# METHODS FOR DISCOVERING AND ANALYSIS OF REGULARITIES SYSTEMS - Approach based on Optimal Partitioning of Explanatory Variables Space

### Senko Oleg, Kuznetsova Anna

#### Abstract

The goal of discussed Optimal valid partitioning (OVP) method is discovering of regularities describing effect of explanatory variables on outcome value. OVP method is based on searching partitions of explanatory variables space with best possible separation of objects with different levels of outcome variable. Optimal partitions are searched inside several previously defined families by empirical (training) datasets. Random permutation tests are used for assessment of statistical validity and optimization of used models complexity. Additional mathematical tools that are aimed at improving performance of OVP approach are discussed. They include methods for evaluating structure of found regularities systems and estimating importance of explanatory variables. Paper also represents variant of OVP technique that allows to compare effects of explanatory variables on outcome in different groups of objects.

#### References

- Abdolell, M., LeBlanc, M., Stephens, D., Harrison, R. V., 2002. Binary partitioning for continuous longitudinal data: categorizing a prognostic variable. In Statistics in Medicine, 21:3395-3409.
- Breiman, L., Friedman, J. H., Olshen, R. A. and Stone, C. J., 1984. Classification and Regression Trees, Chapman & Hall, New York
- Dedovets M, Senko O., 2010. The Algorithm Based on Metric Regularities. In International Journal “Information Theories and Applications”, Vol. 17, Number 1, 27-29.
- Ernst, M. J., 2004. Permutation methods: A basis for exact inference. In Statistical Science, 19: 676-685.
- Kim, H., Loh, W. Y., 2003. Classification Trees with Bivariate Linear Discriminant Node Models, In Journal of Computational and Graphical Statistics, 12: 512-530.
- Kostomarova, I., Kuznetsova, A., Malygina, N., Senko, O., 2010. Methods for evaluating of regularities systems structure. In New Trends in Classification and Data Mining, ITHEA, Sofia, Bulgaria, 40-46.
- Kostomarova, I., Kuznetsova, A., Malygina, N., Senko, O., 2011. Method for evaluating discrepancy between regularities systems in different groups. In International Journal "Information Technologies & Knowledge" Vol.5, Number 1, 46-53
- Kovshov, V. V., Moiseev, V. L., Ryazanov, V. V., 2008. Algorithms for finding Logical Regularities in Pattern Recognition. In Computational mathematics and Mathematical Physics, 48: 314-328.
- Ryazanov, V. V., 2007. Logical Regularities in Pattern Recognition (parametric approach). In Computational mathematics and Mathematical Physics, 47: 1793- 1808.
- Sen'ko, O. V., Kuznetsova, A. V., 1998. The use of partitions constructions for stochastic dependencies approximation. In Proceedings of the International conference on systems and signals in intelligent technologies. Minsk (Belarus), 291-297.
- Sen'ko, O. V., Kuznetsova, A. V., 2006. The Optimal Valid Partitioning Procedures. In Statistics on the Internet http://statjournals.net/
- Senko, O. V., Kuznetsova A. V. 2009. Methods of Regularities Searching Based on Optimal Partitioning. In International Book Series “Information Science and Computing”, N 8, Classification, Forecasting, Data Mining, ITHEA, Sofia, 136-141

#### Paper Citation

#### in Harvard Style

Oleg S. and Anna K. (2011). **METHODS FOR DISCOVERING AND ANALYSIS OF REGULARITIES SYSTEMS - Approach based on Optimal Partitioning of Explanatory Variables Space** . In *Proceedings of the International Conference on Knowledge Discovery and Information Retrieval - Volume 1: KDIR, (IC3K 2011)* ISBN 978-989-8425-79-9, pages 415-418. DOI: 10.5220/0003639104230426

#### in Bibtex Style

@conference{kdir11,

author={Senko Oleg and Kuznetsova Anna},

title={METHODS FOR DISCOVERING AND ANALYSIS OF REGULARITIES SYSTEMS - Approach based on Optimal Partitioning of Explanatory Variables Space},

booktitle={Proceedings of the International Conference on Knowledge Discovery and Information Retrieval - Volume 1: KDIR, (IC3K 2011)},

year={2011},

pages={415-418},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0003639104230426},

isbn={978-989-8425-79-9},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the International Conference on Knowledge Discovery and Information Retrieval - Volume 1: KDIR, (IC3K 2011)

TI - METHODS FOR DISCOVERING AND ANALYSIS OF REGULARITIES SYSTEMS - Approach based on Optimal Partitioning of Explanatory Variables Space

SN - 978-989-8425-79-9

AU - Oleg S.

AU - Anna K.

PY - 2011

SP - 415

EP - 418

DO - 10.5220/0003639104230426