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Under what circumstances would a soft margin SVM be a better choice than a linear SVM?
2 Answers. I would expect soft-margin SVM to be better even when training dataset is linearly separable. The reason is that in a hard-margin SVM, a single outlier can determine the boundary, which makes the classifier overly sensitive to noise in the data.
What is the basic difference between hard and soft margin SVM?
The difference between a hard margin and a soft margin in SVMs lies in the separability of the data. If our data is linearly separable, we go for a hard margin. However, if this is not the case, it won’t be feasible to do that.
What is the SVM optimization problem with slack variables?
The formulation of the SVM optimization problem with slack variables is: The optimization problem is then trading off how fat it can make the margin versus how many points have to be moved around to allow this margin. The margin can be less than 1 for a point by setting , but then one pays a penalty of in the minimization for having done that.
How is slack variable used in soft margin?
The idea is: for every data point x_i, we introduce a slack variable ξ_i. The value of ξ_i is the distance of x_i from the corresponding class’s margin if x_i is on the wrong side of the margin, otherwise zero. Thus the points that are far away from the margin on the wrong side would get more penalty.
How does a support vector machine ( SVM ) work?
Let’s see what they are and how they work. This idea is based on a simple premise: allow SVM to make a certain number of mistakes and keep margin as wide as possible so that other points can still be classified correctly. This can be done simply by modifying the objective of SVM.
When do support vectors have a small margin?
Typically, the support vectors will be a small proportion of the training data. However, if the problem is non-separable or with small margin, then every data point which is misclassified or within the margin will have a non-zero .