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I'm trying to do this classification problem, depicted in the following Figure. The task is to separate the blue elements from the red elements in a cartesian (x,y) coordinate system. I have to:

● Find a transformation to map the 2D points in 3D points (by adding one component) that is able to make the data linearly separable.

● Make a graph (by hand) to show the transformed 3D space.

● Assuming that a Support Vector Machine (SVM) classifier is used to classify those points, add the separating hyperplane in the depicted plot.

● Explain how SVMs work. What are kernel functions?

● Explain the use of the C parameter in building a SVM model. What happens if C=0+ (a small positive value)? What happens if C=Infinite?

Figure

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    $\begingroup$ This looks like an assignment problem. What have you tried, where did you get stuck? $\endgroup$ – TYZ Mar 24 at 14:34
  • $\begingroup$ I have no idea which kernel and transformation i have to use to solve the problem $\endgroup$ – steph Mar 24 at 14:42
  • $\begingroup$ Can you give me an advice? $\endgroup$ – steph Mar 24 at 14:47
  • $\begingroup$ Someone have an idea or a tip? $\endgroup$ – steph Mar 24 at 15:22
  • $\begingroup$ You have studied SVM right? is there something you don't understand about it? $\endgroup$ – Erwan Mar 24 at 17:26
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@TYZ, @Erwan https://www.kdnuggets.com/2017/08/support-vector-machines-learning-svms-examples.html/2 Maybe here there's something useful, but I don't know how one could derive the transformation sqrt2 x1x2 without reading it somewhere

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  • $\begingroup$ Multiplying x1 and x2 to get x3 isn't a terribly complex transformation, and it's certainly not the only one that would work - absolute values are also handy here. Heck, you could define a piecewise function defined only over those 16 points which would work. $\endgroup$ – Nuclear Wang Mar 24 at 18:11

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