Dimension reduction by local principal component analysis
Neural Computation
Self-Organizing Maps
Learning multiple linear manifolds with self-organizing networks
International Journal of Parallel, Emergent and Distributed Systems
Embedding new data points for manifold learning via coordinate propagation
PAKDD'07 Proceedings of the 11th Pacific-Asia conference on Advances in knowledge discovery and data mining
Modeling the manifolds of images of handwritten digits
IEEE Transactions on Neural Networks
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This paper proposes an online-learning neural model which maps nonlinear data structures onto mixtures of low-dimensional linear manifolds. Thanks to a new distortion measure, our model avoids confusion between local sub-models common in other similar networks. There is no local extremum for learning at each neuron. Mixtures of local models are achieved by competitive and cooperative learning under a self-organizing framework. Experiments show that the proposed model is better adapted to various nonlinear data distributions than other models in comparison. We further show a successful application of this model to discovering low-dimensional manifolds of handwritten digit images for recognition.