Does SVM use hinge loss?
SVM uses hinge loss where as logistic regression using logistic loss function for optimizing the cost function and arriving at the weights. The way the hinge loss is different from logistic loss can be understood from the plot below (from wikipedia — Purple is the hinge loss, Yellow is the logistic loss function).
What is the loss function for an SVM?
The loss function of SVM is very similar to that of Logistic Regression. Looking at it by y = 1 and y = 0 separately in below plot, the black line is the cost function of Logistic Regression, and the red line is for SVM. Please note that the X axis here is the raw model output, θᵀx.
Is hinge loss continuous?
For example, hinge loss is a continuous and convex upper bound to the task loss which, for binary classification problems, is the 0/1 loss.
Can hinge loss be negative?
The hinge loss is a loss function used for training classifiers, most notably the SVM. A negative distance from the boundary incurs a high hinge loss. This essentially means that we are on the wrong side of the boundary, and that the instance will be classified incorrectly.
Is there a penalty for hinge loss in SVM?
It seems there is no penalty if the instance lies within the margin even on the positive side. Also on Page 95, the author explains: However, from what I read about SVM, there should be penalty as long as the negative instance lies within the negative margin or on the wrong side. I updated the loss function as below with orange color:
Which is the correct expression for the hinge loss?
The correct expression for the hinge loss for a soft-margin SVM is: max (0, 1 − y f (x)) where f (x) is the output of the SVM given input x, and y is the true class (-1 or 1). When the true class is -1 (as in your example), the hinge loss looks like this:
How is the hinge loss used in machine learning?
The hinge loss is a loss function used to train the machine learning classifier, which is where = -1 or 1 indicating two classes and represents the output from our classifier. So what is the relation between the two? Are they just two perspectives to look at the same model? To derive hinge loss, we will start from (2).
When is the hinge loss nonzero for misclassified points?
When the true class is -1 (as in your example), the hinge loss looks like this: Note that the loss is nonzero for misclassified points, as well as correctly classified points that fall within the margin.