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[...]... sum of the signal of interest plus the baseline.30 When the baseline has an offset baseline feature (i.e horizontal line), one number can express the baseline, thus subtraction of 9 that number from the signal would remove the baseline When a linearly sloping baseline is present, two or more points that only contain baseline information can be used to estimate a line.30 To remove the sloping... in the fibers’ spectra could be seen; however, utilizing multivariate statistics can provide more information on the variation of the spectra thus providing a better understanding of the groupings of the data as well as the areas of the spectra that provide the most variation The AHC dendrogram of the eleven exemplars is shown in Figure 2.2 The dendrogram provided a visualization of the groupings of. .. area, normalizing to unit length, and normalizing to maximum intensity.27,30 Normalizing to unit area is achieved by dividing each variable in the sample by the sum of the absolute value of all variables in that sample The second approach, normalizing to unit length, is achieved by dividing each variable by the square root of the sum of squares of all the variables in each sample The final approach... variable by the maximum value in the sample so that the maximum intensity is equal to 1 Mean centering the data processes each variable at a time over all the samples In simplest terms, mean centering repositions the centroid of the data set to the origin of the coordinate system by subtracting out the mean value of each variable over all the samples.31 This prevents data points away from the 10... baseline, the estimated line is subtracted from the sample vector Polynomials of higher magnitudes can be estimated using this approach depending on the shape of the baseline Another method of removing the baseline takes the derivative of the spectra with respect to variable number This approach is quite useful because it is not essential to select points that only contain baseline information.30 Taking... depends on the relative orientation in coordinate space of the PC and variable axes.30 The factor loading is determined by taking the cosine of the angle between the variable axis and the PC axis Factor loadings can range 14 from -1 to +1, where a factor loading of -1 indicates a strong negative correlation and a factor loading of +1 indicates a strong positive correlation between the variable... reduction technique that creates linear combinations of the original variables Inherent groupings of the data can be visualized if a significant portion of the variation in the data set can be explained in two or three PCs This technique also explains what original variables contributed the most to the new PC axes via factor loadings PCA has been applied to the analysis of accelerants48,49, fibers44,50,51,... linear combinations of the original variables.27,32 This technique provides a visual representation of the groupings of data along with information on the contributions of the original variables to the latent variables These new variables are called principal components (PCs), and explain all or most of the total variance Principal components are orthogonal to one another and represent directions of maximum... factor loading of 0 signifies no correlation between the two variables There are three common methods for determining the adequate amount of PCs to retain for further analyses like discriminant analysis The first method is to simply determine a percentage of the total variability, usually 95 percent, to be retained In this example, enough PCs would be retained so that they represent 95 percent of the total... plot, which provides a visual representation of the decreasing variation in each principal component by plotting the eigenvalues against each principal component.27,33 A sudden break in the plot indicates the number of significant PCs to retain to the left of the plot Any PC to the right of that break is considered noise However, this method sometimes retains too few PCs for subsequent analysis Overall,