Principal components analysis
[facpr,comprinc,lambda,tsquare] = princomp(x,eco)
pvariables) real matrix.
a boolean, use to allow economy size singular value decomposition.
pmatrix. It contains the principal factors: eigenvectors of the correlation matrix
pmatrix. It contains the principal components. Each column of this 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
pcolumn vector. It contains the eigenvalues of
Vis the correlation matrix.
ncolumn vector. It contains the Hotelling's T^2 statistic for each data point.
This function performs "principal component analysis" on the
p data matrix
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.
To compute principal component analysis with standardized variables may use
princomp(wcenter(x,1)) or use the pca function.
a=rand(100,10,'n'); [facpr,comprinc,lambda,tsquare] = princomp(a);
Saporta, Gilbert, Probabilites, Analyse des Donnees et Statistique, Editions Technip, Paris, 1990.