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Loading vector corresponding to each principal component should be determined based on the criteria that maximizing variance of latent variable as well as correlation coefficient between latent variable and dependent variable at the same time, which could be realized by maximizing the covariance of the latent variable and dependent variable.
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Due to the fact that factor structures depend on intercorrelations, which are influenced by the variability of the individual variables, a forced three-factor extraction with varimax rotation was performed in order to maximize variance of the data set, and to further simplify the interpretations of the generated scales.
From Table 8, it can be seen that the optimum subset (maximizing variance and not linearly related) of unit test case metrics varies from one system to another.
But instead of reconstructing or maximizing variance, I say that what I want to do is to preserve at least a little distance among my points.
Minimizing squared distances equals maximizing variance.
Because principal components maximize variance, the bulk of the information encoded by the selected features is about differences between classes in the dataset.
PCA looks for projections to maximize variance and LDA looks for projections that maximize the ratio of between-class to within-class scatter as depicted in Fig. 3.
A total of 200 data sets were generated to maximize variance [ 56].
Analysis of genetic variance revealed that dividing the genotype set by breeding populations maximized variance among populations while minimizing variance within populations (Qst; Table 5).
For PCA, components are extracted by maximizing the variance of a linear combination of the original genes,, but not maximizing the discriminative power for classifiers like support vector machine (SVM) and k nearest neighbor (kNN).
But in addition to maximizing the variance of the predictors X, at the same time, it maximizes the correlation of X with the response Y. Applied to the choice of summary statistics, it therefore not only decorrelates the summary statistics, but also chooses them according to their relation to α. Hastie et al. (2011) argue that the first aspect dominates over the latter, however.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com