title: SVM in Matlab: Meaning of Parameter 'box constraint' in function fitcsvm
body: <p>I'm new to SVMs in Matlab and need a little bit of help with it.</p>
  <p>I want to train a support vector machine using the build in function fitcsvm of the Statistics Toolbox.
  Of course there are many parameter choices which control how the SVM will be trained.</p>
  <p>The Matlab help is a litte bit wage about how the parameters archive a better training result. Especially the parameter <strong>'Box Contraint'</strong> seems to have an important influence on the number of chosen support vectors and generalization quality.</p>
  <p>The Help (<a href="http://de.mathworks.com/help/stats/fitcsvm.html#bt8v_z4-1" rel="noreferrer">http://de.mathworks.com/help/stats/fitcsvm.html#bt8v_z4-1</a>) says</p>
  <blockquote>
  <p>A parameter that controls the maximum penalty imposed on margin-violating observations, and aids in preventing overfitting (regularization).</p>
  <p>If you increase the box constraint, then the SVM classifier assigns fewer support vectors. However, increasing the box constraint can lead to longer training times.</p>
  </blockquote>
  <p>How exactly is this parameter used?
  Is it the same or something like the soft margin factor C in <a href="https://en.wikipedia.org/wiki/Support_vector_machine#Soft_margin" rel="noreferrer">the Wikipedia</a> reference?
  Or something completely different?</p>
  <p>Thanks for your help.</p>