Self-Organizing Maps for Representing Structures
We propose a novel neural network model for representing data structures. The model consists of a hierarchy of Self-Organizing Maps (SOMs) equipped with leaky integrating units. Each of the maps is thus designed to represent sequences of data in a fashion resembling Barnsley’s iterated function system. Each data structure is decomposed into a hierarchy of sequences where in all but the lowest levels a special symbol is substituted to represent corresponding subtrees. The advantage of this representation is that it is directly computable, and if neurally implemented using SOMs, it is computationally unexpensive. Preliminary simulations using simple symbolic tree structures demonstrate that obtained representations have the required property of systematic order.
KeywordsIterate Function System Symbolic Sequence Input Alphabet Leaky Integrator ofIFS Sequence
Unable to display preview. Download preview PDF.
- 4.T. Plate. Holographic reduced representations. IEEE Transactions on Neural Networks6(3):623–641, 1995 Google Scholar
- 7.D.J. James and R. Miikkulainen. Sardnet: a self-organizing feature map for sequences. In Advances in Neural Information Processing Systems 7, 1995.Google Scholar
- 8.K. Kopecz. Unsupervised learning of sequences on maps with lateral connectivity. In ICANN’95, pages 431–436, Paris, France, 1995.Google Scholar
- 9.J. Göppert and W. Rosenstiel. Dynamic extensions of self-organizing maps. InProceedings of ICANN’94pages 330–333, 1994 Google Scholar
- 10.G.J. Chappell and J.G. Taylor. The temporal Kohonen map.Neural Networks6:441–445, 1993 Google Scholar
- 11.T. Koskela et al. Time series prediction using recurrent SOM with local linear models. Int. Journal of Knowledge-Based Intell. Eng. Systems, 2: 60–68, 1998.Google Scholar
- 12.M. Barnsley. Fractals Everywhere. Academic Press, 1988 Google Scholar
- 13.I. Farkas. Invariance of gaussian-vector mapping using a self-organizing map.Neural Network World7(2):153–159, 1997 Google Scholar
- 14.L. Niklasson and M. Bodén. Representing structure and structured representations in connectionist networks. In A. Browne, editor, Neural Network Perspectives on Cognition and Adaptive Robotics, pages 20–50. IOP Press, 1997.Google Scholar
- 15.P. Tino. Spatial representation of symbolic sequences through iterated function systems. IEEE Trans. on Systems, Man and Cybernetics, 29 (4): 386–392, 1999.Google Scholar
- 16.T. Kohonen. Self-organizing maps of symbol strings. Technical report A42Helsinki University of Technology, Espoo, Finland, 1996 Google Scholar
- 17.N.E. Sharkey Connectionist representation techniques.Artificial Intelligence Review5:143–167, 1990 Google Scholar