Handling large datasets and high-dimensional feature vectors is a common challenge in machine learning. Hashing offers techniques to manage this data efficiently, often providing near-constant time $O(1)$ operations for lookups and insertions under ideal conditions.

This chapter examines the core concepts of hash functions and hash tables, including strategies for dealing with collisions when multiple keys map to the same index. We will then apply these ideas to specific machine learning contexts:

• You'll see how feature hashing (the "hashing trick") can represent sparse, high-dimensional data compactly, reducing memory requirements without needing to build a dictionary first.
• We will introduce Locality-Sensitive Hashing (LSH), a technique used for finding approximate nearest neighbors quickly in large datasets, which is particularly useful for similarity search tasks.

Throughout the chapter, we'll consider the practical implementation details using Python and analyze the performance characteristics and trade-offs associated with these hashing methods in machine learning pipelines.