What is Alpha in SVM?

Lagrangian multiplier, usually denoted by α is a vector of the weights of all the training points as support vectors. Suppose there are m training examples. When you say αi=0, it is just that ith training example has zero weight as a support vector.

How is SVM margin calculated?

The margin is calculated as the perpendicular distance from the line to only the closest points. Only these points are relevant in defining the line and in the construction of the classifier. These points are called the support vectors. They support or define the hyperplane.

How do you find W and B in SVM?

Support Vector Machine – Calculate w by hand

1. w=(1,−1)T and b=−3 which comes from the straightforward equation of the line x2=x1−3. This gives the correct decision boundary and geometric margin 2√2.
2. w=(1√2,−1√2)T and b=−3√2 which ensures that ||w||=1 but doesn’t get me much further.

What will be the alpha value for non support vectors?

It is stated that α for all non-support vectors is 0.

What is W in SVM?

w is the normal direction of the plane and b is a form of threshold. Given a data point w, if w⋅x is evaluated to to be bigger than b, it belongs to a class. If it is evaluated to be less than b, then it belongs to another class.

What is hard margin in SVM?

A hard margin means that an SVM is very rigid in classification and tries to work extremely well in the training set, causing overfitting.

What is primal and dual in SVM?

This comes from the duality principle which states that optimization problems may be viewed as primal (in this case minimising over w and b) or dual (in this case, maximising over a). For a convex optimisation problem, the primal and dual have the same optimum solution.

What is Gamma in SVM?

Intuitively, the gamma parameter defines how far the influence of a single training example reaches, with low values meaning ‘far’ and high values meaning ‘close’. The gamma parameters can be seen as the inverse of the radius of influence of samples selected by the model as support vectors.

How do you write the objective function of a SVM?

So the SVM objective function can be written as: Suppose that the positive training example has been mis-classified by the optimal w. This means that The first intuition is as follows. Since the norm of w is penalized using a quadratic, and the hinge loss is linear (when you’re far from the margin).

What are the characteristics of SVMs?

•SVMs maximize the margin (Winston terminology: the ‘street’) around the separating hyperplane. •The decision function is fully specified by a (usually very small) subset of training samples, the support vectors. •This becomes a Quadratic programming problem that is easy to solve by standard methods.

What is support vector machine (SVM)?

Support Vector Machine (SVM) SVMs maximize the margin(Winston terminology: the ‘street’)around the separating hyperplane. The decision function is fullyspecified by a (usually very small)subset of training samples, thesupport vectors. This becomes a Quadraticprogramming problem that is easyto solve by standard methods

What does a higher \\alpha value mean?

In the dual, a higher value of \\alpha means that that example has a higher contribution to the weight vector. You can check mathematically that higher the \\alpha is for a given example, the lower the loss on that example.