How good can Nearest Neighbor, Naive Bayes and a Decision Tree classifier solve the given classification problem?

Question

The 3 diagramms (i), (ii), (iii) show training sets having 2 numerical attributes (x and y axis) and a target attribute with two classes (circle and square).

I am now wondering how good the data mining algorithms (Nearest Neighbor, Naive Bayes and Decision Tree) solve each of the classification problems.

I suppose that the Naive Bayes (with the naive assumption that the attributes are uncorrelated) solves the second problem better than (i) and (iii) because here the numerical attributes tend to be more independent from each other.

Answer 1

If you want to use each of given methods on such scenarios:

First one could be solved best with a decision tree approach cos classes can separate by axises. I mean draw a perpendicular line on x axis that separates values into left and right side and draw another line perpendicular on y axis so you will see that classes will be separated well.

Second one can be considered as a Naive Bayes problem as you mentioned.

Third one can be solved with k nearest neighborhood approach. Square classes are at near positions on coordinate system and circle classes can be classified with some error too.