Fast BMU Search in SOMs Using Random Hyperplane Trees
One of the most prominent Neural Networks (NNs) reported in the literature is the Kohonen’s Self-Organizing Map (SOM). In spite of all its desirable capabilities and the scores of reported applications, it, unfortunately, possesses some fundamental drawbacks. Two of these handicaps are the quality of the map learned and the time required to train it. The most demanding phase of the algorithm involves determining the so-called Best Matching Unit (BMU), which requires time that is proportional to the number of neurons in the NN. The focus of this paper is to reduce the time needed for this tedious task, and to attempt to obtain an approximation of the BMU is as little as logarithmic time. To achieve this, we depend heavily on the work of [3,6], where the authors focused on how to accurately learn the data distribution connecting the neurons on a self-organizing tree, and how the learning algorithm, called the Tree-based Topology-Oriented SOM (TTOSOM), can be useful for data clustering [3,6] and classification . We briefly state how we intend to reduce the training time for identifying the BMU efficiently. First, we show how a novel hyperplane-based partitioning scheme can be used to accelerate the task. Unlike the existing hyperplane-based partitioning methods reported in the literature, our algorithm can avoid ill-conditioned scenarios. It is also capable of considering data points that are dynamic. We demonstrate how these hyperplanes can be recursively defined, represented and computed, so as to recursively divide the hyper-space into two halves. As far as we know, the use of random hyperplanes to identify the BMU is both pioneering and novel.
KeywordsApproximate BMU search Random Hyperplane Trees SOM TTOSOM VQ
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- 1.Astudillo, C.A., Oommen, B.J.: A novel self organizing map which utilizes imposed tree-based topologies. In: 6th International Conference on Computer Recognition Systems, vol. 57, pp. 169–178 (2009)Google Scholar
- 7.Astudillo, C.A., Oommen, B.J.: Topology-oriented self-organizing maps: A survey. Pattern Analysis and Applications (2014), http://dx.doi.org/10.1007/s10044-014-0367-9
- 11.Frank, A., Asuncion, A.: UCI machine learning repository (2010), http://archive.ics.uci.edu/ml
- 12.Friedman, M., Kandel, A.: Introduction to Pattern Recognition: Statistical, Structural, Neural and Fuzzy Logic Approaches. Imperical College Press (1999)Google Scholar
- 16.Koikkalainen, P., Oja, E.: Self-organizing hierarchical feature maps. In: IJCNN International Joint Conference on Neural Networks, vol. 2, pp. 279–284 (June 1990)Google Scholar
- 18.Lampinen, J., Oja, E.: Fast self-organization by the probing algorithm. In: International Joint Conference on Neural Networks, IJCNN, vol. 2, pp. 503–507 (June 1989)Google Scholar
- 21.Rahmel, J.: SplitNet: learning of tree structured Kohonen chains. In: IEEE International Conference on Neural Networks, vol. 2, pp. 1221–1226 (June 1996)Google Scholar
- 22.Rahmel, J., Blum, C., Hahn, P.: On the role of hierarchy for neural network interpretation. In: IJCAI 1997: Proceedings of the Fifteenth International Joint Conference on Artifical Intelligence, pp. 1072–1077. Morgan Kaufmann Publishers Inc., San Francisco (1997)Google Scholar