Interpreting LD1 and LD2 in lda in R

Question

I'm conducting an experiment in R. I am using the rattle library that contains a sample of the wine related data.

Within this data, it sorts the wine into 3 types (1,2,3). That is, K = 3.

So did the following test within R:

test <- lda(Type ~ Malic+Ash , data=wine)

The result was as follows:

Call:
lda(Type ~ Malic + Ash, data = wine)
Prior probabilities of groups:
        1         2         3 
0.3314607 0.3988764 0.2696629 
Group means:
     Malic      Ash
1 2.010678 2.455593
2 1.932676 2.244789
3 3.333750 2.437083
Coefficients of linear discriminants:
             LD1        LD2
Malic -0.9992257  0.3702831
Ash   -1.0283229 -3.7678317
Proportion of trace:
   LD1    LD2 
0.7992 0.2008

My question is, what do LD1 and LD2 mean in practice?

Because by my understanding since K = 3, we should also have an LD3, because we would have three linear discriminant functions, and through these three functions we would classify new data.

These are the extracted discriminant functions. Their number is always min(number of variables, number of groups -1). — ttnphns, Jun 24 '15 at 13:45
Yes, let's assume that we have a new data (x *), as I use the LD1 and LD2 to decide which of the three categories it will be classified? — pedro.parreira, Jun 24 '15 at 14:29
Please see my reply about how discriminants classify objects to classes. — ttnphns, Jun 24 '15 at 15:27

Interpreting LD1 and LD2 in lda in R

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