# Efficient Codebook and Factorization for Second Order Representation Learning

## TL;DR

This paper introduces a novel method combining codebook and factorization techniques to produce compact, high-performing second order representations for image retrieval, outperforming previous approaches.

## Contribution

The proposed approach jointly integrates codebook and factorization schemes to maintain second order performance with fewer parameters, achieving state-of-the-art results.

## Key findings

- State-of-the-art results on three image retrieval datasets
- Compact representations with minimal additional parameters
- Effective preservation of second order performance

## Abstract

Learning rich and compact representations is an open topic in many fields such as object recognition or image retrieval. Deep neural networks have made a major breakthrough during the last few years for these tasks but their representations are not necessary as rich as needed nor as compact as expected. To build richer representations, high order statistics have been exploited and have shown excellent performances, but they produce higher dimensional features. While this drawback has been partially addressed with factorization schemes, the original compactness of first order models has never been retrieved, or at the cost of a strong performance decrease. Our method, by jointly integrating codebook strategy to factorization scheme, is able to produce compact representations while keeping the second order performances with few additional parameters. This formulation leads to state-of-the-art results on three image retrieval datasets.