Modeling the manifolds of images of handwritten digits
IEEE Transactions on Neural Networks
Robust recursive least squares learning algorithm for principal component analysis
IEEE Transactions on Neural Networks
Local Dimensionality Reduction for Non-Parametric Regression
Neural Processing Letters
Space Perception through Visuokinesthetic Prediction
Anticipatory Behavior in Adaptive Learning Systems
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An abstract recurrent neural network trained by an unsupervised method is applied to the kinematic control of a robot arm. The network is a novel extension of the Neural Gas vector quantization method to local principal component analysis. It represents the manifold of the training data by a collection of local linear models. In the kinematic control task, the network learns the relationship between the 6 joint angles of a simulated robot arm, the corresponding 3 end-effector coordinates, and an additional collision variable. After training, the learned approximation of the 10-dimensional manifold of the training data can be used to compute both the forward and inverse kinematics of the arm. The inverse kinematic relationship can be recalled even though it is not a function, but a one-to-many mapping.