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In this paper we review Lattice Machine, a learning paradigm that “learns” by generalising data in a consistent, conservative and parsimonious way, and has the advantage of being able to provide additional reliability information for any classification. More specifically, we review the related concepts such as hyper tuple and hyper relation, the three generalising criteria (equilabelledness, maximality, and supportedness) as well as the modelling and classifying algorithms. In an attempt to find a better method for classification in Lattice Machine, we consider the contextual probability which was originally proposed as a measure for approximate reasoning when there is insufficient data. It was later found to be a probability function that has the same classification ability as the data generating probability called primary probability. It was also found to be an alternative way of estimating the primary probability without much model assumption. Consequently, a contextual probability based Bayes classifier can be designed. In this paper we present a new classifier that utilises the Lattice Machine model and generalises the contextual probability based Bayes classifier. We interpret the model as a dense set of data points in the data space and then apply the contextual probability based Bayes classifier. A theorem is presented that allows efficient estimation of the contextual probability based on this interpretation. The proposed classifier is illustrated by examples.
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Tom
Strony
241--256
Opis fizyczny
Bibliogr. 21 poz., rys.
Twórcy
autor
- Faculty of Computer Science and Technology, Inner Mongolia University of the Nationalities, Tongliao, Inner Mongolia, China
autor
- Computer Science Department, Brock University, St. Catharines, Ontario, Canada
autor
- School of Computing and Mathematics, University of Ulster, Jordanstown, Northern Ireland, UK
Bibliografia
- [1] Anew, R.: Ockham’s Razor: A Historical and Philosophical Analysis of Ockham’s Principle of Parsimony, University of Illinois press, Champaign-Urbana, 1976.
- [2] Chen, S., Ma, B., Zhang, K.: On the Similarity and the Distance Metric, Theoretical Computer Science, 410(24-25), 2009, 2365-2376.
- [3] Duda, R. O., Hart, P. E.: Pattern Classification and Scene Analysis, John Wiley & Sons, 1973.
- [4] Elzinga, C., Wang, H.: Kernels for Acyclic Digraphs, Pattern Recognition Letters, 33(16), 2012, 2239-2244.
- [5] Lin, Z., Wang, H., McClean, S.: A Multi-dimensional Sequence Approach to Measuring Tree Similarity, IEEE Transactions on Knowledge and Data Engineering, 24(2), 2012, 197-208.
- [6] Lin, Z., Wang, H., McClean, S., Wang, H.-Y.: All Common Embedded Subtrees for Clustering XML Documents by Structure, Proceedings of ICMLC09: IEEE International Conference in Machine Learning and Cybernetics, 2009.
- [7] Mitchell, T. M.: Machine Learning, The McGraw-Hill Companies, Inc, 1997, ISBN 0-07-042807-7.
- [8] Plotkin, G. D.: A Note on Inductive Generalization, in: Machine Intelligence (B. Meltzer, D. Michie, Eds.), vol. 5, Elsevier North-Holland, New York, 1970, 153-163.
- [9] Smith, D. J., Vamanamurthy, M. K.: How Small Is a Unit Ball?, Mathematics Magazine, 62, 1989, 101?07.
- [10] Wang, H.: Contextual Probability, Journal of Telecommunications and Information Technology, 3, 2003, 92-97, ISSN 1509-4553.
- [11] Wang, H.: Nearest Neighbors by Neighborhood Counting, IEEE Transactions on Pattern Analysis and Machine Intelligence, 28(6), 2006, 942-953.
- [12] Wang, H.: A Novel Clustering Method based on Spatial Operations, Flexible and efficient information handling: 23rd British National Conference on Databases (D. Bell, J. Hong, Eds.), LNCS 4042, Springer, 2006.
- [13] Wang, H.: All Common Subsequences, Proc. IJCAI-07, 2007.
- [14] Wang, H.: Contextual Probability and Neighbourhood, International Journal of Software and Informatics, 6, 2012, 435-452.
- [15] Wang, H., Bell, D.: Extended k-Nearest Neighbours based on Evidence Theory, The Computer Journal, 47(6), 2004.
- [16] Wang, H., Dubitzky, W.: A Flexible and Robust Similarity Measure based on Contextual Probability, Proceedings ofIJCAI-05, 2005.
- [17] Wang, H., Dubitzky, W., Diintsch, I., Bell, D.: A Lattice Machine Approach to Automated Casebase Design: Marrying Lazy and Eager Learning, Proc. IJCAI99, Stockholm, Sweden, 1999.
- [18] Wang, H., Dimtsch, I., Bell, D.: Data Reduction based on Hyper Relations, Proceedings ofKDD98, New York, 1998.
- [19] Wang, H., Diintsch, I., Gediga, G.: Classificatory Filtering in Decision Systems, International Journal of Approximate Reasoning, 23, 2000, 111-136.
- [20] Wang, H., Diintsch, I., Gediga, G., Skowron, A.: Hyperrelations in Version Space, International Journal of Approximate Reasoning, 36(3), 2004, 223-241.
- [21] Wang, H., Murtagh, F.: A Study of Neighbourhood Counting Similarity, IEEE Transactions on Knowledge and Data Engineering, 20(4), 2008, 449-461.
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Bibliografia
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