[facpr,comprinc,lambda,tsquare, explained, mu] = 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.
a column vector of length "number of components". The percentage of variance explained by each principal component.
a row vector of length p
. The estimated mean of each variable of
x
.
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.
a=rand(100,10,'n'); [facpr,comprinc,lambda,tsquare] = princomp(a); | ![]() | ![]() |
x = [1 2 1;2 1 3; 3 2 3] [facpr, comprinc, lambda, tsquare, explained, mu] = princomp(x, %t); comprinc * facpr' + ones(3, 1) * mu // == x | ![]() | ![]() |
Saporta, Gilbert, Probabilités, Analyse des Données et Statistique, Editions Technip, Paris, 1990.
Version | Description |
2024.1.0 | princomp now returns the percentage of the variance explained by each principal component and
the estimated mean of each variable of x. |
2025.0.0 | Tagged obsolete and will be removed in Scilab 2026.0.0. |