Local Adaptive Subspace Regression
Sethu Vijayakumar and Stefan Schaal
Abstract of paper published in Neural Processing Letters.
Incremental learning of sensorimotor transformations in high dimensional
spaces is one of the basic prerequisites for the success of autonomous
robot devices as well as biological movement systems. So far,
due to sparsity of data in high dimensional spaces, learning in such
settings requires a significant amount of prior knowledge about
the learning task, usually provided by a human expert. In this paper
we suggest a partial revision of the view. Based on empirical studies,
we observed that, despite being globally high dimensional
and sparse, data distributions from physical movement systems
are locally low dimensional and dense.
Under this assumption, we derive a learning
algorithm, Locally Adaptive Subspace Regression, that exploits 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 are
illustrated for a synthetic data set, and for data of the inverse dynamics
of human arm movements and an actual 7 degree-of-freedom anthropomorphic robot arm.
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