# Looking for good, recent examples of Discriminant Analysis (Linear, Quadratic or else) in applied research

We have looked at LDA/QDA several times during my stats masters coursework, but I'm not convinced that it's due to the usefulness of the techniques more than my school being stuck with a 20-year old curriculum.

This answer by Frank Harrell suggests that these techniques aren't very useful nowadays, and even the textbook we're using indicates that LDA/QDA is only expected to perform significantly better than logistic regression when the assumptions are met, which seems fairly disqualifying for most purposes.

To make my title request more specific, I'm looking for at least two different examples (i.e. not the same type of problem, preferably different disciplines) that are

• Good: clearly the most optimal tool to solve the problem at hand, not just being used in place of logistic regression because of researcher preference

• Recent: published in the last six years

• "... or else": need not be textbook LDA/QDA. It's okay if the technique is an extension of the above models, but it should obviously follow the same reasoning i.e. related to a decision rule based on distributional assumptions on predictors conditional to the outcome of interest

Alternatively, it would also be acceptable if someone can provide proof that any formulation of a discriminant-type model can be re-expressed as a regression problem (e.g. linear regression produces results equivalent to LDA).

I am using LDA for neuroscience research. Traditionally in neuroscience people "analyze one neuron at a time" and use the measures of all the sampled neurons to test statistical significance.

In recent years population-level analysis is gaining its attention. Especially for high level cognition, single neuron usually does not have a one-on-one relation to behavior. By building a classifier on the neuronal population, one can get insight on how information is encoded in the brain.

LDA, albeit simple, has advantages for my and most neuroscience projects. (some are specific to the comparison to LR, some are not)

1. comparing to logistic regression, most importantly it's easier to classify more than 2 classes with LDA.

2. usually in neuroscience datasets are high dimensional low sample size. As a linear classifier, LDA fits relatively less parameters. Fancier classifiers may lead to overfitting. LR seems also to perform worse in this case.

3. LDA is simple to understand and to interpret. In neuroscience, performance is not all that matters. The rationale is to micmic living brain and to understand it. Thus LDA is suitable, textbook LDA is even the best. In multi class situation, classes in LDA are interpreted as the clusters in discriminant space.

4. Analogy can be drawn between LDA and neurobiology. LDA, assuming identical covariance matrix for each class, use linear combination as discriminant axes, which is feasible biologically and is usually how theoretical neuroscientists assume the neural network to work.

5. LDA is also a dimensionality reduction algorithm, which is extremely useful to neuroscience, of which the principle is to compress the over-complicated biological data and make understandable visualization...

there is also a good thread here: Logistic regression vs. LDA as two-class classifiers

One recent paper that used LDA for neuroscience. https://doi.org/10.1038/s41593-017-0003-2

A book chapter on patter classification in neuroscience. It compares a dozen of decoders for the purpose of neuroscience. http://klab.tch.harvard.edu/publications/PDFs/8404_019.pdf

• +1 I like the way you refer to domain specific examples - cool answer welcome to SE Jul 10, 2018 at 10:24
• Thanks for the answer! Please link to a specific paper or review that shows the technique being applied as you describe and I will accept this. Jul 10, 2018 at 19:44
• 2 links updated. hope it's useful to you. Jul 12, 2018 at 7:47
• +1 Nice detailed answer. Domain-specific examples reveal new insights, always helpful Mar 12, 2021 at 17:16