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en:pca [2020/03/29 08:57]
David Zelený
en:pca [2020/03/29 10:52] (current)
David Zelený [Simplified description of PCA algorithm]
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 ==== Simplified description of PCA algorithm ==== ==== Simplified description of PCA algorithm ====
-**(a)** Use the matrix of samples species (or, generally, samples descriptors), and display each sample into the multidimensional space where each dimension is defined by an abundance of one species (or descriptor). In this way, the samples will produce a cloud located in the multidimensional space.\\+**(a)** Use the matrix of samples × species (or, generally, samples × descriptors, where descriptors could be also environmental variables), and display each sample into the multidimensional space where each dimension is defined by an abundance of one species (or descriptor). In this way, the samples will produce a cloud located in the multidimensional space.\\
 **(b)** Calculate the centroid of the cloud.\\ **(b)** Calculate the centroid of the cloud.\\
 **(c)** Move the centres of axes to this centroid.\\ **(c)** Move the centres of axes to this centroid.\\
-**(d)** Rotate the axes in such a way that the first axis goes through the cloud in the direction of the highest variancethe second is perpendicular to the first and goes in the direction of the second highest variance, and so on. The position of samples on resulting rotated axes are sample scores on ordination axes.\\+**(d)** Rotate the axes in such a way that the first axis goes through the cloud in the direction of the highest variancethe positions of samples on this axis become //sample scores//. The second axis is constructed in the way to be perpendicular to the first axis, which means that the correlation of the sample scores on the first axis and sample scores on the second axis is zero. If more axes can be constructed (which is not the case of this example since the original space defined by two species is only two-dimensional), then each higher ordination axis is perpendicular to all previous ones).
  
 <imgref pca_2d> (from Legendre & Legendre 1998) illustrates this algorithm on a very simple case with only two species (descriptors) and five samples. <imgref pca_3d> illustrates the same logic on the data cloud in three-dimensional space (three species/descriptors). <imgref pca_2d> (from Legendre & Legendre 1998) illustrates this algorithm on a very simple case with only two species (descriptors) and five samples. <imgref pca_3d> illustrates the same logic on the data cloud in three-dimensional space (three species/descriptors).
en/pca.txt · Last modified: 2020/03/29 10:52 by David Zelený