Trjtdtk

I would be very grateful if I could receive some help regarding generating hyperplane equation. I need to generate an equation for hyperplane, I have two independent variables and one binary dependent variable.

Regarding this following equation for svm , f(x)=sgn( sum_i alpha_i K(sv_i,x) + b )

I have two independent variables (say P and Q) with 130 point values for each variable. I used svm radial basis function for binary classification (0 and 1) and I calculated for radial basis kernelized case,and now I have one column of 51 y (i) alpha (i) or (dual coeffficients), two columns of 51 sv (support vectors)for P and Q, and one single value for b . I received these using scikit SVC.

https://scikit-learn.org/stable/modules/svm.html

So, how can I generate the equation now? Can I multiply those 51 y (i) alpha (i) or (dual coeffficients) with 51 sv (support vectors) for each variable P and Q so that I have two coefficients for P and Q so that finally my equation appears as : f(x)=sgn( mP + nQ +b) where m = sum of the (product of 51 sv of P with 51 dual coefficients) and n = sum of the (product of 51 sv of Q with 51 dual coefficients).
i would be grateful for any kind of suggestion. Many thanks in advance.

I'm not sure if I've fully understood you. Radial basis kernel assumes that you transform your features into an infinite space and the dot product of your transformed vectors is exactly the radial basis kernel.

$k(x,y)=phi(x)cdot phi(y)$

$phi(x)$ - mapping

The main reason for using a kernel trick is the ability to transform features into higher dimensions without knowing the map function explicitly. Your hyperplane has infinite number of coefficients. You can always expend the radial basis kernel into Taylor series and get some of the initial coefficients.

Let me explain my question in terms of logistic regression. Suppose i am trying to use logistic regression to predict probabilities, i have two independent variables (P and Q) and a binary dependent variable C. I will use logistic regression to calculate individual coefficients of P and Q (let us say m and n respectively) plus a constant(let us say b). The fundamental equation of generalized linear model will be (mP + nQ + b). I can now use this equation to calculate probabilities.

Similarly, if I am using support vector, how am I going to get this kind of generalised linear model equation? I have used scikit in Python and also R, all i get is total number of support vectors and their values and value for (alpha (i) x X(i)). I need to assign individual weight to the two variable P and Q plus bias (b) so that I could use this equation as a generaised linear model. I am getting the constant term from Python but how am i suppose to generate coefficients of P and Q using SVM radial kernel?
Therefore I was wondering if there is some way I could assign weights to my two variables and create the linear function which i could use. I would be very grateful for an explanation.