Why Vector Search Works? Using LSH and Cosine Similarity for High-Dimensional Data Retrieval.

Think about the last time you searched for something. Maybe you typed a question into a chatbot, or perhaps you uploaded a photo to find a similar pair of shoes. On the surface, it feels like magic. But underneath the hood, the computer isn't looking at "shoes" or "words"—it’s looking at geometry. Exactly. We’re talking about Vector Retrieval. This is the mathematical backbone of almost every modern AI system, from Recommendation Engines to RAG (Retrieval-Augmented Generation). It’s the art of turning the messy, "unstructured" world of text, audio, and images into high-dimensional coordinates…