from the driving data. The efficiency of the algorithm can be significantly improved if we can decompose the complex driving tasks into motion primitives (MPs) which represent the elementary composition of driving skills. Therefore, the purpose of this paper is to represent MPs, extract MPs from unlabeled driving data, and then connect the learned MPs in the established library. By applying a probabilistic inference based on an Expectation-Maximization (EM) algorithm and initial segmentation, the extraction method segments the observed trajectories while learning a set of MPs represented by the modified dynamic movement primitives (DMPs). Moreover, the proposed connection algorithm transforms the connection problem into the re-representation problem of the MP sequence. This paper demonstrates that the modified DMP method can not only represent the driver's trajectory with acceptable accuracy but also have strong generalization ability. We also present how to utilize the mutual dependency between the representation and extraction to achieve MP segmentation and MP library establishment. Besides, this paper shows how the proposed connection algorithm correlates the independent MPs in the sequence to ensure a smooth transition and evaluates the tracking accuracy. The results show that the proposed method realizes the extraction of MPs and the re-generation of trajectory by making use of the interdependence relationship that is often neglected between the representation of a single MP, extraction of different types of MP and combination of multiple MPs.