Building Recommendation Systems in Python and JAX

Chapter 10. Low-Rank Methods

In the preceding chapter, we lamented at the challenge of working with so many features. By letting each item be its own feature, we were able to express a lot of information about user preference and item-affinity correlations, but we were in big trouble in terms of the curse of dimensionality. Combine this with the reality of very sparse features, and you’re in danger. In this chapter, we’ll turn to smaller feature spaces. By representing users and items as low-dimensional vectors, we can capture the complex relationships between them in a more efficient and effective way. This allows us to generate more personalized and relevant recommendations for users while also reducing the computational complexity of the recommendation process.

We will explore the use of low-dimensional embeddings and discuss the benefits and some of the implementation details of this approach. We will also look at code in JAX that uses modern gradient-based optimization to reduce the dimension of your item or user representations.

Latent Spaces

You are already familiar with feature spaces, which are usually categorical or vector-valued direct representations of the data. This can be the raw red, green, and blue values of an image, counts of items in a histogram, or attributes of an object like length, width, and height. Latent features, on the other hand, do not represent any specific real value feature of the items but are initialized randomly and then learned to suit a ...