Classification is similar to regression analysis, however in this setting we are now dealing with categorical data (e.g. an animals dataset my have categories for cat, dog, etc). In a classification problem we will be given \(K\) classes and some data \(X\) which we use to train a model for class predictions. The process of building models and training them is the same as for what we did in regression analysis.
One last important thing to mention is that since our data is categorical we one hot encode it so that our models can use the data. As an example if we have the classes cat, dog and pig we can one hot encode cat as \((1,0,0)^T\), dog as \((0,1,0)^T\) and pig as \((0,0,1)^T\). So one hot encoding is mapping class i to \(e_{i}\), the vector of all zeros except a one in the ith position.