title: Issues in Convergence of Sequential minimal optimization for SVM
body: <p>I have been working on Support Vector Machine for about 2 months now. I have coded SVM myself and for the optimization problem of SVM, I have used Sequential Minimal Optimization(SMO) by Dr. John Platt.</p>
  
  <p>Right now I am in the phase where I am going to grid search to find optimal C value for my dataset. ( Please find details of my project application and dataset details here <a href="https://stackoverflow.com/questions/2284059/svm-classification-minimum-number-of-input-sets-for-each-class">SVM Classification - minimum number of input sets for each class</a>) </p>
  
  <p>I have successfully checked my custom implemented SVM`s accuracy for C values ranging from 2^0 to 2^6. But now I am having some issues regarding the convergence of the SMO for C> 128.
  Like I have tried to find the alpha values for C=128 and it is taking long time before it actually converges and successfully gives alpha values.</p>
  
  <p>Time taken for the SMO to converge is about 5 hours for C=100. This huge I think ( because SMO is supposed to be fast. ) though I`m getting good accuracy?
  I am screwed right not because I can not test the accuracy for higher values of C.</p>
  
  <p>I am actually displaying number of alphas changed in every pass of SMO and getting 10, 13, 8... alphas changing continuously. The KKT conditions assures convergence so what is so weird happening here?</p>
  
  <p>Please note that my implementation is working fine for C&lt;=100 with good accuracy though the execution time is long. </p>
  
  <p>Please give me inputs on this issue.</p>
  
  <p>Thank You and Cheers. </p>