Fast Exact Retrieval for Nearest-neighbor Lookup (FERN)
Richard Zhu

TL;DR
FERN introduces a novel algorithm that achieves logarithmic time complexity for exact nearest neighbor retrieval in high-dimensional spaces, maintaining 100% recall on large datasets, thus bridging the gap between efficiency and accuracy.
Contribution
The paper presents FERN, a new algorithm inspired by kd-trees, that enables exact nearest neighbor search with $O(d ext{log}N)$ complexity in high dimensions.
Findings
Achieves $O(d ext{log}N)$ retrieval time for high-dimensional data.
Maintains 100% recall on 10 million vectors.
Outperforms traditional methods in speed while preserving accuracy.
Abstract
Exact nearest neighbor search is a computationally intensive process, and even its simpler sibling -- vector retrieval -- can be computationally complex. This is exacerbated when retrieving vectors which have high-dimension relative to the number of vectors, , in the database. Exact nearest neighbor retrieval has been generally acknowledged to be a problem with no sub-linear solutions. Attention has instead shifted towards Approximate Nearest-Neighbor (ANN) retrieval techniques, many of which have sub-linear or even logarithmic time complexities. However, if our intuition from binary search problems (e.g. vector retrieval) carries, there ought to be a way to retrieve an organized representation of vectors without brute-forcing our way to a solution. For low dimension (e.g. or cases), \texttt{kd-trees} provide a algorithm for retrieval.…
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Taxonomy
TopicsAdvanced Image and Video Retrieval Techniques · Advanced Neural Network Applications · Machine Learning and Data Classification
