What IS the support vector machine? Can someone clarify my confusion?
Possible answers:
- The SVM is the problem: given data $(x_n, y_n), n = 1, \ldots, N$
$$\min_{w, b}\frac{1}{2}||w||^2$$ $$\text{ subject to: } y_n(w \cdot x_n + b) \geq 1, n=1,...,N$$
See Solving Support Vector Machine with Many Examples Paweł Białoń, "...Various methods of dealing with linear support vector machine (SVM) problems with a large number of examples are presented and compared..."
See http://www.cs.tau.ac.il/~mansour/ml-course-10/scribe9.pdf "We begin with building the intuition behind SVMs, continue to define SVM as an optimization problem"
SVM is the algorithm that solves the problem,
given data $(x_n, y_n), n = 1, \ldots, N$
$$\min_{w, b}\frac{1}{2}||w||^2$$ $$\text{ subject to: } y_n(w \cdot x_n + b) \geq 1, n=1,...,N$$
See reference, "SVM is a supervised learning algorithm"
But this means that QP solvers are SVMs...
SVM is the solution to the following problem:
given data $(x_n, y_n), n = 1, \ldots, N$
$$\min_{w, b}\frac{1}{2}||w||^2$$ $$\text{ subject to: } y_n(w \cdot x_n + b) \geq 1, n=1,...,N$$
See, https://cel.archives-ouvertes.fr/cel-01003007/file/Lecture1_Linear_SVM_Primal.pdf (Page 22) "SVM is the solution to the problem...." (but then the author immediately contradicts himself by calling the SVM a quadratic programming problem - so is it the solution or the problem??)
See, reference "SVM is a discriminative classifier"