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I was reading Chapter 4 (LDA) of the book Introduction to Statistical learning with R (http://www-bcf.usc.edu/~gareth/ISL/ISLR%20Sixth%20Printing.pdf) and could not understand the "coefficients of linear discriminants" part in the output of the lda() function from the MASS package.

The example code is on page 161.
Specifically, my questions are:

  1. How does function lda() choose the reference group? In the example, the $Y$ variable has 2 groups: "Up" and "Down". Is it that group "Down" would be automatically chosen as the reference group according to the alphabetical order?

  2. I don't understand what the "coefficients of linear discriminants" are for and which group the "LD1" represents, "Down" or "Up": enter image description here

On page 143 of the book, discriminant function formula (4.19) has 3 terms: enter image description here

So my guess is that the coefficients of linear discriminants themselves don't yield the $\delta_k(x)$ directly. So is there any command that can calculate the $\delta_k(x)$?

  1. Why are there at most $K-1$ groups of coefficients of linear discriminants and what's the relationship between the coefficients among different groups?
ttnphns
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conamore
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    Conamore, please take a tour of this site over tag [discriminant-analysis]. You will find answers (including mine) which explain your points: what are discriminant coefficients, what are Fisher's classification functions in LDA, how LDA is equivalent to canonical correlation analysis with k-1 dummies. – ttnphns Jan 13 '17 at 10:05
  • I don't understand what the "coefficients of linear discriminants" are for and which group the "LD1" represents LD1 is the discriminant function which discriminates the classes. The coefficients are the weights whereby the variables compose this function. – ttnphns Jan 13 '17 at 10:08

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