Let's look at a simple example. Consider some training samples with only two features (x and y values) and a corresponding target label (positive (+) or negative (-)). Since the labels are categorical, we know that this is a classification task. Moreover, because we only have two distinct classes (+ and -), it's a binary classification task.
In a binary classification task, a decision boundary is a line that partitions the training set into two subsets, one for each class. An optimal decision boundary partitions the data such that all data samples from one class (say, +) are to the left of the decision boundary, and all other data samples (say, -) are to the right of it.
An SVM updates its choice of a ...
