What makes the soft SVM formulation different from the hard SVM formulation?
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. The result is that soft-margin SVM could choose decision boundary that has non-zero training error even if dataset is linearly separable, and is less likely to overfit.
Why do we need the soft margin formulation in an SVM classifier?
In practice, real data is messy and cannot be separated perfectly with a hyperplane. The constraint of maximizing the margin of the line that separates the classes must be relaxed. This is often called the soft margin classifier. This change allows some points in the training data to violate the separating line.
How to solve the first problem of SVM?
Along the way, we’ll notice some neat features of the SVM. To solve the first problem, we can use a trick. We want to know whether for a labeled training point . The trick is to multiply them together. If their signs agree, then their product will be positive, otherwise it will be negative.
How does the support vector machine ( SVM ) work?
SVM draws a hyperplane parallel to the actual hyperplane intersecting with the first point of class A (also known as Support Vectors) and another hyperplane parallel to the actual hyperplane intersecting with the first point of class B. SVM tries to maximize these margins.
What is the shifted decision rule in SVM?
The shifted decision rule is: Now the hypothesis is the pair of vector-and-scalar . The key intuitive idea behind the formulation of the SVM problem is that there are many possible separating hyperplanes for a given set of labeled training data. For example, here is a gif showing infinitely many choices.
What is the soft margin formulation of SVM?
In the given Soft Margin Formulation of SVM, C is a hyperparameter. C hyperparameter adds a penalty for each misclassified data point. Large Value of parameter C implies a small margin, there is a tendency to overfit the training model. Small Value of parameter C implies a large margin which might lead to underfitting of the model.