Syntax
[facpr,comprinc,lambda,tsquare, explained, mu] = princomp(x,eco)
Arguments
- x
is a
n
-by-p
(n
individuals,p
variables) real matrix.- eco
a boolean, use to allow economy size singular value decomposition.
- facpr
A
p
-by-p
matrix. It contains the principal factors: eigenvectors of the correlation matrixV
.- comprinc
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 conditionu'_i M^(-1) u_i=1
- lambda
is a
p
column vector. It contains the eigenvalues ofV
, whereV
is the correlation matrix.- tsquare
a
n
column vector. It contains the Hotelling's T^2 statistic for each data point.- explained
a column vector of length "number of components". The percentage of variance explained by each principal component.
- mu
a row vector of length
p
. The estimated mean of each variable ofx
.
Description
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.
Examples
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
See also
Bibliography
Saporta, Gilbert, Probabilités, Analyse des Données et Statistique, Editions Technip, Paris, 1990.
History
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. |
Report an issue | ||
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