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I've read the answers in What are "coefficients of linear discriminants" in LDA?, but I still don't understand what coefficients of linear discriminants on output of R means.

What is it? (How) Is it related to the decision boundary?

nb: my knowledge about LDA can be summed up in this slide. 

library(ISLR, MASS)
train <- (Smarket$Year < 2005)
lda.fit <- lda(Direction ~ Lag1 + Lag2, data = Smarket, subset = train)    
Call:
lda(Direction ~ Lag1 + Lag2, data = Smarket, subset = train)

Prior probabilities of groups:
    Down       Up 
0.491984 0.508016 

Group means:
            Lag1        Lag2
Down  0.04279022  0.03389409
Up   -0.03954635 -0.03132544

Coefficients of linear discriminants:
            LD1
Lag1 -0.6420190
Lag2 -0.5135293
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  • http://stats.stackexchange.com/q/92109/3277 is similar question – ttnphns Apr 11 '14 at 07:59
  • @ttnphns Your answer:'"Coefficients" are the regressional weights to compute the LDs by the Xs.' Linear discriminant function based on the slide I gave above is: $\delta_k (x) = x^T \Sigma ^{-1} \mu_k - \frac{1}{2} \mu^T_k \Sigma ^{-1} \mu_k + \log(\pi_k)$ Do you mean the coefficients is $\Sigma ^{-1} \mu_k$ in this case? – hans-t Apr 11 '14 at 09:52
  • I didn't examine the presentation under your link. And I'm not agile to decipher formulas. I meant there (by the coefficients) what I've outlined in a description of LDA algorithm [here](http://stats.stackexchange.com/a/48859/3277). You might want to take _iris data_ and do LDA, and compare results with [my output](http://stats.stackexchange.com/a/83114/3277). – ttnphns Apr 11 '14 at 10:14
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    I believe that pdf doc you base yourself on is sure correct (and is quite mathematical). But I suspect it is for 2-class case only. The algorithm outlined by me ([extraction](http://stats.stackexchange.com/a/48859/3277), [classification](http://stats.stackexchange.com/a/31384/3277)) is general k-class LDA algorithm. – ttnphns Apr 11 '14 at 10:55

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