title: Support Vector Machines
body: <p>I had these questions in an exam today. State True or False and explain.</p>
  
  <ol>
  <li><p>If k<sub>1</sub>(.,.) and k<sub>2</sub>(.,.) are two valid kernel functions, then if h = k<sub>1</sub> - k<sub>2</sub>, is h(.,.) a valid kernel function?</p></li>
  <li><p>A standard soft margin SVM is used to classify data set. We have a fixed C parameter. Two different algorithms A<sub>1</sub> and A<sub>2</sub> are used to obtain the support vector set {S: 
  &#945;
  <sub>i</sub> > 0}. Call them S1 and S2. Is S1 = S2 in all cases? Assume both algorithm use the same kernel function.</p></li>
  </ol>
  
  <p>EDITED:</p>
  
  <p>I guessed as: </p>
  
  <ol>
  <li><p>As kernel function need to be positive semi definite (PSD), the difference between two kernel functions need not be PSD. Hence FALSE. </p></li>
  <li><p>α<sub>i</sub> can be different among the two algorithms, the number of support vectors can differ as well. Hence FALSE again.</p></li>
  </ol>