An Application of Classifier Combination Methods in Hand Gesture Recognition

Algorithm 3

The detailed steps of rotation forest method.

● Input

  A training set ℒ={(𝐱_𝑖,𝑦_𝑖)}^𝑁𝑖=1=[𝐗𝐘]; Number of input features 𝑀 contained in each feature

   subset; A base learner 𝒲; Number of iterations 𝑇; A new data point 𝐱 to be classified.

● Training Phase

  For 𝑡=1,2,…,𝑇

  – Calculate the rotation matrix 𝐑^𝑎𝑡 for the 𝑡th classifier 𝐶_𝑡

    (1) Randomly split the feature set 𝐹={𝑋₁,𝑋₂,…,𝑋_𝑝} into 𝐾 subsets 𝐹_𝑡,𝑘(𝑘=1,2,…,𝐾).

    (2) For 𝑘=1,2,…,𝐾

      (a) Select the columns of 𝐗 that correspond to the attributes in 𝐹_𝑡,𝑘 to compose a

      submatrix 𝐗_𝑡,𝑘.

       (b) Draw a bootstrap sample 𝐗^𝑡,𝑘 (with sample size smaller than that of 𝐗_𝑡,𝑘,

     generally taken to be 75%) from 𝐗_𝑡,𝑘.

      (c) Apply PCA to 𝐗^𝑡,𝑘 to obtain a matrix 𝐃_𝑡,𝑘 whose 𝑖th column consists of the

      coefficients of the 𝑖th principal component.

     (3) EndFor

     (4) Arrange the matrices 𝐃_𝑡,𝑘(𝑘=1,2,…,𝐾) into a block diagonal matrix 𝐑_𝑡.

     (5) Construct the rotation matrix 𝐑^𝑎𝑡 by rearranging the rows of 𝐑_𝑡 so that

     they correspond to the original features in 𝐹.

  – Provide [𝐗𝐑^𝑎𝑡𝐘] as the input of 𝒲 to build a classifier 𝐶_𝑡.

  EndFor

● Output

  – The class label for 𝐱 predicted by the ensemble classifier 𝐶^∗ as

             𝐶^∗(𝐱)=argmax_{𝑇𝑦∈Φ}∑_𝑡=1𝐼(𝐶_𝑡(𝐱𝐑^𝑎𝑡)=𝑦).