Conditional Random Fields and Supervised Learning in Automated Skin Lesion Diagnosis

Algorithm 1

Calculating the CRF parameter vector 𝑤 using gradient descent and saddle-point approximation.

Require:  𝑥,𝑦,𝑤⁰,𝜎²>0,𝛾<0,𝜖>0,𝑁_𝑖𝑡𝑟>0

  max←0  

  for   𝑖←1  to  𝑁_itr  do

   𝑔^𝑖←0

   𝑎←0

   for   𝑚←1  to  𝑁_𝐼  do

    𝑦^∗←argmax_𝑦𝑃(𝑦∣𝑥^𝑚;𝑤^𝑖−1)

    𝑎←𝑎+accuracy(𝑦^∗,𝑦^𝑚)/𝑁_𝐼

    𝑔^𝑖←𝑔^𝑖+Φ(𝑦^𝑚,𝑥^𝑚)−Φ(𝑦^∗,𝑥^𝑚)−𝑤^𝑖−1/(𝑁_𝐼𝜎²)  

   end  for

   if   𝑎>max  then

    max←𝑎  

      𝑤^∗←𝑤^𝑖−1

   end  if

   𝑤^𝑖←𝑤^𝑖−1+𝛾𝑔^𝑖  

   for  all   𝑗∈𝔼  do

    if  𝑤^𝑖_𝑗<0  then

     𝑤^𝑖_𝑗←0  

    end  if

   end  for

   if   ‖𝑤^𝑖−𝑤^𝑖−1‖<𝜖  then

    break

   end  if

  end  for

  return  𝑤^∗