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By Equation 4, this location has hf = hm = 0, the cell with the maximal variance in Figure 8.
Differently to PCA where the data are projected on the directions of maximal variance, in Laplacian-eigenmaps the first eigenvectors entail the direction preserving the distance among the examples.
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Considering wild-derived and lab-derived strains independently, principal component analyses (PCA, an unsupervised linear feature extraction method that discovers the directions of maximal variances in data) found highly significant correlations between non-synonymous SNP distribution and phylogeny within lab strain V2Rs (Two-way ANOVA, variance by V2R clade F12,858 = 17.99, P < 0.0001).
For the specific case of s 1, 0 = 1 2, the total contribution for which the maximal variance occurs in Figure 3, we illustrate the variance at several locations in the allowed range for s 1, 0 f and s 1, 0 m.
As in Figure 8, Figure 9, Figure 10, and Figure 11, the maximal variance occurs in the cell with s 1 m = s 2 m = 0.5 at s 1 f = s 2 f = 0.5.
Typically, the PCs are uncorrelated, i.e. the first PC points in the direction of maximal variance and the second PC shows in the direction of maximal variance orthogonal to the first PC and so on.
The focus of their work is on consistency in terms of estimating the true direction of maximal variance which corresponds to consistency in the parameter estimation of a statistical model.
Convenience sampling was used in order to reach maximal variance.
In Figure 10, the maximal variance occurs at the origin (hf = hm = h = 0) of the cell with s 1 f = s 1 m = s 1 = 0.5.
Rotating the high dimensional data, they are projected onto a 2 dimensional planar in a way that maximal variance can be seen according to the first and second axis.
Geometrically, this amounts to repositioning the origin at the centroid of the points in q-dimensional space and then rotating the coordinate axes in such a way as to satisfy the maximal variance property.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com