Kernel functions are the functions that map one space to a higher dimensional space. This question...

 

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Kernel functions are the functions that map one space to a higher dimensional space. This question demon- strates the primary use of kernel functions in SVM. Consider four points: A = (1, 1), B = (2, 2), C = (2, 1), D = (1, 2) and two labels red, blue. Suppose A, B belong to the label red and C, D belong to the label blue. (a) Are labels red and blue linearly separable? Explain your reasoning in words with visualization. (b) Consider the kernel function: p(x) = (22, x x], x1 + x2) where x = (x1, x2). We can observe that this kernel function maps 2-dimensional space to 3-dimensional space. What are the points A, B, C, D after transformation? (c) Are labels red and blue linearly separable after the transformation? Explain your reasoning. Kernel functions are the functions that map one space to a higher dimensional space. This question demon- strates the primary use of kernel functions in SVM. Consider four points: A = (1, 1), B = (2, 2), C = (2, 1), D = (1, 2) and two labels red, blue. Suppose A, B belong to the label red and C, D belong to the label blue. (a) Are labels red and blue linearly separable? Explain your reasoning in words with visualization. (b) Consider the kernel function: p(x) = (22, x x], x1 + x2) where x = (x1, x2). We can observe that this kernel function maps 2-dimensional space to 3-dimensional space. What are the points A, B, C, D after transformation? (c) Are labels red and blue linearly separable after the transformation? Explain your reasoning.