Can interestingness measures be usefully visualized?

Robert Susmaga ; Izabela Szczech

International Journal of Applied Mathematics and Computer Science, Tome 25 (2015), p. 323-336 / Harvested from The Polish Digital Mathematics Library

Résumé

The paper presents visualization techniques for interestingness measures. The process of measure visualization provides useful insights into different domain areas of the visualized measures and thus effectively assists their comprehension and selection for different knowledge discovery tasks. Assuming a common domain form of the visualized measures, a set of contingency tables, which consists of all possible tables having the same total number of observations, is constructed. These originally four-dimensional data may be effectively represented in three dimensions using a tetrahedron-based barycentric coordinate system. At the same time, an additional, scalar function of the data (referred to as the operational function, e.g., any interestingness measure) may be rendered using colour. Throughout the paper a particular group of interestingness measures, known as confirmation measures, is used to demonstrate the capabilities of the visualization techniques. They cover a wide spectrum of possibilities, ranging from the determination of specific values (extremes, zeros, etc.) of a single measure, to the localization of pre-defined regions of interest, e.g., such domain areas for which two or more measures do not differ at all or differ the most.

Détail

Publié le : 2015-01-01

Zbl 1322.68194

EUDML-ID : urn:eudml:doc:270403

Bibliographie

[000] Agrawal, R., Imielinski, T. and Swami, A. (1993). Mining associations between sets of items in massive databases, Proceedings of the 1993 ACM-SIGMOD International Conference on Management of Data, Washington, DC, USA, pp. 207-216.

[001] Alaíz-Rodríguez, R., Japkowicz, N. and Tischer, P.E. (2008). Visualizing classifier performance on different domains, ICTAI 2008, Dayton, OH, USA, pp. 3-10.

[002] Carnap, R. (1962). Logical Foundations of Probability, 2nd Edn., University of Chicago Press, Chicago, IL. | Zbl 0040.07001

[003] Christensen, D. (1999). Measuring confirmation, Journal of Philosophy 96(9): 437-461.

[004] Crupi, V., Tentori, K. and Gonzalez, M. (2007). On Bayesian measures of evidential support: Theoretical and empirical issues, Philosophy of Science 74(2): 229-252.

[005] Drummond, C. and Holte, R.C. (2006). Cost curves: An improved method for visualizing classifier performance, Machine Learning 65(1): 95-130.

[006] Eells, E. (1982). Rational Decision and Causality, Cambridge University Press, Cambridge. | Zbl 0476.03016

[007] Everson, R.M. and Fieldsend, J.E. (2006). Multi-class ROC analysis from a multi-objective optimisation perspective, Pattern Recognition Letters 27(8): 918-927.

[008] Fitelson, B. (1999). The plurality of Bayesian measures of confirmation and the problem of measure sensitivity, Philosophy of Science 66: 362-378.

[009] Fitelson, B. (2001). Studies in Bayesian Confirmation Theory, Ph.D. thesis, University of Wisconsin, Madison, WI.

[010] Floater, M.S., Hormann, K. and Kos, G. (2006). A general construction of barycentric coordinates over convex polygons, Advances in Computational Mathematics 24(1-4): 311–331. | Zbl 1095.65016

[011] Fukuda, T., Morimoto, Y., Morishita, S. and Tokuyama, T. (1996). Data mining using two-dimensional optimized association rules: Scheme, algorithms, and visualization, Proceedings of the 1996 ACM-SIGMOD International Conference on the Management of Data, Montreal, Quebec, Canada, pp. 13-23.

[012] Geng, L. and Hamilton, H. (2006). Interestingness measures for data mining: A survey, ACM Computing Surveys 38(3), Article no. 9.

[013] Greco, S., Pawlak, Z. and Słowiński, R. (2004). Can Bayesian confirmation measures be useful for rough set decision rules?, Engineering Applications of Artificial Intelligence 17(4): 345-361.

[014] Greco, S., Słowiński, R. and Szczęch, I. (2012). Properties of rule interestingness measures and alternative approaches to normalization of measures, Information Sciences 216: 1-16. | Zbl 1251.68178

[015] Healey, C. (1996). Choosing effective colors for data visualization, Proceedings of the 7th Conference on Visualization, VIS'96, San Francisco, CA, USA, pp. 263-270.

[016] Hernández-Orallo, J., Flach, P.A. and Ramirez, C.F. (2011). Brier curves: A new cost-based visualisation of classifier performance, Proceedings of the 28th International Conference on Machine Learning, ICML 2011, Bellevue, WA, USA, pp. 585-592.

[017] IBM (1996). Intelligent miner user guide, Version 1, Release 1, Technical report, International Business Machines, San Jose, CA.

[018] Kemeny, J. and Oppenheim, P. (1952). Degrees of factual support, Philosophy of Science 19(4): 307-324.

[019] Mortimer, H. (1988). The Logic of Induction, Prentice Hall, Paramus, NJ. | Zbl 0683.60001

[020] Morzy, T. and Zakrzewicz, M. (2003). Data mining, in J. Blazewicz, W. Kubiak, T. Morzy and M.E. Rusinkiewicz (Eds.), Handbook on Data Management Information Systems, Springer, Heidelberg, pp. 487-565.

[021] Nozick, R. (1981). Philosophical Explanations, Clarendon Press, Oxford.

[022] Pawlak, Z. (2002). Rough sets, decision algorithms and Bayes' theorem, European Journal of Operational Research 136(1): 181-189. | Zbl 1089.68127

[023] Pawlak, Z. (2004). Some issues on rough sets, Transactions on Rough Sets I, Elsevier Science Publishers, New York, NY, pp. 1-58. | Zbl 1104.68108

[024] Susmaga, R. and Szczęch, I. (2013). Visualization of interestingness measures, Proceedings of the 6th Language & Technology Conference: Human Language Technologies as a Challenge for Computer Science and Linguistics, Poznań, Poland, pp. 95-99.

[025] Susmaga, R. and Szczęch, I. (2014). Visual-based detection of properties of confirmation measures, in T. Andreasen, H. Christiansen, J.C.C. Talavera and Z.W. Ras (Eds.), Proceedings of the 21st International Symposium on Methodologies for Intelligent Systems, ISMIS 2014, Lecture Notes in Computer Science, Vol. 8502, Springer, Heidelberg, pp. 133-143.

[026] Tan, P., Kumar, V. and Srivastava, J. (2002). Selecting the right interestingness measure for association patterns, Proceedings of the 8th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Edmonton, Alberta, Canada, pp. 32-41.

[027] Ware, C. (2004). Information Visualization: Perception for Design, 2nd Edition, Morgan Kaufmann, Waltham, MA.

[028] Shaikh, M., McNicholas, P.D., Antonie, M.L. and Murphy, T.B. (2013). Standardizing interestingness measures for association rules, Computing Research Repository, http://arxiv.org/abs/1308.3740.

[029] Warren, J. (2003). On the uniqueness of barycentric coordinates, in R. Goldman and R. Krasauskas (Eds.), Topics in Algebraic Geometry and Geometric Modeling, Contemporary Mathematics, Vol. 334, American Mathematical Society, Providence, RI, USA, pp. 93-99. | Zbl 1043.52009

[030] Zhou, Y., Wischgoll, T., Blaha, L.M., Smith, R. and Vickery, R.J. (2014). Visualizing confusion matrices for multidimensional signal detection correlational methods, Proceedings of the SPIE Conference on Visualization and Data Analysis, San Francisco, CA.