Unit variance component scores

Analysis of diversity in response to polar and nonpolar vapors of all screened polymers was performed using PCA analysis followed by cluster analysis. The scores plots of the first three PCs (Fig. 5.12) illustrate the diversity of performance of all sensing polymers. The larger the distance between polymer data points, the larger the difference in the response pattern between the respective CdSe/polymer nanocomposites. To quantify this diversity, cluster analysis was further performed where the distances based on principal component scores were adjusted to unit variance.45 This distance measure, known as Mahalanobis distance, accounts for the different amount of variation in different directions. An example of such difference is shown in Fig. 5.12a, b, where the distance between polymer 4 and other polymers is much larger on the plot of PC 1 vs. PC 2 when compared with the plot of PC 2 vs. PC 3. 

The goal of Q-mode FA is to determine the absolute abundance of the dominant components (i.e., physical or chemical properties) for environmental contaminants. It provides a description of the multivariate data set in terms of a few end members (associations or factors, usually orthogonal) that account for the variance within the data set. A factor score represents the importance of each variable in each end member. The set of scores for all factors makes up the factor score matrix. The importance of each variable in each end member is represented by a factor score, which is a unit vector in n (number of variables) dimensional space, with each element having a value between -1 and 1 and the... 

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