A Novel Two-Stage Spectrum-Based Approach for Dimensionality Reduction: A Case Study on the Recognition of Handwritten Numerals

Algorithm 2

Two-stage dimensionality reduction procedure.

Extract most-used features (in literature) from input dataset, and Create initial features set Initial_𝑆;

𝑛∶= Number of features in initial features set Initial_𝑆;

first reduced version of feature vector 𝑆₁∶= null;

Stage 1:

 Choosing threshold 𝑇₁, by investigating 1D_MM spectrum diagrams.

 for (𝑘=1 : 𝑛)

 {

  Compute the coordinate of all 1D_SD spectrum lines corresponding to feature 𝑓_𝑘;

  for (𝑐=1 : number of classes)

  {

   If (overlapping of spectrum line of class 𝐜 with all the rest spectrum lines has the value less than threshold 𝑇₁) then

   {

     Insert feature 𝑓_𝑘 to 𝑆₁;

     goto  𝐿1;

   }

  }

 𝐿1: continue;

 }

𝑚∶= Number of features in first reduced version of features vector 𝑆₁;

final reduced versions of feature vectors 𝑆₂∶= null;

Stage 2:

 Choosing threshold  𝑇₂, by investigating 2D_MM spectrum diagrams.

 for (𝑘=1 : 𝑚)

    for (ℎ=1 : 𝑚)

    {

       Compute the coordinate of all 2D_SD spectrum ellipses corresponding to features pair (𝑓_𝑘, 𝑓_ℎ);

       for (𝑐=1 : number of classes)

       {

        if (overlapping of spectrum ellipses of class 𝐜 with all the rest spectrum ellipses has the value less than

        threshold 𝑇₂) then

       {

        Insert feature pair 𝑓_𝑘 and 𝑓_ℎ to 𝑆₂;

        goto  𝐿2;

       }

       }

    }

  𝐿2: continue;

 }

 delete the repetitive features from 𝑆₂;