Calculating Entropy

Question

I've tried for several hours to calculate the Entropy and I know I'm missing something. Hopefully someone here can give me an idea!

EDIT: I think my formula is wrong!

CODE:

 info <- function(CLASS.FREQ){
      freq.class <- CLASS.FREQ
      info <- 0
      for(i in 1:length(freq.class)){
        if(freq.class[[i]] != 0){ # zero check in class
          entropy <- -sum(freq.class[[i]] * log2(freq.class[[i]]))  #I calculate the entropy for each class i here
        }else{ 
          entropy <- 0
        } 
        info <- info + entropy # sum up entropy from all classes
      }
      return(info)
    }

I hope my post is clear, since it's the first time I actually post here.

This is my dataset:

buys <- c("no", "no", "yes", "yes", "yes", "no", "yes", "no", "yes", "yes", "yes", "yes", "yes", "no")

credit <- c("fair", "excellent", "fair", "fair", "fair", "excellent", "excellent", "fair", "fair", "fair", "excellent", "excellent", "fair", "excellent")

student <- c("no", "no", "no","no", "yes", "yes", "yes", "no", "yes", "yes", "yes", "no", "yes", "no")

income <- c("high", "high", "high", "medium", "low", "low", "low", "medium", "low", "medium", "medium", "medium", "high", "medium")

age <- c(25, 27, 35, 41, 48, 42, 36, 29, 26, 45, 23, 33, 37, 44) # we change the age from categorical to numeric

Answer 1

Ultimately I find no error in your code as it runs without error. The part I think you are missing is the calculation of the class frequencies and you will get your answer. Quickly running through the different objects you provide I suspect you are looking at buys.

buys <- c("no", "no", "yes", "yes", "yes", "no", "yes", "no", "yes", "yes", "yes", "yes", "yes", "no")
freqs <- table(buys)/length(buys)
info(freqs)
[1] 0.940286

As a matter of improving your code, you can simplify this dramatically as you don't need a loop if you are provided a vector of class frequencies.

For example:

# calculate shannon-entropy
-sum(freqs * log2(freqs))
[1] 0.940286

As a side note, the function entropy.empirical is in the entropy package where you set the units to log2 allowing some more flexibility. Example:

entropy.empirical(freqs, unit="log2")
[1] 0.940286

Answer 2

There is an another way similar to above answer but using a different function.

> buys <- c("no", "no", "yes", "yes", "yes", "no", "yes", "no", "yes", "yes", "yes", "yes", "yes", "no")

> probabilities <- prop.table(table(buys))

> probabilities
buys
       no       yes 
0.3571429 0.6428571 

> -sum(probabilities*log2(probabilities))

[1] 0.940286

Also there is a built in function entropy.empirical(probabilities, unit = "log2")