Introduction of Nonlinear Principal Component Analysis with an Application in Health Science Data

Abstract

Nonlinear Principal Component Analysis is one of the explanatory dimension reducing technique and presents numerical and graphical results for variable set included linear or nonlinear relationships. In this study, Nonlinear Principal Components Analysis was introduced and the relationship between students' sexual and physical trauma stories and demographic characteristics was examined with this method. In the study, the relationship between trauma and 9 variables obtained by questionnaire from 548 students was evaluated by non-linear principal components analysis. The total eigenvalue of first dimension has been found to be 1.766 and the total eigenvalue of second dimension has been found to be 1.504 The variance explanation rate of these eigenvalues are 17.656% and 15.044% respectfully. The total explained variance is seen as 28.550%. With nonlinear principal component analysis, categorical variables are scaled to the desired size in the most appropriate way, and thus, nonlinear relationships can be modeled as well as linear relationships between variables. With this analysis, gender, age, marital status and suicide variables were found to be effective on trauma.