Mathematical Problems in Engineering

Research Article

An Application of Classifier Combination Methods in Hand Gesture Recognition

Algorithm 2

The main steps for the AdaBoost algorithm.
● Input
  A training set β„’ = { ( 𝐱 𝑖 , 𝑦 𝑖 ) } 𝑁 𝑖 = 1 ; A base learner 𝒲 ; Number of iterations 𝑇 ; A new data point 𝐱
  to be classified.
● Training Phase
  Initialization: Set the weight distribution over β„’ as 𝐷 1 ( 𝑖 ) = 1 / 𝑁 ( 𝑖 = 1 , 2 , … , 𝑁 ) .
  For 𝑑 = 1 , … , 𝑇
  (1) According to the distribution 𝐷 𝑑 , draw 𝑁 training instances at random from β„’ with
   replacement to compose a new set β„’ 𝑑 = { ( 𝐱 𝑖 ( 𝑑 ) , 𝑦 𝑖 ( 𝑑 ) ) } 𝑁 𝑖 = 1 .
  (2) Provide β„’ 𝑑 as the input of 𝒲 to train a classifier 𝐢 𝑑 , and then compute the weighted
   training error of 𝐢 𝑑 as            
          πœ€ 𝑑 = P r 𝑖 ∼ 𝐷 𝑑 ( 𝐢 𝑑 ( 𝐱 𝑖 ) β‰  𝑦 𝑖 ) = 𝑁 βˆ‘ 𝑖 = 1 𝐼 ( 𝐢 𝑑 ( 𝐱 𝑖 ) β‰  𝑦 𝑖 ) 𝐷 𝑑 ( 𝑖 ) ,     (1)
   where 𝐼 ( β‹… ) takes value 1 or 0 depending on whether the 𝑖 th training instance is
   misclassified or by 𝐢 𝑑 or not.
  (3) If πœ€ 𝑑 > 0 . 5 or πœ€ 𝑑 = 0 , then set 𝑇 = 𝑑 βˆ’ 1 and abort loop.
  (4) Let 𝛼 𝑑 = ( 1 / 2 ) l n ( ( 1 βˆ’ πœ€ 𝑑 ) / πœ€ 𝑑 ).
  (5) Update the weight distribution 𝐷 𝑑 over β„’ as
             𝐷 𝑑 + 1 𝐷 ( 𝑖 ) = 𝑑 ( 𝑖 ) 𝑍 𝑑 Γ— ⎧ βŽͺ ⎨ βŽͺ ⎩ 𝑒 βˆ’ 𝛼 𝑑 , i f 𝐢 𝑑 ( 𝐱 𝑖 ) = 𝑦 𝑖 𝑒 𝛼 𝑑 , i f 𝐢 𝑑 ( 𝐱 𝑖 ) β‰  𝑦 𝑖 ,   (2)
   where 𝑍 𝑑 is a normalization factor being chosen so that 𝐷 𝑑 + 1 is a probability
   distribution over β„’ .
  Endfor
● Output
  – The class label for 𝐱 predicted by the ensemble classifier 𝐢 βˆ— as
              𝐢 βˆ— ( 𝐱 ) = a r g m a x 𝑇 𝑦 ∈ Ξ¦ βˆ‘ 𝑑 = 1 𝛼 𝑑 𝐼 ( 𝐢 𝑑 ( 𝐱 ) = 𝑦 ) .