The nearest neighbor search problem involves a database of embeddings and a set of queries where we aim to find the embedding closest to a query. Exact methods such as linear search and space partitioning demonstrate time complexity issues as we increase database and query set size. This has led to the development of approximation algorithms where we pick points some distance close to our query using methods such as navigable small worlds or vector quantization. However, while this increases speed, these methods bring up issues with accuracy when adapting algorithms to different datasets. In this research project, we determine if there is a normalization scheme that allows for perfect accuracy when using approximate nearest neighbor algorithms on any dataset. We draw initial conclusions from the current state-of-art approximation algorithm ScaNN and then generalize to other approximation algorithms.
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