Principal Component Analysis Based on a Subset of Variables for Qualitative Data

Acceleration of Convergence of the Alternating Least Squares Algorithm for Nonlinear Principal Components Analysis

“…In order to find a subset of q variables, we employ Backward elimination and Forward selection of Mori et al [Mori et al, 1998;Mori et al, 2006] as cost-saving stepwise selection procedures in which only one variable is removed or added sequentially.…”

Classification of Moving Targets Based on Motion and Appearance

“…In forward selection, features are progressively incorporated into larger and larger subsets, while backward elimination starts with the set of all features and progressively eliminates the least promising ones. It is reported in [29] that stepwise-type selection tends to select better subsets than single-type selections. In our experiments we employ a stepwise-type feature selection method that in each iteration eliminates n 1 features according to their predictive power and then uses the same criterion to bring back n 2 eliminated features(n 2 < n 1 ).…”

9. Multidimensional Data Analysis

“…The proportion P indicates the original variations explained by the first r PCs based on the selected q variables, which is computed by > J aj /tr(S) where ~j is the j-th largest eigenvalue of [(S?1 + S12 S21) -A j S11) ]aj = 0, and S, S11 and S12 = 821' are covariance matrices of Y, Yi and Y1 and Y2, respectively. A selected subset of variables for each q was found so that it has the largest proportion P in the sense of the applied selection procedure (see Tanaka and Mori (1997) and Mori et al (1998) for the details). Thus five curves which are very similar to one another were obtained by applying the above four selection procedures and the all-possible selection procedure.…”