- Aide Scilab
Please note that the recommended version of Scilab is 6.0.0. This page might be outdated.
See the recommended documentation of this function
Computes principal components analysis with standardized variables
[lambda,facpr,comprinc] = pca(x)
is a nxp (n individuals, p variables) real matrix. Note that
pcacenter and normalize the columns of
xto produce principal components analysis with standardized variables.
is a p x 2 numerical matrix. In the first column we find the eigenvalues of V, where V is the correlation p x p matrix and in the second column are the ratios of the corresponding eigenvalue over the sum of eigenvalues.
are the principal factors: eigenvectors of V. Each column is an eigenvector element of the dual of
are the principal components. Each column (c_i=Xu_i) of this n x n matrix is the M-orthogonal projection of individuals onto principal axis. Each one of this columns is a linear combination of the variables x1, ...,xp with maximum variance under condition
u'_i M^(-1) u_i=1
This function performs several computations known as "principal component analysis".
The idea behind this method is to represent in an approximative manner a cluster of n individuals in a smaller dimensional subspace. In order to do that, it projects the cluster onto a subspace. The choice of the k-dimensional projection subspace is made in such a way that the distances in the projection have a minimal deformation: we are looking for a k-dimensional subspace such that the squares of the distances in the projection is as big as possible (in fact in a projection, distances can only stretch). In other words, inertia of the projection onto the k dimensional subspace must be maximal.
Warning, the graphical part of the old version of
pca has been removed. It can now be performed
using the show_pca
Saporta, Gilbert, Probabilites, Analyse des Donnees et Statistique, Editions Technip, Paris, 1990.