8 Multiclass Classification
Multiclassification - \(y \in \{0,1,2,3,4\}\). It is not only a boolean classification. E.g. does a patient have a malignant tumor is a binomial classification (yes or no).
TODO - Include graphs
One Versus All
We assign \(y=1\) for one specific class and \(y=0\) for the remaining class and then do normal logistic regression. We would then have as many logistic regression models as we do have classes.
\[ h_\theta^{(i)}(x) = P(y=i|x;\theta) \quad (i=1,2,3,4,\ldots,n) \]Train a logistic regression classifier \(h_\theta^{(i)}(x)\) for each class \(i\) to predict the probability that \(y=i\).
On a new input \(x\), to make a prediction, pick the class \(i\) that \(\max_i h_\theta^{(i)}(x)\).