RMS: Quality criteria for comparing patterns with shifts

Description

Functions to compare patterns with shifted features. These functions compare warped sample patterns to one or more reference patterns. RMS returns the usual root-mean-squared difference measure; WCC returns 1-wcc, where wcc indicates the weighted cross-correlation. Perfect alignment leads to a value of 0 for both criteria. Internal function, not meant to be called directly by the user. In particular, note that the identity warping may lead to slightly different estimates than a direct comparison of the reference and sample signals - a warping even slightly outside the original range of 1 : ncol(ref) leads to NA values.

Usage

RMS(warp.coef, ref, samp, B)
WCC(warp.coef, ref, samp, B, trwdth = 20, wghts, ref.acors = NULL)

Arguments

warp.coef

a vector of warping coefficients

ref

reference signal; a matrix with one or more rows. If the number of rows is greater than one, it should equal the number of rows in samp

samp

sample signal; a matrix with one or more rows

basis for warping function

trwdth

triangle width for the WCC function, expressed in the number of data points

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

ref.acors

autocorrelation of the reference. Since the reference is often unchanged over multiple evaluations (e.g., during an optimization), it is useful to pre-calculate this number

Value

One number - either the WCC or RMS value

Details

All patterns in samp are warped using the same warping function, and then compared to ref, either pair-wise (when ref and samp are of the same size), or with the one pattern in ref.

References

Eilers, P.H.C. (2004) "Parametric Time Warping", Analytical Chemistry, 76 (2), 404 -- 411.