Incremental Optimization Mechanism for Constructing a Decision Tree in Data Stream Mining

Pseudocode 3

Pseudocode of training approach.

PROCEDURE doNodeSplitting (Δ𝐶, 𝑆, 𝑋, 𝐻(⋅), 𝛿):

(1)     FOR each attribute 𝑋_𝑖∈𝑋_𝑙−{𝑋_∅} at the leaf  𝑙

(2)         Compute 𝐻_𝑙𝑋_𝑖

(3)         Let 𝑋_𝑎 be the attribute with highest 𝐻_𝑙(⋅) and 𝑋_𝑎 the second

(4)         Compute HB with 𝛿

(5)         Let Δ𝐻_𝑙=𝐻_𝑙𝑋_𝑎−𝐻_𝑙𝑋_𝑏

(6)     END-FOR

(7)     IF (Δ𝐻_𝑙>𝐻𝐵) or (Δ𝐻_𝑙≤𝑇^LOWER_𝑙 and Δ𝐶_𝑖<Δ𝐶_𝑖−1)

       or (Δ𝐻_𝑙≤𝑇^LOWER_𝑙 and Δ𝐶_𝑖<0)

       or (𝑇^LOWER_𝑙<Δ𝐻_𝑙≤𝑇^UPPER_𝑙 and Δ𝐶_𝑖<Δ𝐶_𝑖−1)

(8)          Replace 𝑙 by an internal node splits on 𝑋_𝑎

(9)          Update adaptive tie 𝑇^LOWER_𝑙 and 𝑇^UPPER_𝑙

(10)        FOR each branch of splitting

(11)  Add a new leaf  𝑙_𝑚 and let 𝑋_𝑚=𝑋−{𝑋_𝑎}

(12)  Let 𝐻_𝑙𝑋_∅ be the 𝐻_𝑙(⋅) obtained by predicting the class in 𝑆

        according to ℱ at  𝑙_𝑚

(13)  FOR each class 𝑦_𝑘 and each value 𝑥_𝑖𝑗 of each attribute

(14)  𝑋_𝑖∈𝑋_𝑚−𝑋_∅ and reset OCD: 𝑛_𝑖𝑗𝑘𝑙_𝑚=0

(15)  END-FOR

(16)      END-FOR

(17) END-IF

(18) Return updated HT