Lecture 7: Chemometrics Part 2

Question 1

What does PC do if the first principle component doesn’t sufficiently describe the data?

Answer 1

• If the first PC is not sufficient to describe the spread of data, the calculation is repeated to find PC2
• The process is continued until all the variability within the dataset has been accounted for and modelled

Question 2

PC2 is…

Answer 2

PC2 is orthogonal to PC1 as that’s where you will find the next largest variation within the data set.

Question 3

What does PC2 look at?

Answer 3

The residual variation

Question 4

Data =

Answer 4

Data = Model + Error

Question 5

Data = S

Answer 5

Data = Structure + Noise

Question 6

Structure = ?

Answer 6

The bits that are important, the bits that tell you where the sample groupings are

Question 7

Noise

Answer 7

Could be random noise from instrument, could be fluctuations in instrument, temperature changes, etc

Question 8

What is residual variance?

Answer 8

Residual variance is random noise, this is not useful or helpful to model the data.

Question 9

What happens if you model noise?

Answer 9

It means when you start to use the model for classification you’re trying to force an unknown sample into a model that has lots of noise going on

Question 10

What is the ideal model in PCA?

Answer 10

We want to create a model that captures as much of the information in the dataset, in as few PCs as possible

Question 11

What do the PCs describe?

Answer 11

The PCs will describe the structure (explained variance)

Question 12

How do you determine the optimum number of PCs in PCA?

Answer 12

Determination of the optimum number of principle components is achieved via the inspection of loadings plot, scores plot, explained variance plot.

Question 13

How is a score generated for PCs?

Answer 13

• Each PC is a linear combination of the original variables
• The distance along each PC from the mean gives a sample its “score”

Question 14

What does the distance between each sample and PC give you?

Answer 14

Distance between each sample and the principle component gives you the residuals (residual variation)

Question 15

What does the distance between each sample and the mean of all the samples give you?

Answer 15

• Distance between each sample and the mean of all the samples gives you your score (this score can be positive or negative)
• Each sample will have a different score for each principle component.

Question 16

Where is the majority of the information found in PCA?

Answer 16

The majority of the information is in the first few PCs, particularly if you have a good data set.

Question 17

What does an explained variance / scores plot tell you?

Answer 17

An explained variance (or score) plot reveals the optimum number of PCs

Question 18

What will happen if your samples have lots of variance?

Answer 18

If your samples have lots of variance and lots of samples you’ll need more PCs to accurately account for the variation within the data set.

Question 19

What is a scores plot?

Answer 19

• The scores plot is a map of the samples
• Samples closest together are the most similar

Question 20

What happens to the score of a sample depending om the PC used?

Answer 20

Each sample will have a different score for every PC so the map will change depending on the PC chose.

Question 21

What is an advantage of a scores plot?

Answer 21

You can separate data points that would overlap on other PCs

Question 22

Why is PCA better than CA?

Answer 22

It tells you why samples group together.

Question 23

What are loadings?

Answer 23

Loadings are the link between the scores plot and the chemistry of the samples

Question 24

What is a loadings plot?

Answer 24

• A loadings plot is a map of variables
• The loading plots are the links between the scores plot and the chemistry of the samples
• Loadings plots relate directly to the spectra and then relate directly back to the chemical composition because the spectrums give you your molecular fingerprint

Question 25

What do loadings explain?

Answer 25

It explains why samples are grouping

Question 26

For something that is negatively correlated to a PC, where should you expect to see it on a scores plot?

Answer 26

Anything that is negatively correlated to any PC means we will find it on the negative side of the scores plot for that PC because they are directly comparable.

Question 27

What does the magnitude of the loadings indicate?

Answer 27

The weighting of the variables

Question 28

What type of technique is linear discriminant analysis?

Answer 28

Supervised

Question 29

How does Linear Discriminant Analysis (LDA) create classification rules?

Answer 29

It uses principle components

Question 30

Why are loadings calculated in Linear Discriminant Analysis (LDA)?

Answer 30

Loadings are calculated to maximise separation between known groups

Question 31

What are the principle components called in linear discriminant analysis?

Answer 31

Discriminant functions

Question 32

What does LDA ask you at the start?

Answer 32

If you want to use PCA scores and if so how many scores.

Question 33

What does LDA do?

Answer 33

It tries to make samples from known groups as different as we can, so when we classify, the groups are sufficiently far apart so when we add new unknowns it can be grouped

Question 34

What is the fisher ratio? (LDA)

Answer 34

Loadings are tweaked that the difference between the samples is as large as possible whilst simultaneously trying to make the difference between samples of known group as small as possible.

Question 35

What does LDA try to minimise?

Answer 35

LDA tries to minimise variation within groups to maximise separation between groups by prioritising loadings

Question 36

What discriminant values are given to samples belonging to the same and different groups?

Answer 36

Samples belonging to the same group are given similar discriminant values and those from different groups are given different discriminant values

Question 37

What are the drawbacks of chemometrics?

Answer 37

• It doesn’t fix data
• Preprocessing is needed
• Requires large sample size which is difficult for trace evidence
• Samples need to reflect population
• Sample collection has to be controlled and reproducible
• Not a substitute for human interpretation
• Communicating it to a jury can be difficult

Question 38

What do you have to be careful of when applying spectral preprocessing in chemometrics?

Answer 38

Over processing will over fit your data and force your data to be what you want it to to be but then it loses what it should be.

Question 39

What is spectral preprocessing?

Answer 39

• Changing spectral output so you’re minimising random noise
  E.g baseline correction, smoothing, detrending, derivatives, etc

Question 40

What bias do you need to be aware of in chemometrics?

Answer 40

Cognitive bias