Contents
What is the shape of the loss landscape during optimization of SVM?
The data loss is a sum of multiple terms, each of which is either independent of a particular weight, or a linear function of it that is thresholded at zero. The full SVM data loss is a 30,730-dimensional version of this shape.
What is SVM hinge loss?
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.
How to implement loss and gradient update in SVM?
Equipped with equations (1), (2) and (3), we have enough information to implement a loss function and gradient update. The IPython Notebook svm.ipynb from Stanford CS231n is a great starting point to understand implementation of the SVM classifier.
Why is the loss function not vectorized in SVM?
No because the loss function has a 0.5 scalar applied to the regularization terms. Have a look at the code computing the loss before the gradient calculation. Therefore the 0.5 and 2 when multiplied together cancel when you add in the regularization terms. The explanation for vectorized version is wrong, just like Jeremy Allen mentioned.
How is gradient descent used in SVM multiclass classification?
SVM multiclass classification computes scores, based on learnable weights, for each class and predicts one with the maximum score. Gradient descent is a common technique used to find optimal weights.
How is the hinge loss function used in SVM?
The dependent variable takes the form -1 or 1 instead of the usual 0 or 1 here so that we may formulate the “hinge” loss function used in solving the problem: Here, the constraint has been moved into the objective function and is being regularized by the parameter C. Generally, a lower value of C will give a softer margin.