ML – Candidate Elimination Algorithm

The candidate elimination algorithm incrementally builds the version space given a hypothesis space H and a set E of examples. The examples are added one by one; each example possibly shrinks the version space by removing the hypotheses that are inconsistent with the example. The candidate elimination algorithm does this by updating the general and specific boundary for each new example. 

  • You can consider this as an extended form of Find-S algorithm.
  • Consider both positive and negative examples.
  • Actually, positive examples are used here as Find-S algorithm (Basically they are generalizing from the specification).
  • While the negative example is specified from generalize form.

Terms Used:  

  • Concept learning: Concept learning is basically learning task of the machine (Learn by Train data)
  • General Hypothesis: Not Specifying features to learn the machine.
  • G = {‘?’, ‘?’,’?’,’?’…}: Number of attributes
  • Specific Hypothesis: Specifying features to learn machine (Specific feature)
  • S= {‘pi’,’pi’,’pi’…}: Number of pi depends on number of attributes.
  • Version Space: It is intermediate of general hypothesis and Specific hypothesis. It not only just written one hypothesis but a set of all possible hypothesis based on training data-set.

Algorithm:

Step1: Load Data set
Step2: Initialize General Hypothesis  and Specific  Hypothesis.
Step3: For each training example  
Step4: If example is positive example  
          if attribute_value == hypothesis_value:
             Do nothing  
          else:
             replace attribute value with '?' (Basically generalizing it)
Step5: If example is Negative example  
          Make generalize hypothesis more specific.


Example:

Consider the dataset given below:

Algorithmic steps:

Initially : G = [[?, ?, ?, ?, ?, ?], [?, ?, ?, ?, ?, ?], [?, ?, ?, ?, ?, ?], 
                 [?, ?, ?, ?, ?, ?], [?, ?, ?, ?, ?, ?], [?, ?, ?, ?, ?, ?]]
            S = [Null, Null, Null, Null, Null, Null]
            
For instance 1 : <'sunny','warm','normal','strong','warm ','same'> and positive output.
            G1 = G
            S1 = ['sunny','warm','normal','strong','warm ','same']
            
For instance 2 : <'sunny','warm','high','strong','warm ','same'> and positive output.
            G2 = G
            S2 = ['sunny','warm',?,'strong','warm ','same']
            
For instance 3 : <'rainy','cold','high','strong','warm ','change'> and negative output.
            G3 = [['sunny', ?, ?, ?, ?, ?], [?, 'warm', ?, ?, ?, ?], [?, ?, ?, ?, ?, ?], 
                  [?, ?, ?, ?, ?, ?], [?, ?, ?, ?, ?, ?], [?, ?, ?, ?, ?, 'change']]
            S3 = S2     
            
For instance 4 : <'sunny','warm','high','strong','cool','change'> and positive output.
            G4 = G3
            S4 = ['sunny','warm',?,'strong', ?, ?]       
  
At last, by synchronizing  the G4 and S4 algorithm produce the output.

Output :

G = [['sunny', ?, ?, ?, ?, ?], [?, 'warm', ?, ?, ?, ?]]
S = ['sunny','warm',?,'strong', ?, ?] 
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