Question

We decide to run the kernel perceptron algorithm over this dataset using the quadratic kernel. The number of mistakes made on each point is displayed in the table below. (These points correspond to those in the plot above.)

Label -1 -1 -1 -1 -1 +1 +1 +1 +1 +1
Coordinates (0,0) (2,0) (1,1) (0,2) (3,3) (4,1) (5,2) (1,4) (4,4) (5,5)
Perceptron mistakes 1 65 11 31 72 30 0 21 4 15
Define the feature map of our quadratic kernel to be:


Assume all parameters are set to zero before running the algorithm.

Based on the table, what is the output of theta and theta_0 ?

Answer 1

It is not possible to determine the output of theta and theta_0 based solely on the table of mistakes made during the kernel perceptron algorithm. Further information about the algorithm and the specific values of the feature map for each data point would be needed to calculate the final values of theta and theta_0.