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While the type of information generally captured by the first components is also seen for other descriptor sets, noteworthy here is the clustering of Leucine and Isoleucine, which is intuitively correct due to their high chemical similarity.
We found that highly correlated scores of chromatin marks were defined usually by the first components (ξ1, ξ1), which were also highly correlated (co-localized).
The values in the similarity matrix are computed as the correlation between the two types of projected variables onto the space spanned by the first components retained in the analysis.
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On average, by construction, the first components tend to have higher amplitudes than later components.
Thus a significant part of the chemical noise can be separated from the main spectrum by removing the first components.
In other words, 18.66 % variance is explained by the first component followed by 18%% by the second component and the coefficients decrease thereof.
15.894% of the test variance was explained by the first component and a cumulative variance of 60.02% was explained by the first six components (see Table 8).
Using two components and eliminating obvious outliers, more than 99% of the variation can be explained by the first component, PC1, and ca. 1% by PC2.
The proportion of variance explained by the first component is 0.58, 0.67 and 0.68 for the abstract, manual, and routine aspects respectively (see "Appendix B" for further information).
Finally, a ratio index was developed to further highlight soil covers through dividing the NDSI by the first component of tasseled cap transformation (TC1).
This can be done using an argument from Föllmer and Protter (2011), where the inverse three-dimensional Bessel process is projected on the filtration generated by the first component of the Brownian motion.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com