Question

Generate 2000 points from two equally weighted sphericalGaussiansN(0, I), N((3,0, . . . ,0), I) inRp,p= 1,11,21, . . .101 (note, youhave to first flip a coin to decide from which Gaussian to sample), whereIis the identity matrix and the centers of Gaussians are distance 3 apart.Implement 1-NN and 3-NN classifiers. Test the resulting classifier on aseparately generated dataset with 1000 pts. Plot the error rate as a functionofp. Observations?

Answer 1

Answer:

struct SG

{

   float3 Amplitude;

   float3 Axis;

   float Sharpness;

};

float3 EvaluateSG(in SG sg, in float3 dir)

{

   float cosAngle = dot(dir, sg.Axis);

   return sg.Amplitude * exp(sg.Sharpness * (cosAngle - 1.0f));

}

SG SGProduct(in SG x, in SG y)

{

   float3 um = (x.Sharpness * x.Axis + y.Sharpness * y.Axis) /

               (x.Sharpness + y.Sharpness);

   float umLength = length(um);

   float lm = x.Sharpness + y.Sharpness;

   SG res;

   res.Axis = um * (1.0f / umLength);

   res.Sharpness = lm * umLength;

   res.Amplitude = x.Amplitude * y.Amplitude *

                   exp(lm * (umLength - 1.0f));

   return res;

}