CA S - Correspondence Analysis - Solution

PURPOSE

Execute correspondence (CORAN) analysis, or Principal Component Analysis (PCA) of image data.

SEE ALSO

CA SM	[Correspondence Analysis - Show Map & Eigen Values]
CA SR	[Correspondence Analysis - Reconstitute images]
CA SRD	[Correspondence Analysis - Reconstitute Differential images]
CA SRI	[Correspondence Analysis - Reconstitute Importance images]
CA VIS	[Correspondence Analysis - Create Visual map]
SD C	[Save Document - from CA S (_IMC) file]

USAGE

.OPERATION: CA S

.ENTER IMAGE FILE TEMPLATE : SEC***
[Enter a file name template identifying the image series to be analyzed.]

.ENTER FILE NUMBERS OR SELECTION DOC. FILE NAME 1-40,45,50-70
[Enter numbers of image files in the series. If the images are supplied as a 3D stack, then the numbers are interpreted as slice numbers.]

.MASK FILE: MAS002
[Enter the name of the file containing a mask. Only image pixels where mask pixels are greater than 0.5 are analyzed in CORAN or PCA. Enter '*' if no masking is desired.]

.NUMBER OF FACTORS: 20
[Enter the number of factors to be used. Note that eigenvectors and eigenvalues are only computed up to this number. ]

.CORAN, PCA, ITERATIVE PCA, OR SKIP ANALYSIS (C/P/I/S): C
[Choose type of analysis
C: Coran.,
P: Principal Component Analysis.
I: Iterative Principal Component Analysis.,
S: Skip analysis and just create _SEQ file.]

If CORAN is used the following question appears:

.ADDITIVE CONSTANT: 0.0
[CORAN analysis can not accept images containing negative values. If images contain negative values this can be overcome by specifying an additive constant that will be added to all (within-mask) pixels of all images].

.OUTPUT FILE PREFIX: coran
[Enter the prefix used for the output files where data are to be stored. 'CA S' creates five or six files to store the results. In these files the variable definitions are:

NUMIM = NUMBER OF IMAGES
NPIX = NUMBER OF PIXELS UNDER MASK
NFAC = NUMBER OF FACTORS
NSAM = IMAGE X DIMENSION
NROW = IMAGE Y DIMENSION
PCA = 1 if PCA, 0 if CORAN
FIM = ORIGINAL IMAGE NUMBER
FPIX = PIXEL NUMBER

The files are:

PREFIX_SEQ Unformatted sequential file having image values under the mask. This file decreases memory requirements.

NUMIM, NPIX
IMAGE(1) VALUES(1...NPIX), FIM(1)
IMAGE(2) VALUES(1...NPIX), FIM(2)


IMAGE(NUMIM) VALUES(1...NPIX), FIM(NUMIM)

PREFIX_SET Transposed direct access file having image values under the mask. This file decreases memory requirements. Only created if transposition occurs.

PIXEL(1) VALUES(1...NUMIM)
PIXEL(2) VALUES(1...NUMIM)


PIXEL(NPIX) VALUES(1...NUMIM)

PREFIX_IMC Text file with image coordinates.

NUMIM, NFAC, NSAM, NROW, NUMIM, PCA
IMAGE(1) COORDINATES (1..NFAC), WEIGHTP(1), DOR, FIM(1)
IMAGE(2) COORDINATES (1..NFAC), WEIGHTP(2), DOR, FIM(2)


IMAGE(NUMIM) COORDINATES (1..NFAC), WEIGHTP(NUMIM), DOR, FIM(NUMIM)

PREFIX_PIX Text file with pixel coordinates.

NPIX, NFAC, NSAM , NROW , NUMIM, PCA
PIXEL(1) COORDINATES (1..NFAC), WEIGHTP(1), CO(1), FPIX
PIXEL(2) COORDINATES (1..NFAC), WEIGHTP(2), CO(2), FPIX


PIXEL(NPIX) COORDINATES (1..NFAC), WEIGHTP(NPIX),CO(NPIX), FPIX

PREFIX_EIG Text file with eigenvalues.

 NFAC, TOTAL WEIGHT, TRACE, PCA, N
EIGENVALUE(1), %, CUMULATIVE %
EIGENVALUE(2), %, CUMULATIVE %


EIGENVALUE(NFAC), %, CUMULATIVE %
IF (PCA)
IMAGE OR PIXEL AVERAGES (1..10)
IMAGE OR PIXEL AVERAGES (11..20)

PREFIX_MAS Mask FILE in SPIDER image format

NOTES

1. In general, it is advisable to request a large number of factors (even larger than number of pixels under the mask, the system will automatically limit the number of factors to the permitted number).

2. WARNING: for very large problems (the size of covariance matrix in the order of thousands) the methods used for Coran and PCA analysis are slow and inaccurate, the system may fail on numerical accuracy or enter an endless loop. In these cases use Iterative PCA Analysis instead.

SUBROUTINES

JPMSK1, SCORAN3, SPCA3, INCOR3, INCORT, GETCOO, GETCOOT, VPROP, FILELIST

CALLER

UTIL1