Abstract
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 [5]. 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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
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)
Astudillo, C.A., Oommen, B.J.: On using adaptive binary search trees to enhance self organizing maps. In: Nicholson, A., Li, X. (eds.) AI 2009. LNCS, vol. 5866, pp. 199–209. Springer, Heidelberg (2009)
Astudillo, C.A., Oommen, B.J.: Imposing tree-based topologies onto self organizing maps. Information Sciences 181(18), 3798–3815 (2011)
Astudillo, C.A., Oommen, B.J.: Semi-supervised classification using tree-based self-organizing maps. In: Wang, D., Reynolds, M. (eds.) AI 2011. LNCS, vol. 7106, pp. 21–30. Springer, Heidelberg (2011)
Astudillo, C.A., Oommen, B.J.: On achieving semi-supervised pattern recognition by utilizing tree-based soms. Pattern Recognition 46(1), 293–304 (2013)
Astudillo, C.A., Oommen, B.J.: Self-organizing maps whose topologies can be learned with adaptive binary search trees using conditional rotations. Pattern Recognition 47(1), 96–113 (2014)
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
Bentley, J.L.: Multidimensional binary search trees used for associative searching. Commun. ACM 18(9), 509–517 (1975)
Chen, S.X., Li, F.W., Zhu, W.L.: Fast searching algorithm for vector quantisation based on features of vector and subvector. IET Image Processing 2(6), 275–285 (2008)
Devroye, L., King, J., McDiarmid, C.: Random hyperplane search trees. SIAM J. Comput. 38(6), 2411–2425 (2009)
Frank, A., Asuncion, A.: UCI machine learning repository (2010), http://archive.ics.uci.edu/ml
Friedman, M., Kandel, A.: Introduction to Pattern Recognition: Statistical, Structural, Neural and Fuzzy Logic Approaches. Imperical College Press (1999)
Gordon, L., Olshen, R.A.: Asymptotically efficient solutions to the classification problem. Annals of Statistics 6, 515–533 (1978)
Gray, R.: Vector quantization. IEEE ASSP Magazine 1(2), 4–29 (1984)
Kasai, W., Tobe, Y., Hasegawa, O.: A fast BMU search for support vector machine. In: Alippi, C., Polycarpou, M., Panayiotou, C., Ellinas, G. (eds.) ICANN 2009, Part I. LNCS, vol. 5768, pp. 864–873. Springer, Heidelberg (2009)
Koikkalainen, P., Oja, E.: Self-organizing hierarchical feature maps. In: IJCNN International Joint Conference on Neural Networks, vol. 2, pp. 279–284 (June 1990)
Lai, J.Z.C., Liaw, Y.-C.: Fast-searching algorithm for vector quantization using projection and triangular inequality. IEEE Transactions on Image Processing 13(12), 1554–1558 (2004)
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)
Lin, Y.K., Fu, K.S.: Automatic classification of cervical cells using a binary tree classifier. Pattern Recognition 16(1), 69–80 (1983)
Pakkanen, J., Iivarinen, J., Oja, E.: The Evolving Tree — a novel self-organizing network for data analysis. Neural Processing Letters 20(3), 199–211 (2004)
Rahmel, J.: SplitNet: learning of tree structured Kohonen chains. In: IEEE International Conference on Neural Networks, vol. 2, pp. 1221–1226 (June 1996)
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)
Samet, H.: The quadtree and related hierarchical data structures. ACM Comput. Surv. 16, 187–260 (1984)
Sproull, R.F.: Refinements to nearest-neighbor searching in k-dimensional trees. Algorithmica 6(4), 579–589 (1991)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Astudillo, C.A., Oommen, B.J. (2014). Fast BMU Search in SOMs Using Random Hyperplane Trees. In: Pham, DN., Park, SB. (eds) PRICAI 2014: Trends in Artificial Intelligence. PRICAI 2014. Lecture Notes in Computer Science(), vol 8862. Springer, Cham. https://doi.org/10.1007/978-3-319-13560-1_4
Download citation
DOI: https://doi.org/10.1007/978-3-319-13560-1_4
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-13559-5
Online ISBN: 978-3-319-13560-1
eBook Packages: Computer ScienceComputer Science (R0)