How to get Equation of a decision boundary in matlab svm plot? - svm

Question

my data
y n Rh y2
1 1 1.166666667 1
-1 2 0.5 1
-1 3 0.333333333 1
-1 4 0.166666667 1
1 5 1.666666667 2
1 6 1.333333333 1
-1 7 0.333333333 1
-1 8 0.333333333 1
1 9 0.833333333 1
1 10 2.333333333 2
1 11 1 1
-1 12 0.166666667 1
1 13 0.666666667 1
1 14 0.833333333 1
1 15 0.833333333 1
-1 16 0.333333333 1
-1 17 0.166666667 1
1 18 2 2
1 19 0.833333333 1
1 20 1.333333333 1
1 21 1.333333333 1
-1 22 0.166666667 1
-1 23 0.166666667 1
-1 24 0.333333333 1
-1 25 0.166666667 1
-1 26 0.166666667 1
-1 27 0.333333333 1
-1 28 0.166666667 1
-1 29 0.166666667 1
-1 30 0.5 1
1 31 0.833333333 1
-1 32 0.166666667 1
-1 33 0.333333333 1
-1 34 0.166666667 1
-1 35 0.166666667 1
my codes r
data=xlsread('btpdata.xlsx',1.)
A = data(1:end,2:3)
B = data(1:end,1)
svmStruct = svmtrain(A,B,'showplot',true)
hold on
C = data(1:end,2:3)
D = data(1:end,4)
svmStruct = svmtrain(C,D,'showplot',true)
hold off
How can i get the approximate equations of this black lines in the given mat-lab plot?

Answer 1

It depends what package you did use, but as it is a linear Support Vector Machine there are more or less two options:
Your trained svm contains the equation of the line in a property coefs (sometimes called w or weights) and b (or intercept), so your line is <coefs, X> + b = 0
Your svm containes alphas (dual coefficients, Lagrange multipliers) and then coefs = SUM_i alphas_i * y_i * SV_i where SV_i is i'th support vector (the ones in circles on your plot) and y_i is its label (-1 or +1). Sometimes alphas are already multiplied by y_i, then your coefs = SUM_i alphas_i * SV_i.
If you are trying to get the equation from the actual plot (image), then you can only read it (and it is more or less y = 0.6, meaning that coefs = [0 1] and b = -0.6. Image analysis based approach (for arbitrary such plot) would require:
detecting image part (object detection)
reading the ticks/scale (OCR + object detection) <- this would be actually the hardest part
filtering out everything non-black and performing linear regression to points left, then trasforming through scale detected earlier.

Answer 2

I have had the same problem. To build the linear equation (y = mx + b) of the decision boundary you need the gradient (m) and the y-intercept (b). SVMStruct.Bias is the b-term. The gradient is determined by the SVM beta weights, which SVMStruct does not contain so you need to calculate them from the alphas (which are included in SVMStruct):
alphas = SVMStruct.Alpha;
SV = SVMStruct.SupportVectors;
betas = sum(alphas.*SV);
m = betas(1)/betas(2)
By the way, if your SVM has scaled the data, then I think you will need to unscale it.