# Linear Discriminant Analysis vocabulary question

I am doing a descriptive LDA on a dataset with two (known, easily separable) classes and many features (and many more observations). I intend to use the latent variable values as a dimensionally-reduced quantitive index of where on the spectrum between the two classes each observation inhabits.

Would it be correct to describe this procedure as "The discriminant function obtained from a descriptive linear discriminant analysis was used as an index describing ...".

Or in other word, What is the difference between "latent variable" and "discriminant function" in this context.

Thank you.

## 1 Answer

Latent variable simply means a variable that is hidden, so is quite generic. The discriminant function is indeed latent, and is typically a weighted linear combination of other latent variables, where the weights are optimised for classification.

Your quote is not appropriate though, you do not use the function as an index. Rather you use it to calculate a classification score, which can be used for indexing.

• Thank you. In my case, the classification scores are binary (the classes are perfect separable), and for my-two class case there is only one discriminant function. As I am seeking a quantitative index of how much each observation belongs to one class, is the using the discriminant function not appropriate? Feb 19, 2019 at 20:02
• You would use the scores calculated by applying the function to the data. If you have o observations and v variables then your function is a vector of length v, while your scores will be a vector of length o. This means that the scores (or can be transformed to probabilities of group membership) give the index you would use to assess distribution . This is often explored using ROC curve and a range of other metrics. Feb 19, 2019 at 20:13
• Ah, I have done exactly what you describe (without transforming to group membership probability) , but I didn't know what to call them, having only seen LDA "classification scores" expressed as probabilities. So the "discriminant function" is essentially the list of weights and the (raw) "classification score" is the value for each observation yielded by applying them. Thank you. Feb 19, 2019 at 20:22