Département de Mathématiques et Informatique

1. Construct our decision tree model:
   1. Extract rules and calculate their information gain:  
      • Gender :

• • • • gender = male => p = 5/8, E(gender=male) = - (1/5) log2(1/5) - (1/5)log2(1/5) - (3/5)log2(3/5) = 1.3710
      • gender = female =>  p= 3/8, E(gender=female) = -1/3 log2(1/3) - 1/3 log(1/3) - 1/3 log(1/3) = 1.5850
      • E(Parent) = -4/8 log2(4/8) - 1/8 log2(1/8) - 2/8 log2(2/8) -1/8log2(1/8) = 1.75
      • Information Gain(Gender) = 1.75 - ((5/8*1.3710)+(3/8*1.5750)) = 0.3025
    • Edu level:
      • EL = Bachelor => p = 3/8, E(EL=Bachelor) = -1/3 log2(1/3) - 2/3log2(2/3) = 0.9183
      • EL = Master => p= 4/8, E(EL=Master) = -1/4 log2(1/4) -2/4 log2(2/4) - 1/4 log2(1/4) = 1.5
      • EL = Doctorate => 1/8 E(EL= doctorate) = 0
      • E(Parnet) = 1.75
      • Information Gain = 1.75 - (3/8*0.9183+4/8*1.5+1/8*0) = 0.6556
    • Marital:
      • Marital = Single => p=2/8, E(M=S) = -1/2 log2(1/2) - 1/2 log2(1/2) = 1
      • Marital = Married => p=4/8, E(M=Married) = -1/4log2(1/4)*4= 2
      • Marital = Divorced => p= 2/8, E(M=Divorced) = 0
      • E(Parent) = 1.75
      • Information Gain = 1.75 - (2/8*1+4/8*2+2/8*0)  = 0.50

First feautre that give us the highest value of information gain is Marital:So the first node in our tree is Marital:                             If( marital = Divorced ) The performance is always Good :(so the decision tree should look like this):

If (marital = Married) we calculate the other two feautres's information gain:

1. 1. 1. Marital = Married => 4 rows:
         • Gender :
           
           • G = Male => P = 3/4, e(G=male) = -1/3 log2(1/3) * 3 = 1.5850
           • G = Female => p = 1/4 e(G=Female) = 0
           • E(Parent) = E(Marital=Married) = 2
           • Information Gain = 2-(3/4*1.5850 + 1/4*0) = 0.8113
         • Education Level :
           • EL = Master => p = 2/4, E(EL=master) = 1
           • EL = Doctorate =>p=1/4, E(EL=Doctorate) = 0
           • EL = Bachelor => p=1/4, E(EL=Bachelor) = 0
           • E(Parent ) = E(Marital=Married) = 2
           • Information Gain = 2- (2/4*1+1/4*0+1/4*0) = 1.5

• • • • The Education level features has the highest value so our Tree should be like this:

If (marital = Single) we calculate the other two feautres's information gain:

• P(Marital = Single ) = 2
  • • Gender:
      • Gender = Male-> p= 1/2, E(Gender=Male) =0
      • Gender = Female -> p = 1/2 , E(Gender = Female ) = 0
      • E(Parent) = E(Marital=Single) = 1
      • Information Gain = 1-0 = 1
    • Education Level
      • EL = Bachelor => p= 1/2, E = 0
      • EL = Master=> p= 1/2, E = 0
      • Information Gain = 1-0 = 1
  • As we see they both have the same information gain so the rank doesn't matter so we draw our tree:

• • If Marital = Married And Education Level = Bachelor -> The performance is always = Low
  • If Marital = Married And Education Level = Master ->
    • if gender = Male => The performance = Normal
    • if gender = Female=> The performance = Bad
  • If Marital = Married And Education Level = Doctorate -> The performance is Good

our tree should look like this:

For the last node (Marital = Single) :

• if ( EL= Bachelor) or (Gender = Male) Performance = Good
• if(El = master) or (Gender = Female) Performance = Normal

Final Decition tree :

    II. Parse the new data into the decistion tree model:

1. 1. Ahmed:
      • Marital = Divorced ===> Performance = Good (based on the training data)
   2. Amel:
      • Marital = Single ----> Gender = Female =====> Performance = Normal

So Ahmed is the suitable candidate to recruit.

ahmed is good

amel is good