In this and the next three chapters, we will walk through a remarkable landscape of intellectual foundations. But sometimes we will also see significant gaps between theory and practice.

A Short Answer

We continue with the theme of recommendation. Webpage ranking in Chapter 3 turns a graph into a rank-ordered list of nodes. Movie ranking in Chapter 4 turns a weighted bipartite user–movie graph into a set of rank-ordered lists of movies, with one list per user. We now examine the aggregation of a vector of rating scores by reviewers of a product or service, and turn that vector into a scalar for each product. These scalars may in turn be used to rank order a set of similar products. In Chapter 6, we will further study aggregation of many vectors into a single vector.

When you shop on Amazon, likely you will pay attention to the number of stars shown below each product. But you should also care about the number of reviews behind that averaged number of stars. Intuitively, you know that a product with two reviews, both 5 stars, might not be better than a competing product with one hundred reviews and an average of 4.5 stars, especially if these one hundred reviews are all 4 and 5 stars and the reviewers are somewhat trustworthy. We will see how such intuition can be sharpened.

In most online review systems, each review consists of three fields:

1. rating, a numerical score often on the scale of 1–5 stars (this is the focus of our study),

2. review, in the form of text, and

3. review of review, often a binary up or down vote.