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As objective function (24a) we choose the arithmetic mean of the diagonal element of the projected variance-covariance matrix, the so-called A criterion, corresponding to the average of the half-axes of the confidence ellipsoid, see [30].
Fig. 3 shows a CA projecting the variance of the genes according to these cluster-centroids, explaining 98.3% of the inter-cluster variance (upper right corner).
E 1 has a very small variance projected onto a, σ a,1, compared to the variance for E 2, σ a,2.
On the contrary, ellipsoid E 2 has a very large variance projected onto a which produces a lower η value.
PCs are found as linear combinations of explanatory variables by maximising the variance of projected data.
The variability of the whole data was projected onto a scale, dividing variance into sub classes called principal components or factors.
The way the algorithm achieves this goal is by defining the axes of this subspace (called Principal Components) as those along which the variance of the projected data is maximized, under the additional constraint of orthogonality.
The normalized variance of the projected data is plotted across direction in Fig. 3B.
The eigenvalue is the sample variance of the projected data points.
It shows that the variance of the projected data had a broad profile, which is evidence that the patterns of correlation changed progressively across target direction.
For each contrast, six features (i.e., the log-transformed variance of the projected data) were computed using the three largest and three smallest eigenvectors from W to construct a low dimensional feature representation.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com