Artificial neural network approach for nonlinear principal components analysis

Background: Nonlinear Principal Component Analysis (NLPCA) is one of the explanatory dimension reduction techniques and presents numerical and graphical results for variable sets including linear or nonlinear relationships. In Nonlinear Principal Component Analysis, categorical and ordinal variables, as well as numerical variables, can be included in the analysis. Linearity assumption for observed variables is not required for Nonlinear Principal Component Analysis. In this study, an artificial neural network approach for NLPCA is explained and applied. Methods: The hypothyroid data with 19 variables from 422 patients were used in the application. In order to see the difference of NLPCA from PCA, the results obtained using Principal Component Analysis (PCA) together with NLPCA were interpreted by presenting in tables and graphics. Results: The first two principal components explained 95.65% of the total variance in the NLPCA, while they explained 90.08% of the total variance in the PCA. Conclusion: In the analysis conducted by reducing the number of observations, it was seen that NLPCA has a high explanation rate compared to PCA, regardless of the number of observations. This can be attributed to NLPCA's ability to identify nonlinear relationships. Accordingly, it can be said that NLPCA gives effective results in the analysis made with both numerical and categorical variables.