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Title: An empirical study on nonlinear structure extraction with measures of dependence Authors:  Shoma Ishimoto - Hokkaido University (Japan) [presenting]
Hiroyuki Minami - Hokkaido University (Japan)
Masahiro Mizuta - The Institute of Statistical Mathematics (Japan)
Abstract: A method is proposed for extracting nonlinear structure from multi-dimensional data by extending dimension reduction with measures of dependence; various measures of dependence have been proposed to evaluate the strength of linear or nonlinear relationships between 2 variables. To achieve our goal, we adopt the measures in place of the indices in popular dimension reduction, and find the directions that maximize them. We apply our idea to numerical examples with typical nonlinear structures (quadratic, cubic, sinusoid, circle, power) with random noise. We introduce 7 types of measures of dependence (MIC, TIC, Hoeffding's D, distance correlation, KSG Estimator, HSIC, RDC) and project the simulated data into lower space according to the measures. Through 100 times simulation, we discuss the results from the viewpoints of performance, specific features and our competence. We conclude the most suitable one to meet our idea.