I have draw the graph but I have no idea how to determine the Support Vector Mac

Question

I have draw the graph but I have no idea how to determine the Support Vector Machine for this problem. Kindly please help me to solve. Many thanks.

c) The following table shows some measurements for dogs and cats on their height and length. You now need to identify these two classes with Support Vector Machines. Table Q1 (b) Class Dogs Dogs Dogs Dogs Dogs Cats Cats Cats Cats Cats Feature #1 185 180 173 170 165 168 160 158 155 152 Feature #2 80 65 74 87 73 60 52 67 50 Identify all the relevant support vectors. (9 marks Total: 25 markst

Explanation / Answer

***************Answer*****************

Now you have to find the line equation such that it will differentiate the cats and dogs.

So first we have to take 2 random nodes from dogs and two random nodes from cats.

From one of them you have to take as +ve and othere -ve

like

if we take two random nodes from dogs, (185, 80), (170,87)

and from cats => (160,52), (152, 55)

let us assume dogs +ve and cats -ve

now we have to make 4 equations

w1x + w2y + w3 = 0

so those 4 equations are:

w1(185)+w2(80)+w3 = 1
w1(170)+w2(87)+w3 = 1

w1(160)+w2(52)+w3 = -1
w1(152)+w2(55)+w3 = -1

now from these 4 equations we have to find w1, w2, w3

and then we have to substitute them in w1x + w2y + w3 = 0

here you will get line equation draw that line in the graph then you can distinguish the cats and dogs

if you want to check using points then substitue any point in the line equation you have got if you get +ve then dogs else cats

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