Incremental learning of sensorimotor transformations in high dimensional spaces is one of the basic prerequisties for the success of autonomous robot devices as well as biological movement systems. So far, due to sparsity of data in high demensional spaces, learning in such settings requires a significant amount of proor knowledge about the learning taks, usually provided by a human expert. In this paper, we suggest a partial revision of this view. Based on empricial studies, we observed that, despote being globally high dimensional and sparse, data distributions from physical movement systems are locally low dimensional and dense. Under this assumption, we deive a learning algorithm, Locally Adaptive Subspace Regression, that explotis this property by combining a dynamically growing local dimensionality reduction technique as a preprocessing step with a nonparametric learning technique, locally weighted regression, that also learns the region of validity of the regression. The usefulness of the algorithm and the validity of its assumptions re illustrated for a synthetic data set, and for data of the inverse dynamics of human arm ovements and an actualy 7 degree-of-freedom anthropomorphic robot arm.
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