This paper proposes numerical algorithms for reducing the computational cost of semi-supervised and active learning procedures for visually guided mobile robots from O(M 3 ) to O(M ), while reducing the storage requirements from M 2 to M . This reduction in cost is essential for real-time interaction with mobile robots. The considerable speed ups are achieved using Krylov subspace methods and the fast Gauss transform. Although these state-of-the-art numerical algorithms are known, their

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... ion to semisupervised learning, active learning and mobile robotics is new and should be of interest and great value to the robotics community. We apply our fast algorithms to interactive object recognition on Sony's ERS-7 Aibo. We provide comparisons that clearly demonstrate remarkable improvements in computational speed. Index Terms-Visually guided mobile robots, interactive robots, learning, Krylov subspace methods, fast Gauss transform.