PCA on its own can be used to differentiate sets of data, and the loadings of the PCs can give an indication of the spectroscopic origin of the discrimination.

“Understanding the molecular information contained in Principal Component Analysis of Vibrational Spectra of Biological Systems”,

F. Bonnier, H.J. Byrne,

Analyst, 137, 322-332 (2012)

We tend to use PCA-LDA only if we want to further classify data.

 Sorry - I should add, the PC Loadings are easiest to understand if the analysis is done pairwise.

Dear Mayra Alejandra, 

You are talking about the multivariate statistical methods which provide the ability to analyze the vast spectral distribution. Those methods are recommended for data has minor changes.

First, you should start by the preprocessing stage. This stage is needed to enhance subtle differences between different samples through reducing the effect of unwanted signals such as (signals from cell media or glass substrate, fluorescence, Mie scattering, detector noise, calibration errors, cosmic rays, laser power fluctuations, ).

The preprocessing stage for Ramman is included many steps:

* Cosmic Ray/spike removal

* baseline removal ( includes several methods: Differentiation based methods, Polynomial Fitting based methods, Asymmetric Least Squares based   methods, Frequency Domain Analysis based methods)

* alignments of Spectral axis  

Multivariate data analysis 

The multivariate analysis methods are broadly divided into two groups:

- Unsupervised methods

- Supervised methods  

Classification models contain different models:

- Linear Discriminant Analysis (LDA)

- Soft Independent Modeling of Class Analogy (SIMCA)

- Artificial Neural Networks (ANN)

- Support Vector Machines (SVM)  

Performance metrics of statistical models:

True Negative (TN): Number of observations which are originally negative and also classified as negative.

True Positive (TP): Number of observations which are originally positive and also classified as positive.

False Negative (FN): Number of observations which are originally positive but classified as negative. These errors are called Type-II errors.

False Positive (FP): Number of observations which are originally negative but classified as positive. These errors are called Type-I errors.      

Infrared and Raman Spectroscopy in Forensic Science "book"--- a good reference for your question.

Best regards,

Musab TR 

Both PCA and LDA are essentially linear transformation methods. When applied to spectroscopic data, the wavenumbers are your variables and through PCA you can find out the most important wavenumbers which result in the variability in your dataset (which is described by their weightage or so called ‘loading’). PCA is an unsupervised method and it considers the entire dataset as one ‘block’. From the scores plot you can check if there are three distinct groups or not and the confidence levels as ellipses.

LDA is an supervised classification method, meaning you tell it that three classes exist. Via PCA you can achieve preliminary data reduction and see the variance. Subsequently, you can derive vectors from the PCs by LDA to minimize the within-category variations (which could be due to factors responsible for variations beyond the three classes you mentioned) while maximising discriminating characteristics across the three categories. What it means is- the score values of PCA are to be used for LDA. This could help you to visualize separation between the 3 groups to be seen more clearly. You have to report the accuracy after validation tests for classification of new spectra or using 'leave one out' approach.

SOME CAUTION:

A lot depends on what your research objective is. If you wish to find out the wavenumbers in Raman spectrum (which of course correspond to functional group vibrations) responsible for the difference between the three classes, then use PCA and use the loadings for PC1 and PC2 (or even PC3) for this information. If you are trying to develop a method to classify every new spectrum into one of the three classes, use LDA or PCA-LDA. Finally, note that PCA alone would not necessarily give you three distinct classes where as PCA-LDA assumes that a spectrum has to be a member of one of the 3 classes included in the analysis.

NOTE: I would prefer programming; not sure if Unscrambler has a separate LDA- you might try any other classification method like SIMCA.

Dear,

There is a a video of Chemometric on youtube, using Unscrambler.

https://www.youtube.com/watch?v=wpSBdwOJTnY

https://www.youtube.com/watch?v=g9ltdXVZzoc

This software is very easy to use if your goal is to do PCA-LDA.

I recommend you to do first the appropriate pre-processing of the data. A baseline correction using ModPoly with many iteration works well, then a normalization of your data (vector nom or SNV).

Then you perform a PCA on your data, and check for outliers, like technical outliers, that should be removed because PCA is very sensitive to outliers. Re-perform the PCA after removing outliers.

Then save the 10 first PCA components.

Then perform a LDA based on the 10 first PCA components. This method works well but you must make sure that the PCs components are meaningful.

Best regards,

Are there any free softwares to do the Principal Component Analysis other than Unscrambler?   

Dear colleague

you can follow these papers :

http://www3.ntu.edu.sg/home/quanliu/Ong-2012-OptExp-PCAvsBCAForRaman.pdf

http://www.ejournal.unam.mx/rmf/no565/RMF005600504.pdf

https://innovareacademics.in/journals/index.php/ijpps/article/viewFile/10886/4980

Regards

@Simantini The open source R program is best option. There is an R package named 'FactoMineR' with excellent documentation, an accompanying paper in stats software journal and video tutorials for newbies. Yet another R package is "Exposition" which gives some "pretty" plots. It should only take a week to be up and running with R even for someone new to programming world.

I have lost track of this, but agree with N.N. Misra, R is a good option.

There is also an R platform specifically for Raman/FTIR applications

http://hyperspec.r-forge.r-project.org/ 

@N.N. Misra: Thank  you so much Sir for providing the information.

Dear all,

Can anyone recomend a free available software for LDA analysis (user friendly for non-programing users) once the principal components are identified by PCA analysis?

I Have used https://biit.cs.ut.ee/clustvis/ for PCA analysis of Raman data.

First question: How do I identify the main components? Without much experience I would asume these are the Raman wavelenghts with higher PC scores in absolut numbers. Am I right? Is there any criteria to decide the PC score values cut-off?

Second question: How to use the identified main components (set of wavelenghts) to do a LDA analysis to classify spectra? Arno Germond suggested to use the 10 first PCA components (PC1, PC2, PC3,..., PC10). Is it possible to include that much components in LDA analysis? Every component would be a set of different wavelenths.

Appologies if my questions are not appropiate. I am quite new to this area. I have understood more or less how to perform PCA analysis but I do not quite understand how to move to the LDA afterwards and classify spectra.

Thanks,

Joan

Joan Martí Mayra Alejandra Jaimes Dear all,

Once I done PCA, it is good to save the first 10-15 first components in some table. From there you should choose only the most meaningful one to perform a classification model such as LDA based on the PCs components. Typically I prefer simple models that include only 2 to 5 components (dimensions), and one of my mentor, Rasmus Bro, do the same. Simple & robust is the best. Interpretation gets easier.

However, by experience, I find that sometimes it is not necessarily the PC1, 2, 3 and 4 that are selected. In fact, depending on datasets, sometimes PC6, 7, 8 ... can bear unique information about my dataset. Few of my colleague from Osaka University will agree (eg. Nicolas Pavillon, Nicolas Smith)

How to select the PCs is the trick, and it will depends on the software you use, as some software will not provide solutions to do this. I use JMP SAS for that, as it gives a fisher score that will rank the PC components (by most significant), and update the associated p values each time I add a PCs in the model, so you avoid to overfit. More detail here: https://www.nature.com/articles/s41598-018-30276-1

I am not sure how to do this procedure in python or R, I m still looking for a solution.

Then you can do your Linear DA analysis, or Quadratic DA. Quadratic DA considers that the intra-group covariance matrices are not assumed to be equal.

I also do a lot of comparisons between 2 groups, such as a 'control' versus 'disease' group, to identify the peaks (or biomarkers) that best distinguish them. To do so I select 2 groups and perform PC & LDA. Once I do a LDA plot which reveal a structure in my data, I save the canonical structures, (total canonical structures), which are coefficient weights associated to each dimension (axes). Then, you can multiply the PCA loading with the weights to obtain scores, then you SUM them to obtain a single metric called the F1 score which help you visualise the peaks that most discriminate between 2 groups.

You may contact me if you have inquiries, I am also open for collaborations,

Please check the following article for example or citation.

Preprint Following Embryonic Stem Cells, Their Differentiated Progeny...