# Sparse Ternary Codes for similarity search have higher coding gain than dense binary codes

## TL;DR

This paper introduces sparse ternary codes for approximate nearest neighbor search, demonstrating they outperform dense binary codes in coding gain and complexity by leveraging an information-theoretic approach.

## Contribution

It proposes a novel ternary encoding scheme for ANN search that surpasses traditional binary codes in coding gain and efficiency.

## Key findings

- Ternary codes achieve higher coding gain than binary codes.
- Properly designed ternary encoding reduces complexity.
- Information-theoretic analysis guides optimal encoding design.

## Abstract

This paper addresses the problem of Approximate Nearest Neighbor (ANN) search in pattern recognition where feature vectors in a database are encoded as compact codes in order to speed-up the similarity search in large-scale databases. Considering the ANN problem from an information-theoretic perspective, we interpret it as an encoding, which maps the original feature vectors to a less entropic sparse representation while requiring them to be as informative as possible. We then define the coding gain for ANN search using information-theoretic measures. We next show that the classical approach to this problem, which consists of binarization of the projected vectors is sub-optimal. Instead, a properly designed ternary encoding achieves higher coding gains and lower complexity.