Applying Data Clustering Feature to Speed Up Ant Colony Optimization

Algorithm 1

Input parameters:

𝑇: Training Set

𝑚: The number of classes

𝜀: The stop threshold for clustering.

𝐶⁽⁰⁾={𝑐⁰_𝑖(1≤𝑖≤𝑚)}: Initial centroids set.

𝑝: A parameter to adjust the size of compact subs-ets 𝐾_𝑖^(𝑡)(𝑝≥0).

Output:

𝜑(𝑇)={𝐾₁^(𝑡),𝐾₂^(𝑡),…,𝐾_𝑖^(𝑡),…,𝐾_𝑚^(𝑡)} (i.e., the set of co-mpact subset, see Figure 1)

𝜎(𝑇)={𝐵₁^(𝑡),𝐵₂^(𝑡),…,𝐵_𝑖^(𝑡),…,𝐵_𝑚^(𝑡)}, where 𝐵_𝑖^(𝑡)=𝑅_𝑖^(𝑡)−𝐾_𝑖^(𝑡), and it is comprised by dispersive points

(1≤𝑖≤𝑚, see Figure 1)

Void Subroutine  1  (𝑇,𝑚,𝜀,𝐶⁽⁰⁾,𝑝,𝜑(𝑇),𝜎(𝑇))

{

Step  1. Initialization: Let iteration number 𝑡=0. Let 𝐶𝑜𝑢𝑛𝑡𝑒𝑟=𝑚. Let 𝜑(𝑇)=𝜙 and 𝜎(𝑇)=𝜙, where 𝜙

denotes empty set. According to initial centroids set 𝐶⁽⁰⁾, generate initial partition of training set

𝜑⁰={𝑅⁰_𝑖∣𝑅⁰_𝑖⊂𝑇,1≤𝑖≤𝑚}.

Step  2. While (𝐶𝑜𝑢𝑛𝑡𝑒𝑟>0){

 Step  2.1. Generate new centroids set 𝐶^(𝑡+1)={𝑐_𝑖^(𝑡+1)∣1≤𝑖≤𝑚} and new partition 𝜑^(𝑡+1)={𝑅_𝑖^(𝑡+1)∣1≤𝑖≤𝑚}

/* Note: Check whether entropy sequence {𝐻_𝑖⁽⁰⁾,𝐻_𝑖⁽¹⁾,…,𝐻_𝑖^(𝑡),𝐻_𝑖^(𝑡+1),…} is convergent. If it is convergent,

let the convergent marker StableMarker (𝑅_𝑖^(𝑡+1))=𝑇𝑟𝑢𝑒 */

 Step  2.2. For (𝑖=1;𝑖≤𝐶𝑜𝑢𝑛𝑡𝑒𝑟;𝑖++){

  Estimate the entropy of class 𝑅_𝑖^(𝑡+1), that is, 𝐻(𝑅_𝑖^(𝑡+1))=log₂𝑅_𝑖^(𝑡+1).

  If 𝐻𝑅_𝑖^(𝑡)−𝐻𝑅_𝑖^(𝑡+1)𝐻𝑅_𝑖^(𝑡)<𝜀 StableMarker𝑅_𝑖^(𝑡+1)=𝑇𝑟𝑢𝑒;

  Else StableMarker𝑅_𝑖^(𝑡+1)=𝐹𝑎𝑙𝑠𝑒

 }

/* Note: Extract the data around the centroid of class as a genuine class */

 Step  2.3. For (𝑖=1;𝑖≤𝐶𝑜𝑢𝑛𝑡𝑒𝑟;𝑖++){

  If StableMarker𝑅_𝑖^(𝑡+1)=𝑇𝑟𝑢𝑒{

  Calculate compact central region 𝐾_𝑖^(𝑡) according to formula (3)

  Calculate 𝐵_𝑖^(𝑡): 𝐵_𝑖^(𝑡)=𝑅_𝑖^(𝑡+1)−𝐾_𝑖^(𝑡)

  Let 𝜑(𝑇)=𝜑(𝑇)∪𝐾_𝑖^(𝑡)

  Let 𝜎(𝑇)=𝜎(𝑇)∪𝐵_𝑖^(𝑡)

  Update Training Set: 𝑇=𝑇−𝑅_𝑖^(𝑡)

  Update centroids set: 𝐶^(𝑡+1)=𝐶^(𝑡+1)−{𝑐_𝑖^(𝑡+1)}

   𝐶𝑜𝑢𝑛𝑡𝑒𝑟=𝐶𝑜𝑢𝑛𝑡𝑒𝑟−1

 }

 }

  𝑡=𝑡+1

 }

}