This question may seem too trivial but my basics are not strong and I shall appreciate help in these concepts.

For an n dimensional feature vector and 3 class problem does linear separability need to be checked?,

  1. I am familiar with XOR problem which cannot be modeled by neural network since the class is not linearly separable. What exactly do we mean by linearly separable? If the class boundary can be drawn as a curve and we can divide the patterns into 2 classes then can it be called linearly separable?

  2. How to decide if the classes are linearly separable?

  3. Does linear separability apply to more than 2 class problem? Say for 3 classes, how does one decide? Thank you.

  1. No. To be linearly separable, you have to able to separate data with a straight line for 2D, plane for 3D, etc: a1*x1+a2*x2+ ...an*xn = b is equation for nD. If you need a curve, then data is not linearly separable.
  2. With 2D or 3D feature vector - plot different classes with different colors and look at them :) For nD you can just try to separate them with linear SVM.
  3. Yes, the same story.
  • $\begingroup$ By linearly separable, we mean the features to be linearly separable or the class?Another question, which is not based on this and it shall be grateful if you can answer which will spare another question which is - In learning or training, using input-output pairs, what exactly are we learning?IS network learning the inputs or the outputs? $\endgroup$ – Ria George Jul 30 '14 at 3:47
  • $\begingroup$ Class, i.e. all points from class A intogether are linearly separable from class B. Network is learning the line (in general case, not straight), which separates classes. $\endgroup$ – old-ufo Jul 30 '14 at 5:33
  • $\begingroup$ SO, network is learning the decision boundary which means the classes? $\endgroup$ – Ria George Jul 30 '14 at 5:37
  • $\begingroup$ Yes. And if you have a deep network, the first layers learns feature transformation, which makes decision boundary simpler. $\endgroup$ – old-ufo Jul 30 '14 at 6:57

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