Variance The Estimation Eigen Value of Principal Component Analysis and Nonlinear Principal Component Analysis

Abstract

Nonlinear Principal Component Analysis (PRINCALS) is an extension of Principal Component Analysis (Linear), which can reduce the variables of mixed scale multivariable data (nominal, ordinal, interval, and ratio) simultaneously. This study investigated variance the estimation eigen value of Principal Component Analysis Linear and Nonlinear. The result showed that variance the estimation eigen value of Principal Component Analysis is $ {\rm Var}({\tilde{\hat{\lambda}}}_{S})=\mathbf H_{S}^{\prime}\mathbf V_{S}\mathbf H_{S} $ and variance the estimation eigen value of Nonlinear Principal Component Analysis is $ {\rm Var}({{\hat{\lambda}}}_{R})=\mathbf H_{R}^{\prime}\mathbf V_{R}\mathbf H_{R} $ Variance the estimation eigen value of Nonlinear Principal Component Analysis better (efficient) than variance the estimation eigen value of Principal Component Analysis.