Calculate the W-correlation matrix

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Description

Function calculates the W-correlation matrix for the series.

Usage

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## S3 method for class 'ssa'
wcor(x, groups, Fs, ..., cache = TRUE)
## S3 method for class 'ossa'
wcor(x, groups, Fs, ..., cache = TRUE)
## Default S3 method:
wcor(x, L = (N + 1) %/% 2, ..., weights = NULL)
## S3 method for class 'wcor.matrix'
plot(x,
     grid = c(),
     ...,
     col = grey(c(1, 0)),
     cuts = 20,
     zlim = range(abs(x), 0, 1),
     at)

Arguments

x

the input object. This might be ssa object for ssa method, or just a matrix with elementary series in columns for default implementation.

L

window length.

weights

additional weights

groups

list of numeric vectors, indices of elementary components used for reconstruction.

Fs

list of series (e.g. 'ssa.reconstruction' object) for W-cor computation. If missing, reconstructed series from the input 'ssa' object x will be used.

...

further arguments passed to reconstruct routine for wcor or to plot for plot.wcor.matrix

cache

logical, if 'TRUE' then intermediate results will be cached in 'ssa' object.

grid

numeric vector, indices of matrix blocks (groups) which will be separated by grid line. Lines will be drawn on the left of and under noted blocks. Also this argument can be list of two numeric vectors with names 'x' and 'y', for control vertical and horizontal grid lines separately.

col

color vector for colorscale, given by two or more colors, the first color corresponds to the minimal value, while the last one corresponds to the maximal value (will be interpolated by colorRamp)

cuts

integer, the number of levels the range of W-cor values will be divided into.

zlim

range of displayed W-cor values.

at

A numeric vector giving breakpoints along the range of the image. if missing, will be evaluated automatically (see description of the cuts argument).

Details

W-correlation matrix is a standard way of checking for weak separability between the elementary components. In particular, the strongly correlated elementary components should be placed into the same group. The function calculates such a matrix either directly from 'ssa' object or from the matrix of elementary series.

For plotting additional (non-standard) graphical parameters which can be passed via ...:

useRaster

logical, indicates whether raster plot should be used. 'FALSE' by default

For class ‘ossa’, checking of Frobenius orthogonality is performed. If there are reconstructed matrices, which are not F-orthogonal (it is a usual case for Oblique SSA), the warning about possible irrelevancy will be shown, since then weighted correlations do not indicate weak separability properly. In such a case, the use of owcor is preferred.

Value

Object of type 'wcor.matrix'.

References

Golyandina, N., Nekrutkin, V. and Zhigljavsky, A. (2001): Analysis of Time Series Structure: SSA and related techniques. Chapman and Hall/CRC. ISBN 1584881941

See Also

reconstruct owcor.

Examples

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# Decompose co2 series with default parameters
s <- ssa(co2)
# Calculate the w-correlation matrix between first 20 series
# for a guess for grouping
w <- wcor(s, groups = 1:20)
plot(w, grid = c(2,4, 5,7))
# Calculate the w-correlation matrix for the chosen groups
# to check separability
w <- wcor(s, groups = list(c(1,4), c(2,3), c(5,6)))


# Artificial image for 2D SSA
mx <- outer(1:50, 1:50,
            function(i, j) sin(2*pi * i/17) * cos(2*pi * j/7) + exp(i/25 - j/20)) +
      rnorm(50^2, sd = 0.1)
# Decompose 'mx' with default parameters
s <- ssa(mx, kind = "2d-ssa")
# Plot wcor for first 12 components
plot(wcor(s, groups = 1:12), grid = c(2, 6))

# Real example: Mars photo
data(Mars)
# Decompose only Mars image (without backgroud)
s <- ssa(Mars, mask = Mars != 0, wmask = circle(50), kind = "2d-ssa")
# Plot wcor for the first 25 components
plot(wcor(s, groups = 1:25), grid = c(13, 15, 17,19))

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