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In a recent exam on machine learning I came across the following question:

"Which of the following techniques can model the decision boundary depicted in the figure? (check all that apply)" See my self-made picture.

  • Logistic regression (with linear features)
  • Neural Networks
  • Naive Bayes
  • Support vector machine (with linear Kernel)

I was convinced the answer is Neural Networks and Naive Bayes. In particular Gaussian Naive Bayes can model circular decision boundaries (see an example here; it works, I also tried it myself).

However I have been told Naive Bayes was not rated as correct. Instead only neural nets was the correct answer.

How is this possible or is it a mistake?

enter image description here

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tomka
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  • Try SVM with Gaussian (RBF) Kernel or [single linkage](http://en.wikipedia.org/wiki/Single-linkage_clustering) [hierachical clustering](http://en.wikipedia.org/wiki/Hierarchical_clustering). The 2nd suggestion is from this [answer](http://stats.stackexchange.com/a/133694/40614). – Iliyan Bobev Oct 31 '16 at 19:27
  • This question seems perhaps more about the semantics of the test writer? My guess is there is supposed to be an implied "(with linear features)" after "Naive Bayes"? – GeoMatt22 Nov 01 '16 at 03:59
  • @GeoMatt22 okay, but there wasn't. – tomka Nov 01 '16 at 06:47
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    wow, I never knew GNB can do that, I thought it is just a dumber version of a common linear classifiers. Even in sklearn examples page it is shown to be able to classify this circular problem http://scikit-learn.org/stable/auto_examples/classification/plot_classifier_comparison.html#sphx-glr-auto-examples-classification-plot-classifier-comparison-py and the explanation in the link you provided is quite convincing. I would say you were right – rep_ho Nov 18 '16 at 21:55
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    @rep_ho yes, I had seen it somewhere and after the exam I went back to check it out. Turns out I was right in the end. – tomka Nov 18 '16 at 22:54
  • @GeoMatt22 I have been thinking about your comment. I do not think it is necessary to have the addition "with linear features" because even then GNB could still fit the circular bound. It does not need non-linear features because it classifies by a difference in variance of the two Gaussians. – tomka Nov 18 '16 at 22:55
  • @tomka Sorry, I had meant more like "Cartesian coordinate" features (i.e. $x,y$, vs. $r^2=x^2+y^2$). – GeoMatt22 Nov 19 '16 at 02:12

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