princomp — Principal components analysis
[facpr,comprinc,lambda,tsquare] = princomp(x,eco)
is a n-by-p
(n individuals, p
variables) real matrix.
a boolean, use to allow economy size singular value decomposition.
A p-by-p
matrix. It contains the principal factors: eigenvectors of
the correlation matrix V.
a n-by-p
matrix. 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
is a p column vector. It contains
the eigenvalues of V, where
V is the correlation matrix.
a n column vector. It contains the Hotelling's
T^2 statistic for each data point.
This function performs "principal component analysis" on the
n-by-p data matrix
x.
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.