New Trends in Classification and Data Mining
Krassimir Markov, V. V. Ryazanov, Vitalii Velychko, Levon H. Aslanyan · 2010
The new method for analysis of regularities systems is discussed. Regularities are related to effect of explanatory variables on outcome. At that it is supposed that different levels of outcome correspond to different subregions of explanatory variables space. Such regularities may be effectively uncovered with the help of optimal valid partitioning technique. The OVP approach is based on searching partitions of explanatory variables space that in the best way separate observations with different levels of outcomes. Partitions of single variables ranges or two-dimensional admissible areas for pairs of variables are searched inside corresponding families. Output system of regularities is formed with the help of statistical validity estimates by two types of permutation tests. One of the problems associated with OVP procedure is great number of regularities in output system in high-dimensional tasks. The new approach for output system structure evaluating is suggested that is based on searching subsystem of small size with possibly better forecasting ability of convex combination of associated predictors. Mean error of convex combination becomes smaller when average forecasting ability of ensemble members becomes better and deviations between prognoses associated with different regularities increase. So minimization of convex combination mean error allows to receive subsystem of regularities with strong forecasting abilities that significantly differ from each other. Each regularity of output system may be characterized by distances to regularities in subsystem.