Now that our data is all set up, we can construct our model that will learn how to classify iris flowers. We'll construct one of the simplest machine learning models—a linear classifier, as follows:

A linear classifier works by calculating the dot product between an input feature vector x and a weight vector w. After calculating the dot product, we add a value to the result called a bias term b. In our case, we have three possible classes any input feature vector could belong to, so we need to compute three different dot products with w¹, w², and w³ to see which class it belongs to. But, rather than writing out three separate dot products, we can just do one matrix multiply between a matrix of weights of shape [3,4] and our input vector. In the following figure, we can see more clearly what it looks like:

We can also just simplify this equation down to the more compact form as follows, where our weight matrix is W, bias is b, x is our input feature vector and the resulting output is s: