Abstract
The amount of computing time for K Nearest Neighbor Search is linear to the size of the dataset if the dataset is not indexed. This is not endurable for on-line applications with time constraints when the dataset is large. However, if there are categorical attributes in the dataset, an index cannot be built on the dataset. One possible solution to index such datasets is to convert categorical attributes into numeric attributes. Categories are ordered and then are mapped to numeric values. In this paper, we propose a new heuristic ordering algorithm to compare with two previously proposed algorithms that borrow the idea from minimal spanning trees. The new algorithm divisively builds a binary tree by recursively partitioning the categories. Then, we in-order traverse the tree and get an ordering of the categories. After mapping and indexing, we can efficiently retrieve a small portion of the dataset and perform K nearest neighbor search on the portion at the cost of a little bit of accuracy. Experiments show the divisive ordering algorithm performs better than the other two algorithms.
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Agrafiotis, D.K., Rassokhin, D.N., Lobanov, V.S.: Multidimensional Scaling and Visualization of Large Molecular Similarity Tables. Journal of Computational Chemistry 22(5), 488–500 (2001)
Bar-Joseph, Z., et al.: K-ary Clustering with Optimal Leaf Ordering for Gene Expression Data. Bioinformatics 19(9), 1070–1078 (2003)
Bennett, K.P., Fayyad, U., Geiger, D.: Density-Based Indexing for Approximate Nearest-Neighbor Queries. ACM KDD, 233–243 (1999)
Berry, M.J.A., Linoff, G.: Memory-Based Reasoning. In: Data Mining Techniques: for Marketing, Sales, and Customer Support, ch. 9, pp. 157–186 (1997)
Cox, T.F., Cox, M.A.A.: Multidimensional Scaling, 2nd edn. Chapman & Hall, Boca Raton (2001)
Ganti, V., Gehrke, J., Ramakrishnan, R.: CACTUS-Clustering Categorical Data Using Summaries. In: ACM KDD, pp. 73–83 (1999)
Gilbson, D., Kleinberg, J., Raghavan, P.: Clustering Categorical Data: An Approach Based on Dynamical Systems. In: VLDB Conference, pp. 311–322 (1998)
Guttman, A.: R-Trees: A Dynamic Index Structure for Spatial Search. In: ACM SIGMOD, pp. 47–57 (1984)
Hettich, S., Bay, S.D.: The UCI KDD Archive, http://kdd.ics.uci.edu . University of California, Department of Information and Computer Science, Irvine, CA (1999)
Indyk, P., Motwani, R.: Approximate Nearest Neighbors: Toward Removing the Curse of Dimensionality. In: ACM Symposium on Theory of Computing, pp. 604–613 (1998)
Kuo, H.-C., Lin, Y.-S., Huang, J.-P.: Distance Preserving Mapping from Categories to Numbers for Indexing. In: Negoita, M.G., Howlett, R.J., Jain, L.C. (eds.) KES 2004. LNCS (LNAI), vol. 3214, pp. 1245–1251. Springer, Heidelberg (2004)
Lee, S.-K., Kim, Y.-H., Moon, B.R.: Finding the Optimal Gene Order in Displaying Microarray Data. In: Genetic and Evolutionary Computation Conference, pp. 2215–2226 (2003)
Sokal, R.R., Michener, C.D.: A Statistical Method for Evaluating Systematic Relationships. University of Kansas Science Bulletin 38, 1409–1438 (1958)
Voorhees, E.M.: Implementing agglomerative hierarchical clustering algorithms for use in document retrieval. Information Processing and Management 22, 465–476 (1986)
Zhang, J.: Selecting Typical Instances in Instance-Based Learning. In: Proceedings of the Ninth International Conference on Machine Learning, pp. 470–479 (1992)
Yu, K., Xu, X., Tao, J., Ester, M., Kriegel, H.-P.: Instance Selection Techniques for Memory-Based Collaborative Filtering. In: Proceedings of the 2nd SIAM International Conference on Data Mining (2002)
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Kuo, HC. (2005). A Divisive Ordering Algorithm for Mapping Categorical Data to Numeric Data. In: Khosla, R., Howlett, R.J., Jain, L.C. (eds) Knowledge-Based Intelligent Information and Engineering Systems. KES 2005. Lecture Notes in Computer Science(), vol 3682. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11552451_135
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DOI: https://doi.org/10.1007/11552451_135
Publisher Name: Springer, Berlin, Heidelberg
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