1. SVM. Consider a supervised learning problem in which the training examples are points in 2-dimensional...

 

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1. SVM. Consider a supervised learning problem in which the training examples are points in 2-dimensional space. The positive examples (samples in class 1) are (1, 1) and (-1,-1). The negative examples (samples in class 0) are (1,-1) and (-1, 1). Are the positive examples linearly separable from the negative examples in the original space? If so, give the coefficients of w. 0 -1 + 0 1. For the example above, consider the feature transformation p(x) = [1, x₁, x2, ₁2], where ₁ and ₂ are, respectively, the first and second coordinates of a generic example x. Can we find a hyperplance wTo(x) in this feature space that can separate the data from positive and negative class. If so, give the coefficients of w (You should be able to do this by inspection, without significant computation). 2. What is the kernel corresponding to the feature map o() in the last part. In other words, provide the kernel function K(x, z): R² x R² → R. 1. SVM. Consider a supervised learning problem in which the training examples are points in 2-dimensional space. The positive examples (samples in class 1) are (1, 1) and (-1,-1). The negative examples (samples in class 0) are (1,-1) and (-1, 1). Are the positive examples linearly separable from the negative examples in the original space? If so, give the coefficients of w. 0 -1 + 0 1. For the example above, consider the feature transformation p(x) = [1, x₁, x2, ₁2], where ₁ and ₂ are, respectively, the first and second coordinates of a generic example x. Can we find a hyperplance wTo(x) in this feature space that can separate the data from positive and negative class. If so, give the coefficients of w (You should be able to do this by inspection, without significant computation). 2. What is the kernel corresponding to the feature map o() in the last part. In other words, provide the kernel function K(x, z): R² x R² → R.

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Answer 1No single line which is drawn can separate ... View the full answer