title: Under what parameters are SVC and LinearSVC in scikit-learn equivalent?
body: <p>I read <a href="https://stackoverflow.com/questions/27912872/what-is-the-difference-between-svc-and-svm-in-scikit-learn">this thread</a> about the difference between <code>SVC()</code> and <code>LinearSVC()</code> in scikit-learn. </p>
  
  <p>Now I have a data set of binary classification problem(For such a problem, the one-to-one/one-to-rest strategy difference between both functions could be ignore.)</p>
  
  <p>I want to try under what parameters would these 2 functions give me the same result. First of all, of course, we should set <code>kernel='linear'</code> for <code>SVC()</code>
  However, I just could not get the same result from both functions. I could not find the answer from the documents, could anybody help me to find the equivalent parameter set I am looking for?</p>
  
  <p>Updated:
  I modified the following code from an example of the scikit-learn website, and apparently they are not the same:</p>
  
  <pre><code>import numpy as np
  import matplotlib.pyplot as plt
  from sklearn import svm, datasets
  
  # import some data to play with
  iris = datasets.load_iris()
  X = iris.data[:, :2]  # we only take the first two features. We could
                        # avoid this ugly slicing by using a two-dim dataset
  y = iris.target
  
  for i in range(len(y)):
      if (y[i]==2):
          y[i] = 1
  
  h = .02  # step size in the mesh
  
  # we create an instance of SVM and fit out data. We do not scale our
  # data since we want to plot the support vectors
  C = 1.0  # SVM regularization parameter
  svc = svm.SVC(kernel='linear', C=C).fit(X, y)
  lin_svc = svm.LinearSVC(C=C, dual = True, loss = 'hinge').fit(X, y)
  
  # create a mesh to plot in
  x_min, x_max = X[:, 0].min() - 1, X[:, 0].max() + 1
  y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1
  xx, yy = np.meshgrid(np.arange(x_min, x_max, h),
                       np.arange(y_min, y_max, h))
  
  # title for the plots
  titles = ['SVC with linear kernel',
            'LinearSVC (linear kernel)']
  
  for i, clf in enumerate((svc, lin_svc)):
      # Plot the decision boundary. For that, we will assign a color to each
      # point in the mesh [x_min, m_max]x[y_min, y_max].
      plt.subplot(1, 2, i + 1)
      plt.subplots_adjust(wspace=0.4, hspace=0.4)
  
      Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])
  
      # Put the result into a color plot
      Z = Z.reshape(xx.shape)
      plt.contourf(xx, yy, Z, cmap=plt.cm.Paired, alpha=0.8)
  
      # Plot also the training points
      plt.scatter(X[:, 0], X[:, 1], c=y, cmap=plt.cm.Paired)
      plt.xlabel('Sepal length')
      plt.ylabel('Sepal width')
      plt.xlim(xx.min(), xx.max())
      plt.ylim(yy.min(), yy.max())
      plt.xticks(())
      plt.yticks(())
      plt.title(titles[i])
  
  plt.show()
  </code></pre>
  
  <p>Result:
  <a href="https://i.stack.imgur.com/ZaX5M.png" rel="noreferrer">Output Figure from previous code</a></p>