Difference between LDA and PLS-DA? Could someone please help by explaining the difference between LDA and PLS-DA? Or are we talking about the same?
 A: Both are supervised classification methods.
LDA aims to find projections that aims to minimize within class distance while maximizing between class distance.
PLS-DA is basically PLS regression to class information (I think this kind of class information is called one-hot-encoding of classes in machine learning) and aims to maximize covariance between independent variables and this class information. PLS-DA provides scores, that is also a projection, so LDA-like visualization can be achieved.
A: First of all, PLS-DA means that you perform a PLS regression and then apply a threshold to assign class labels. 
Now, there are two very different situations where this is done: 


*

*the underlying nature of the problem is metric, and the classes mean that the modeled property is above or below some threshold or limit.
Presence/absence of an analyte (qualitative analysis), legal limits are exceeded or not, ...

*A "normal" classification problem with cluster-shaped classes is modeled by a dummy regression where the class labels are coded as 0 and 1 or -n1 and +n2.
This is the procedure theGD explains. If I may say so, this is mostly abusing the regression. I assume this is the PLS-DA OP is asking about.
Both are discriminative classification approaches as opposed to one-class classifiers. But other than that the "threshold-type" classification 1. is a very different task from the more usual classification settings in 2. 
One important difference is that PLS-DA set up for a situation 1. can deal with classes being "open-ended at the backside" - e.g. analyte concentrations far from the threshold won't disturb the training of the classifier (unless the behaviour of the underlying data over large concentration ranges is more complex).
In contrast, PLS-DA  2. is for cluster-shaped classes (so the same application "group" like LDA). 

There is an interesting relationship between LDA and PLS-DA 2.:
PLS-DA using the full PLS model (i.e. all latent variables) produces the same predictions as LDA. 
OTOH, PLS-DA with only one latent variable produces the same predictions as a Euklidean distance classifier (EDC; i.e. assign the class whose mean is closest). 
We can say that PLS-DA regularizes in a way that behaves like "squeezing" the pooled covariance matrix of the LDA into spherical shape the more the fewer latent variables are used. 
Keep in mind: there is also PLS-LDA, where LDA is performed in PLS score space rather than the dummy regression of PLS-DA.
Literature:


*

*Bereton & Lloyd: Partial least squares discriminant analysis: taking the magic away, J Chemom (2014)

PLS-DA is possibly one of the most misunderstood and misused
  methods for discrimination in chemometrics.


*Barker, M. & Rayens, W.: Partial least squares for discrimination, J Chemom, 17, 166-173 (2003).
DOI: 10.1002/cem.785 

My personal opinion: if I have cluster-shaped classes and want to go for PLS regularization, I use PLS-LDA rather than PLS-DA.
