Calculating margin and bias for SVM's -


i apologise newbishness of question in advance stuck. trying solve question,

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i can parts i)-1v) stuck on v. know calculate margin y, do

y=2/||w||

and know w normal hyperplane, don't know how calculate it. always

w=[1;1] ?

similarly, bias, w^t * x + b = 0

how find value x data points? thank help.

enter image description here

consider building svm on (very little) data set shown in picture example this, maximum margin weight vector parallel shortest line connecting points of 2 classes, is, line between , , giving weight vector of . optimal decision surface orthogonal line , intersects @ halfway point. therefore, passes through . so, svm decision boundary is:

enter image description here

working algebraically, standard constraint , seek minimize . happens when constraint satisfied equality 2 support vectors. further know solution . have that:

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therefore a=2/5 , b=-11/5, , . optimal hyperplane given

enter image description here
, b= -11/5 . margin boundary

enter image description here

this answer can confirmed geometrically examining picture.


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