Let's begin with a simple two-layer sentiment classifier. You might imagine taking our logistic regression classifier of Chapter 5, which corresponds to a 1-layer network, and just adding a hidden layer. The input element x i could be scalar features like those in Fig. 5.2, e .g., x 1 = count(words ∈ doc), x 2 = count(positive lexicon words ∈ doc), x 3 = 1 if "no" ∈ doc, and so on. And the output layer y could have two nodes (one each for positive and negative), or 3 nodes (positive, negative, neutral), in which case y 1 would be the estimated probability of positive sentiment, y 2 the probability of negative and y 3 the probability of neutral. The resulting equations would be just what we saw above for a two-layer network (as sketched in Fig. 7.10 ):