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Paper detail

On the minimal teaching sets of two-dimensional threshold functions

It is known that a minimal teaching set of any threshold function on the twodimensional rectangular grid consists of 3 or 4 points. We derive exact formulae for the numbers of functions corresponding to these values and further refine them in the case of a minimal teaching set of size 3. We also prove that the average cardinality of the minimal teaching sets of threshold functions is asymptotically 7/2. We further present corollaries of these results concerning some special arrangements of lines in the plane.

preprint2014arXivOpen access
Max A. AlekseyevMarina G. BasovaNikolai Yu. Zolotykh
math.COMachine Learningmath.NT
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Max A. AlekseyevMarina G. BasovaNikolai Yu. Zolotykh

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