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Robot skill learning by imitation is an intuitive approach to learn robot skills from the observation of human behaviors. However, due to the discrepancy of mechanism between humans and robots such as the type of joint and the number of degree of freedom (DOF), a robot may not be able to imitate a human's movements faithfully. For a robot arm, the major problem is caused by the lack of a degree of freedom in the shoulder compared to a human arm. In this paper, we develop a similarity metric to evaluate how faithfully a robot arm imitates a human's arm movements. This metric is derived by utilizing the sequence-independent joint angle representation for both human and robot arms because it represents their postures more directly than the sequence-dependent Euler joint angle representation. In addition, the derived metric is formulated with the spatial relationship between human and robot arm postures instead of the Frobenius norm of the difference matrix between human and robot transformation matrices. To investigate the joint angles of the sequence-independent joint angle representation for a human arm, we adopt the particle-swarm optimization (PSO) to numerically derive them from human demonstration data. Computer simulations and experimental work were conducted to validate the proposed approach on a robot arm with two degrees of freedom in the shoulder and a DOF in the elbow.