# What is the difference between MDA and LDA and how is it applied in SciKit-learn?

According to this paper, Canonical Discriminant Analysis (CDA) is basically Principal Component Analysis (PCA) followed by Multiple Discriminant Analysis (MDA). I am assuming that MDA is just Multiclass LDA.

My work uses SciKit-Learn's LDA extensively. According to its description, it is

A classifier with a linear decision boundary, generated by fitting class conditional densities to the data and using Bayes’ rule.

It applies pretty well to cases with multiple classes; can this implementation be also called as MDA?

So to do CDA in Scikit-Learn, should one just apply PCA followed by LDA?

• In my awareness/understanding (see footnote here) CDA is a synonym to (multiclass) LDA. Discriminants in multiclass settings are extracted as canonical variates. Do by MDA you mean multi-class LDA? LDA is not related to PCA closely because PCA is unsupervised dim. reduction but LDA is supervised dim. red. LDA is a particular case of canonical correlation analysis (CCA) which difference from PCA is explained in pics here. – ttnphns Mar 8 '17 at 7:36
• I wrote this comment without having read the article you link to, so I can't appreciate it anyhow. You might wish to search our site for LDA PCA, for more info. – ttnphns Mar 8 '17 at 7:38
• Here is an answer with some important further links in it. Also, search threads with tag discriminant-analysis. – ttnphns Mar 8 '17 at 7:47
• @ttnphns: I agree with the unsupervised and supervised differences. It is just that researchers in the specified domain (gait analysis) prefer the term MDA for all their work. They also often use CDA for gait recognition. I just wanted to be sure what the LDA in SciKit Learn is all about before using the term in my paper. – Ébe Isaac Mar 8 '17 at 7:48
• @amoeba: Thank you but I'm clear with that too. However, is it the same as MDA and is it synonymous with CDA as stated by ttnphns? – Ébe Isaac Mar 8 '17 at 7:54