Solution 6.2 - Chemometrics: Data Analysis for the Laboratory and Chemical Plant

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  • Published: Jan 1, 2000
  • Channels: Chemometrics & Informatics

1. The following numbers should be produced for the eigenvalues.

2. The graphs are given below.

The third eigenvalue models primarily noise, eigenvalues considerably larger than this are significant. We can see that the first eigenvalue always appears well above the noise meaning that there is always at least one component in the data. The second eigenvalue starts to rise at time 7 (forward) and 12 (backward) suggesting that the region between and including these times is composition 2. This is either indicative of an embedded peak eluting over this region, or coelution between two main peaks.

3. The results of WFA against window centre (note there are no values for windows centred at points 1 and 16) are as follows.

The graph is given below.

 

The third eigenvalue is rather noisy, but this is a consequence of the small matrix size (3 ´ 6), whereas for EFA the matrices are much larger. In many practical situations the matrix contains many more variables. However the second eigenvalue show a definite rise in the centre where there is a composition 2 region, consistent with question 2. Because of the small matrix size, WFA is probably not as useful as EFA in this case.

4. There is no single correct answer to this, a chemometrician would look at the data carefully. One method might be to look at the composition 1 region for the first compound at the beginning of the cluster, take an average spectrum over points 1 to 6 in time, and then calculate the correlation between each point in time and this average. If the peak is embedded it is expected that the correlation coefficient will dip over the composition 2 region and then increase again. If this region represents a different compound this will not be so. The last two points cannot be used meaningfully because they are dominated by noise. The graph is given below (using a logarithmic scale for the correlation coefficient).

The correlogram rises at points 12 and 13, suggesting that the spectrum at these points is similar to that of the beginning of the data, consistent with an embedded peak.

Several other answers would be acceptable, and in practice one may use a mix of techniques.

5. A good estimate of the composition 1 regions are 1 to 6 and 13 to 16 (see question 2). The spectrum is as follows.

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