corePCA {ExPosition} | R Documentation |
corePCA performs the core of principal components analysis (PCA), generalized PCA (GPCA), multidimensionsal scaling (MDS), and related techniques.
corePCA(DATA, M = NULL, W = NULL, decomp.approach = 'svd', k = 0)
DATA |
original data to decompose and analyze via the singular value decomposition. |
M |
a vector or diagonal matrix with masses for the rows (observations). If NULL, one is created or the plain SVD is used. |
W |
a vector or diagonal matrix with weights for the columns (measures). If NULL, one is created or the plain SVD is used. |
decomp.approach |
string. A switch for different decompositions (typically for speed). See |
k |
number of components to return (this is not a rotation, just an a priori selection of how much data should be returned). |
This function should not be used directly. Please use epPCA
or epGPCA
unless you plan on writing extensions to ExPosition.
Returns a large list of items which are also returned in epPCA
and epGPCA
(the help files for those functions will refer to this as well).
All items with a letter followed by an i are for the I rows of a DATA matrix. All items with a letter followed by an j are for the J rows of a DATA matrix.
fi |
factor scores for the row items. |
di |
square distances of the row items. |
ci |
contributions (to the variance) of the row items. |
ri |
cosines of the row items. |
fj |
factor scores for the column items. |
dj |
square distances of the column items. |
cj |
contributions (to the variance) of the column items. |
rj |
cosines of the column items. |
t |
the percent of explained variance per component (tau). |
eigs |
the eigenvalues from the decomposition. |
pdq |
the set of left singular vectors (pdq$p) for the rows, singular values (pdq$Dv and pdq$Dd), and the set of right singular vectors (pdq$q) for the columns. |
X |
the final matrix that was decomposed (includes scaling, centering, masses, etc...). |
Derek Beaton and HervĂ© Abdi.
Abdi, H., and Williams, L.J. (2010). Principal component analysis. Wiley Interdisciplinary Reviews: Computational Statistics, 2, 433-459.
Abdi, H. (2007). Singular Value Decomposition (SVD) and Generalized Singular Value Decomposition (GSVD). In N.J. Salkind (Ed.): Encyclopedia of Measurement and Statistics.Thousand Oaks (CA): Sage. pp. 907-912.