(Solved): (a) Show that an SVM that employs the quadratic Kernel function, K(x,y)=xy ...

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(a) Show that an SVM that employs the quadratic Kernel function, $$K(\mathbf{x},\mathbf{y})={\mathbf{x}}^{?}\mathbf{y}$$, can successfully classify all the instances in a dataset with below four instances $$\left\{\left(\left(x_1=1,x_2=1\right),r=1\right),\left(\left(x_1=1,x_2=?1\right),r=?1\right),\left(\left(x_1=?1,x_2=1\right),r=?1\right),\left(\left(x_1=?1,x_2=?1\right),r=1\right)\right\}$$ (b) Consider the following two points in two-dimensional space: $$\left\{\left({\mathbf{x}}^1=\left(x_1^1=0,x_2^1=0\right),r^1=1\right),\left({\mathbf{x}}^2=\left(x_1^2=1,x_2^2=1\right),r^2=?1\right)\right\}$$ We can define a line equation as $${\mathbf{x}}^{?}\mathbf{w}+1=0$$, where $$\mathrm{w}$$ is a vector of length 2 . What $$\mathbf{w}$$ vector separates $${\mathbf{x}}^1$$ and $${\mathrm{x}}^2$$ with the largest margin?