SVM-Example2Question 1The training data for an SVM consists of 5 points: (x1, y1), (x2, y2), (x3, y3), (x4, y4), (x5, y5), where: y1=−1, y2= 1, y3= −1, y4= 1, y5= 1. The values of the feature vectors (x1, . . . , x5) are not known explicitlybut their Gram matrix is known:G =9 0 −3 0 00 0 0 0 0−3 0 1 0 00 0 0 4 −20 0 0 −2 1(Element i, j of the Gram matrix is the dot product of xiand xj.) Let α1, . . . , α5be the Lagrange multipliersassociated with this data. (αiis associated with (xi, yi).)Part Aa.Using the linear kernel, what (dual) optimization problem needs to be solved in terms of the αiin order todetermine their values?Answerb.Using the polynomial kernel of order 2 , and soft margins specified by the parameter C = 10, what (dual)optimization problem needs to be solved in terms of the αiin order to determine their values?AnswerPart BFour optimization problems were solved by a numeric algorithm, and the corresponding Lagrange multipliesare shown below. You should take into consideration the fact that the numeric algorithm is not perfect, sothat the results for the alphas are just an approximation.Case kernel C α1α2α3α4α51 linear ∞ 6.6 · 1079.4 · 1072.0 · 1085.6 · 1071.1 · 1082 2nd order polynomial ∞ 0 0.666 0.666 0 03 linear 10 3.6 4.8 10 2.9 5.84 2nd order polynomial 10 0 0.666 0.666 0 0a.Select one of these cases and show that the SVM correctly classifies the entire training data. Show andexplain your computations.AnswerI am using Case .The following values need to be calculated so that the SVM can be applied:a1 The following computation needs to be carried out to classify (x1, y1):.a2 The following computation needs to be carried out to classify (x2, y2):.a3 The following computation needs to be carried out to classify (x3, y3):.a4 The following computation needs to be carried out to classify (x4, y4):.a5 The following computation needs to be carried out to classify (x5, y5):.b.Select one of these cases and show that the SVM does not correctly classify the entire training data. Showand explain your computations.AnswerI am using Case .The following values need to be calculated so that the SVM can be applied:b1 The following computation needs to be carried out to classify (x1, y1):.b2 The following computation needs to be carried out to classify (x2, y2):.b3 The following computation needs to be carried out to classify (x3, y3):.b4 The following computation needs to be carried out to classify (x4, y4):.b5 The following computation needs to be carried out to classify (x5,
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