i_pca: Incremental Principal Component Analysis (PCA)

In idm: Incremental Decomposition Methods

Incremental Principal Component Analysis (PCA)

Description

This function computes the Principal Component Analysis (PCA) solution on the covariance matrix using the incremental method of Hall, Marshall & Martin (2002).

Usage

i_pca(data1, data2, current_rank, nchunk = 2, disk = FALSE)

Arguments

data1	Matrix or data frame of starting data, or full data if data2 = NULL
data2	Matrix or data frame of incoming data; omitted when full data is given in data1
current_rank	Rank of approximation or number of components to compute; if empty, the full rank is used
nchunk	Number of incoming data chunks (equal splits of 'data2', default = 2) or a Vector with the row size of each incoming data chunk
disk	Logical indicating whether then output is saved to hard disk

Value

rowpcoord	Row scores on the principal components
colpcoord	Variable loadings
eg	A list describing the eigenspace of a data matrix, with components u Left eigenvectors v Right eigenvectors m Number of cases d Eigenvalues orgn Data mean
sv	Singular values
inertia_e	Percentage of explained variance
levelnames	Attribute labels
rowctr	Row contributions
colctr	Column contributions
rowcor	Row squared correlations
colcor	Column squared correlations
nchunk	A copy of nchunk in the return object
disk	A copy of disk in the return object
allrowcoord	A list containing the row scores on the principal components produced after each data chunk is analyzed; returned only when disk = FALSE
allcolcoord	A list containing the variable loadings on the principal components produced after each data chunk is analyzed; returned only when disk = FALSE
allrowctr	A list containing the row contributions after each data chunk is analyzed; returned only when disk = FALSE
allcolctr	A list containing the column contributions after each data chunk is analyzed; returned only when disk = FALSE
allrowcor	A list containing the row squared correlations produced after each data chunk is analyzed; returned only when disk = FALSE
allcolcor	A list containing the column squared correlations produced after each data chunk is analyzed; returned only when disk = FALSE

References

Hall, P., Marshall, D., & Martin, R. (2002). Adding and subtracting eigenspaces with eigenvalue decomposition and singular value decomposition. Image and Vision Computing, 20(13), 1009-1016.

Iodice D' Enza, A., & Markos, A. (2015). Low-dimensional tracking of association structures in categorical data, Statistics and Computing, 25(5), 1009–1022.

Iodice D'Enza, A., Markos, A., & Buttarazzi, D. (2018). The idm Package: Incremental Decomposition Methods in R. Journal of Statistical Software, Code Snippets, 86(4), 1–24. DOI: 10.18637/jss.v086.c04.

See Also

update.i_pca, i_mca, update.i_mca, add_es

Examples

data("segmentationData", package = "caret")
#center and standardize variables, keep 58 continuous attributes
HCS = data.frame(scale(segmentationData[,-c(1:3)]))
#abbreviate variable names for plotting
names(HCS) = abbreviate(names(HCS), minlength = 5)
#split the data into starting data and incoming data
data1 = HCS[1:150, ]
data2 = HCS[151:2019, ]
#Incremental PCA on the HCS data set: the incoming data is 
#splitted into twenty chunks; the first 5 components/dimensions 
#are computed in each update
res_iPCA = i_pca(data1, data2, current_rank = 5, nchunk = 20)
#Static plots 
plot(res_iPCA, animation = FALSE)

#\donttest is used here because the code calls the saveLatex function of the animation package 
#which requires ImageMagick or GraphicsMagick and 
#Adobe Acrobat Reader to be installed in your system 
#See help(im.convert) for details on the configuration of ImageMagick or GraphicsMagick.
#Creates animated plot in PDF for objects and variables
plot(res_iPCA, animation = TRUE, frames = 10, movie_format = 'pdf')


#Daily Closing Prices of Major European Stock Indices, 1991-1998 
data("EuStockMarkets", package = "datasets") 
res_iPCA = i_pca(data1 = EuStockMarkets[1:50,], data2 = EuStockMarkets[51:1860,], nchunk = 5) 

#\donttest is used here because the code calls the saveLatex function of the animation package 
#which requires ImageMagick or GraphicsMagick and 
#Adobe Acrobat Reader to be installed in your system 
#See help(im.convert) for details on the configuration of ImageMagick or GraphicsMagick.
#Creates animated plot in PDF movies for objects and variables
plot(res_iPCA, animation = TRUE, frames = 10, movie_format = 'pdf')

idm documentation built on July 12, 2022, 1:05 a.m.