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We propose a method for learning models of people's motion behaviors in an indoor environment. As people move through their environments, they do not move randomly. Instead, they often engage in typical motion patterns, related to specific locations that they might be interested in approaching and specific trajectories that they might follow in doing so. Knowledge about such patterns may enable a mobile robot to develop improved people following and obstacle avoidance skills. This paper proposes an algorithm that learns collections of typical trajectories that characterize a person's motion patterns. Data, recorded by mobile robots equipped with laser range finders, is clustered into different types of motion using the popular expectation maximization algorithm, while simultaneously learning multiple motion patterns. Experimental results, obtained using data collected in a domestic residence and in an office building, illustrate that highly predictive models of human motion patterns can be learned.