First, cumulative energy criterion is applied for the selection, in which we consider 93 percent of cumulative energy level for (6). An equal to 7 is obtained, which means that the first 7 principal components is selected as the best subspace to represent the data by cumulative energy criterion. Then, we use scree test to draw scree plot as a variance captured by a given principal component and to select another set of principal components. Fig. 2(a) shows full scree plot, where we use k (k = 256 in our case) principal components (X-axis) of a particular dataset and the corresponding variances, namely eigenvalues (Y-axis) to draw a scree plot, and the PCs are sorted in descending order with respect to the values of the corresponding variances. In Fig. 2(a), we look for an a flattening out of the curve. To provide better vision, we magnify the scree plot and ‘elbow’, show the first 25 principal components in Fig. 2(b). It can be observed from Fig. 2(b) that there is a sharp decrease of variance in the front part of the plot and then it starts flattening out after the principal component. In Fig. 2(b), we can observe in the range from 6 to 9 ‘elbow’ somewhere principal components and the first 6 principal components are able to capture about 92 percent = of the variance. After the -th point, the remaining (k - principal components capture only k2) around 8 percent of the total variance and are ignored. Full scree plot (b) Enlarged scree plot with first 25 eigenvectors Fig. 2. Scree test plot We use= 6 as a dominant principal components in our case. However, from Fig. 2(b), we have observed a range of principal components from 6 to 9, and it is not very clear that what is the most appropriate value of To overcome this ambiguity, we use parallel analysis criterion as described in the following and to verify the selection of .
First, cumulative energy criterion is applied for the selection, in which we consider 93 percent of cumulative energy level for (6). An equal to 7 is obtained, which means that the first 7 principal components is selected as the best subspace to represent the data by cumulative energy criterion. Then, we use scree test to draw scree plot as a variance captured by a given principal component and to select another set of principal components. Fig. 2(a) shows full scree plot, where we use k (k = 256 in our case) principal components (X-axis) of a particular dataset and the corresponding variances, namely eigenvalues (Y-axis) to draw a scree plot, and the PCs are sorted in descending order with respect to the values of the corresponding variances. In Fig. 2(a), we look for an ‘elbow’, a flattening out of the curve. To provide better vision, we magnify the scree plot and show the first 25 principal components in Fig. 2(b). It can be observed from Fig. 2(b) that there is a sharp decrease of variance in the front part of the plot and then it starts flattening out after the principal component. In Fig. 2(b), we can observe ‘elbow’ somewhere in the range from 6 to 9 principal components and the first = 6 principal components are able to capture about 92 percent of the variance. After the -th point, the remaining (k - k2) principal components capture only around 8 percent of the total variance and are ignored. Full scree plot (b) Enlarged scree plot with first 25 eigenvectors Fig. 2. Scree test plot We use= 6 as a dominant principal components in our case. However, from Fig. 2(b), we have observed a range of principal components from 6 to 9, and it is not very clear that what is the most appropriate value of To overcome this ambiguity, we use parallel analysis criterion as described in the following and to verify the selection of .
FinalRevisedJournalpaper_18May12.docx