Classification Baselines
Introduction
Classification methods rely on classifying peak and/or baseline segments, similar to selective masking as explained in the polynomial section, but make use of sophisticated techniques to determine the baseline points rather than relying on manual selection.
All classification functions allow inputting weights to override the baseline classification, which can be helpful, for example, to ensure a small peak is not classified as baseline without having to alter any parameters which could otherwise reduce the effectiveness of the classification method. The plot below shows such an example.
Algorithms
dietrich (Dietrich's Classification Method)
dietrich() calculates the power spectrum of the data as the squared derivative
of the data. Then baseline points are identified by iteratively removing points where
the mean of the power spectrum is less a multiple of the standard deviation of the
power spectrum. The baseline is created by first interpolating through all baseline
points, and then iteratively fitting a polynomial to the interpolated baseline.
golotvin (Golotvin's Classification Method)
golotvin() divides the data into sections and takes the minimum standard
deviation of all the sections as the noise's standard deviation for the entire data.
Then classifies any point where the rolling max minus min is less than a multiple of
the noise's standard deviation as belonging to the baseline.
std_distribution (Standard Deviation Distribution)
std_distribution() identifies baseline segments by analyzing the rolling
standard deviation distribution. The rolling standard deviations are split into two
distributions, with the smaller distribution assigned to noise. Baseline points are
then identified as any point where the rolled standard deviation is less than a multiple
of the median of the noise's standard deviation distribution.
fastchrom (FastChrom's Baseline Method)
fastchrom() identifies baseline segments by analyzing the rolling standard
deviation distribution, similar to std_distribution(). Baseline points are
identified as any point where the rolling standard deviation is less than the specified
threshold, and peak regions are iteratively interpolated until the baseline is below the data.
cwt_br (Continuous Wavelet Transform Baseline Recognition)
cwt_br() identifies baseline segments by performing a continous wavelet
transform (CWT) on the input data at various scales, and picks the scale with the first
local minimum in the Shannon entropy. The threshold for baseline points is obtained by fitting
a Gaussian to the histogram of the CWT at the optimal scale, and the final baseline is fit
using a weighted polynomial where identified baseline points are given a weight of 1 while all
other points have a weight of 0.
fabc (Fully Automatic Baseline Correction)
fabc() identifies baseline segments by thresholding the squared first derivative
of the data, similar to dietrich(). However, fabc approximates the first derivative
using a continous wavelet transform with the Haar wavelet, which is more robust to noise
than the numerical derivative in Dietrich's method. The baseline is then fit using
Whittaker smoothing with all baseline points having a weight of 1 and all other points
a weight of 0.
rubberband (Rubberband Method)
rubberband() uses a convex hull to find local minima
of the data, which are then used to construct the baseline using either
linear interpolation or Whittaker smoothing. The rubberband method is simple and
easy to use for convex shaped data, but performs poorly for concave data. To get
around this, Bruker's OPUS spectroscopy software uses a patented method to coerce
the data into a convex shape so that the rubberband method still works. pybaselines
uses an alternate approach of allowing splitting the data in segments, in order
to reduce the concavity of each individual section; it is less user-friendly
than Bruker's method but works well enough for data with similar baselines and
peak positions.
Note
For noisy data, rubberband performs significantly better when smoothing the data beforehand.
By using Whittaker smoothing (or other smoothing interpolation methods) rather than linear interpolation to construct the baseline from the convex hull points, the negative effects of applying the rubberband method to concave data can be slightly reduced, as seen below.
