I am not sure how to find the coefficients of hyperplane. Could you please help me to understand the concept.
Consider a data set with two independent variables, say X1 and X2, and one dependent binary variable, Y, with two class labels denoted by +1 and -1. The data set is plotted along with a separating hyperplane (h) in the figure below.
the following two constraints determine the equation of the maximal margin classifier:
With the above information, answer the questions below.
What are the coefficients of the hyperplane given above? A. W0 =0, W1=1, W2=0 B. W0 =1, W1=1, W2=1 C. W0 =0, W1 = 1/Sqrt2, W2= -1/Sqrt2 D. W0 =1, W1=0, W2=0
If you compare the given hyperplane X1 = X2 with the general equation of 2D hyperplane i.e W0+W1∗X1+W2∗X2=0, you will notice that the given hyper plane can also be written as X1-X2 = 0. Now if you compare it with the general form of equation, you will get W0=0, W1 = 1 and W2 = -1. Imposing the condition that the weights should form a unit vector, i.e. the squares of W1 and W2 should add to 1, W1 = 1/sqrt(2) and W2 = -1/sqrt(2).