An Application of Classifier Combination Methods in Hand Gesture Recognition

Algorithm 4

The pseudocodes for DECORATE ensemble method.

● Input:

  ℒ: training set consisting of 𝑁 instances;

  𝒲: base learner whose output is assumed to be a class probability distribution;

  𝐶_size: desired ensemble size;

  𝐼_max: maximum number of iterations to construct an ensemble classifier;

  𝑅_size: a factor to determine number of artificial instances to generate.

● Training phase

   – Initialization:

    Let 𝑖=1 and trials=1;

    Provide the given training set ℒ as the input of base learner 𝒲 to get a classifier 𝐶_𝑖;

    Initialize ensemble set 𝐶^∗={𝐶_𝑖};

     – Compute ensemble error as

              𝜀=1𝑁^𝑁_𝑖∑₌₁𝐼(𝐶^∗(𝐱_𝑖)≠𝑦_𝑖).     (3)

  – While 𝑖<𝐶_size and trials<𝐼_max

    (1) Generate ⌊𝑅_size×𝑁⌋ training instances, ℛ, according to the distribution of training data;

     (2) Label each instance in ℛ with probabilities that each class label is selected

     being inversely proportional to those predicted by 𝐶^∗;

     (3) Combine ℒ with ℛ to get a new training set ℒ′;

     (4) Apply base learner 𝒲 to ℒ′ to obtain a new classifier 𝐶′;

      (5) Add 𝐶′ to ensemble set 𝐶^∗, namely, let 𝐶^∗=𝐶^∗∪{𝐶′};

      (6) Based on the training set ℒ, compute the ensemble error of 𝐶^∗, say,𝜀′, as

     that done in equation (3);

      (7) If 𝜀′≤𝜀, let 𝑖=𝑖+1 and update ensemble error as 𝜀=𝜀′; Otherwise,

    delete 𝐶′ from the ensemble set 𝐶^∗, that is, 𝐶^∗=𝐶^∗−{𝐶′};

     (8) trials=trials+1;

  – EndWhile

● Prediction phase

  – Let 𝑝_𝑖,𝑗(𝐱) be the probability that 𝐱 comes from class 𝑗 supported by the classifier 𝐶_𝑖.

  Calculate the confidence for each class by the mean combination rule, that is,

           𝑑_𝑗(𝐱)=1𝐿^𝐿_𝑖∑₌₁𝑝_𝑖,𝑗(𝐱),𝑗=1,2,…,𝐽,   (4)

  where 𝐿 stands for the real ensemble size.

  – Assign 𝐱 to the class with the largest confidence.