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We present and examine a technique for estimating the ego-motion of a mobile robot using memory-based learning and a monocular camera. Unlike other approaches that rely heavily on camera calibration and geometry to compute trajectory, our method learns a mapping from sparse optical flow to platform velocity and turn rate. We also demonstrate an efficient method of computing high-quality sparse optical flow, and techniques for using this sparse optical flow as input to a supervised learning method. We employ a voting scheme of many learners that use subsets of the sparse optical flow to cope with variable dimensionality and reduce the dimensionality of each learner. Finally, we perform experiments in which we examine the learned mapping for visual odometry, investigate the effects of varying the reduced dimensionality of the sparse optical flow state, and quantify the accuracy of two variations of our learner scheme. Our results indicate that our learning scheme estimates monocular visual odometry mainly from points on the ground plane, and reflect to a degree the minimum dimensionality imposed by the problem. In addition, we show that while this memory-based learning method cannot yet estimate ego-motion as accurately as recent geometric methods, it is possible to learn, with no explicit model of camera calibration or scene structure, complicated mappings that take advantage of properties of the camera and the environment.