Locality preserving hashing

Locality preserving hashing is a way to store a bunch of things in a way that makes it easier to find them later. Imagine you have a bunch of toy trucks and you want to put them away in a toy box. You could just throw them all inside randomly, but then it would take forever to find the one you want to play with later.

Instead, let's say you group the trucks by color. All the red trucks go in one corner of the toy box, all the blue ones in another, and so on. Now, when you want to find a red truck to play with, you know exactly where to look.

Locality preserving hashing does something similar with data. It takes a bunch of data points and groups them together based on some similarity, like how close they are to each other in some mathematical sense. Then, it assigns each group a unique code, or "hash". So, if you want to find a particular data point later, you can quickly look up its hash and know which group it belongs to, making it much easier to find.

Overall, locality preserving hashing is just a way to organize a lot of data so that it's easier to search through later. It's like sorting your toys to make them easier to find, but with a lot more math involved!