# What is the support vector machine?

What IS the support vector machine? Can someone clarify my confusion?

1. 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"

1. SVM is the algorithm that solves the problem,

given data $$(x_n, y_n), n = 1, \ldots, N$$

$$\min_{w, b}\frac{1}{2}||w||^2$$ $$\text{ subject to: } y_n(w \cdot x_n + b) \geq 1, n=1,...,N$$

"SVMs are among the best (and many believe are indeed the best) “off-the-shelf” supervised learning algorithms." - Andrew Ng

See reference, "SVM is a supervised learning algorithm"

But this means that QP solvers are SVMs...

1. 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"

• it may help to consider svms w.r.t. regular kernel machines to clarify where does the concept apply – fr_andres SupportsMonicaCellio Dec 2 '19 at 13:25
• Why can't it refer to all these things, depending on the context? Do you encounter ambiguous sentences where the meaning would change depending on what exactly is meant by "SVM"? If not, why should it matter? SVM is a name for an approach, it's not a mathematical term and is not usually defined with mathematical precision. – amoeba says Reinstate Monica Dec 3 '19 at 10:42