Learning multiple linear manifolds with self-organizing networks

Authors:
Huicheng Zheng;Pádraig Cunningham;Alexey Tsymbal
Affiliations:
School of Information Science and Technology, Sun Yat-sen University, 510275 Guangzhou, China;School of Computer Science and Informatics, University College Dublin, Dublin 4, Ireland;Siemens AG, Corporate Technology, 91058 Erlangen, Germany
Venue:
International Journal of Parallel, Emergent and Distributed Systems
Year:
2007

Citing 5
Cited 2

Locally Weighted Learning

Artificial Intelligence Review - Special issue on lazy learning
Self-organized formation of various invariant-feature filters in the adaptive-subspace SOM

Neural Computation
Self-Organizing Maps

Self-Organizing Maps
Modeling the manifolds of images of handwritten digits

IEEE Transactions on Neural Networks
Handwritten digit recognition by adaptive-subspace self-organizing map (ASSOM)

IEEE Transactions on Neural Networks

Learning nonlinear manifolds based on mixtures of localized linear manifolds under a self-organizing framework

Neurocomputing
Locally linear online mapping for mining low-dimensional data manifolds

PAKDD'08 Proceedings of the 12th Pacific-Asia conference on Advances in knowledge discovery and data mining

Quantified Score

Hi-index	0.00

Visualization

Abstract

Learning multiple linear manifolds permits one to deal with multiple variations incurred in target objects. The adaptive-subspace self-organizing map (ASSOM) proposed by Kohonen can learn a set of ordered subspaces, i.e. linear manifolds passing through the origin, but not those shifted away from the origin. The linear manifold self-organizing map (LMSOM) proposed in this paper considers offsets of linear manifolds from the origin and aims to learn linear manifolds by minimizing a projection error function in a gradient-descent fashion. At each learning step, the winning module and its neighbours update basis vectors as well as offset vectors of their manifolds towards the negative gradient of the error function. Experiments show that the LMSOM can learn clusters aligned on linear manifolds shifted away from the origin and separate them accordingly. The LMSOM is applied to handwritten digit recognition and shows promising results.