wcc: Weighted auto- and cross-correlation measures

In ptw: Parametric Time Warping

Description

Functions to calculate weighted auto- and cross-correlation measures. The wcc is a suitable measure for the similarity of two patterns when features may be shifted. Identical patterns lead to a wcc value of 1.

Functions wcc and wac are meant for profile data (intensities measured at equidistant time points), whereas wcc.st and wac.st are meant for peak lists. In general, wcc values calculated for profiles will be higher since they will also include the large similarity in the empty spaces, i.e., parts of the profiles where no peaks are present (and that will appear to be perfectly aligned), whereas the peak-based version concentrates only on the peaks.

Usage

wcc(pattern1, pattern2, trwdth, wghts = NULL, acors1 = NULL, acors2 = NULL)
wac(pattern1, trwdth, wghts = NULL)

Arguments

pattern1, pattern2	input patterns, typically spectra. Vectors
trwdth	triangle width, given in the number of data points for the profile functions, and in the actual retention times for the stick-based warpings.
wghts	optional weights vector, will be calculated from triangle width if necessary. Sometimes it is more efficient to pre-calculate it and give it as an argument
acors1, acors2	autocorrelations of the input patterns. If not provided, they are calculated

Details

Functions wcc and wac are defined such that the triangle width stands for the number of points on one side of and including the current point. Thus, a trwdth of 0 signifies a non-existent triangle and results in an error; a trwdth equal to 1 only includes the current point with weight 1 and no neighbouring points. For the stick-based equivalents, the units of the time axis are used for the triangle width.

Value

One number, the weighted autocorrelation or crosscorrelation

Author(s)

Ron Wehrens

References

de Gelder, R., Wehrens, R. and Hageman, J.A. (2001) "A generalized expression for the similarity of spectra: Application to powder diffraction pattern classification", Journal of Computational Chemistry, 22, 273 – 289.

Examples

data(gaschrom)
wcc(gaschrom[1,], gaschrom[2,], 20)

wcc.st(gaschrom.st[[1]], gaschrom.st[[2]], 20)

Example output

[1] 0.9942493
[1] 0.9279658

ptw documentation built on Jan. 19, 2022, 5:07 p.m.