corePCA {ExPosition} R Documentation

## corePCA

### Description

corePCA performs the core of principal components analysis (PCA), generalized PCA (GPCA), multidimensionsal scaling (MDS), and related techniques.

### Usage

corePCA(DATA, M = NULL, W = NULL, decomp.approach = 'svd', k = 0)


### Arguments

 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 pickSVD. k number of components to return (this is not a rotation, just an a priori selection of how much data should be returned).

### Details

This function should not be used directly. Please use epPCA or epGPCA unless you plan on writing extensions to ExPosition.

### Value

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...).

### Author(s)

Derek Beaton and Hervé Abdi.

### References

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.

epPCA, epGPCA