Skip to contents

Wavelet Coefficients of Spectra

Source: R/wavelet.R
wavelet_features.Rd

Computes the discrete wavelet transform (DWT) of spectra and returns its coefficients as features: a compressed representation of the spectra for modeling, with far fewer variables than channels.

Usage

wavelet_features(x, wavelet = "d4", level = 3, coefficients = "approximation")

Arguments

x

A numeric matrix or data frame of spectra, one per row, or a numeric vector (one spectrum).

wavelet

The wavelet: "haar", "d4" (default), "d6", "d8" or "la8".

level

The number of levels of the decomposition. Default is 3.

coefficients

The coefficients returned: "approximation" (default) or "all".

Value

A matrix with one row per spectrum and one column per coefficient, named A<level>_<i> for the approximation and D<j>_<i> for the details of level j.

Details

The DWT decomposes a spectrum, level by level, into approximation coefficients (the smooth part, at half the resolution of the previous level) and detail coefficients (the fine structure removed at that level), with the pyramid algorithm of Mallat (1989) and an orthonormal wavelet:

  • "haar": the Haar wavelet (2 coefficients);

  • "d4", "d6", "d8": Daubechies' extremal phase wavelets with 4, 6 and 8 coefficients;

  • "la8": Daubechies' least asymmetric wavelet with 8 coefficients (symlet 4), whose nearly symmetric shape suits spectral lines.

The coefficients kept are

  • "approximation" (default): the approximation at level, a smoothed version of the spectrum with about \(2^{-level}\) times as many values;

  • "all": the approximation at level and the details of every level, the complete transform (as many values as channels, after padding).

The spectrum is extended by reflection at its end to a length divisible by \(2^{level}\), and the transform is periodic. The transform is orthonormal, so the sum of squares of all the coefficients equals that of the (padded) spectrum. As features for a model, the approximation keeps the broad shape of the spectrum and drops the noise; to keep only the most informative coefficients, step_wavelet() can select those with the largest variance in the training data (Trygg and Wold, 1998).

References

  • Mallat, S.G. (1989). A theory for multiresolution signal decomposition: the wavelet representation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11(7):674-693.

  • Daubechies, I. (1992). Ten Lectures on Wavelets. SIAM, Philadelphia.

  • Trygg, J., Wold, S. (1998). PLS regression on wavelet compressed NIR spectra. Chemometrics and Intelligent Laboratory Systems, 42(1-2):209-220.

See also

step_wavelet(), savitzky_golay()

Author

Christian L. Goueguel

Examples

data(forageLIBS)
spectra <- forageLIBS[1:4, -(1:14)]
approx <- wavelet_features(spectra, wavelet = "la8", level = 4)
dim(approx)   # 7152 channels -> 447 coefficients
#> [1]   4 447