# MTFH: A Matrix Tri-Factorization Hashing Framework for Efficient Cross-Modal Retrieval

arXiv: https://arxiv.org/abs/1805.01963 · HTML: https://mlsanity.com/paper/1805.01963/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 May 2018.

## Built on by (most cited first, 8 of 8)

- [Feature Fusion from Head to Tail for Long-Tailed Visual Recognition](https://mlsanity.com/paper/2306.06963/) (2023)
- [FDDH: Fast Discriminative Discrete Hashing for Large-Scale Cross-Modal Retrieval](https://mlsanity.com/paper/2105.07128/) (2021)
- [ReCon: Enhancing True Correspondence Discrimination through Relation Consistency for Robust Noisy Correspondence Learning](https://mlsanity.com/paper/2502.19962/) (2025)
- [Improving Visual-Semantic Embeddings by Learning Semantically-Enhanced Hard Negatives for Cross-modal Information Retrieval](https://mlsanity.com/paper/2210.04754/) (2022)
- [Discriminative Semantic Transitive Consistency for Cross-Modal Learning](https://mlsanity.com/paper/2103.14103/) (2021)
- [Detail Reinforcement Diffusion Model: Augmentation Fine-Grained Visual Categorization in Few-Shot Conditions](https://mlsanity.com/paper/2309.08097/) (2023)
- [DEMO: A Statistical Perspective for Efficient Image-Text Matching](https://mlsanity.com/paper/2405.11496/) (2024)
- [PI-H2T: Enhancing Long-Tailed Visual Recognition with Permutation-Invariant and Head-to-Tail Feature Fusion](https://mlsanity.com/paper/2506.00625/) (2025)

## Abstract (arXiv)

Hashing has recently sparked a great revolution in cross-modal retrieval because of its low storage cost and high query speed. Recent cross-modal hashing methods often learn unified or equal-length hash codes to represent the multi-modal data and make them intuitively comparable. However, such unified or equal-length hash representations could inherently sacrifice their representation scalability because the data from different modalities may not have one-to-one correspondence and could be encoded more efficiently by different hash codes of unequal lengths. To mitigate these problems, this paper exploits a related and relatively unexplored problem: encode the heterogeneous data with varying hash lengths and generalize the cross-modal retrieval in various challenging scenarios. To this end, a generalized and flexible cross-modal hashing framework, termed Matrix Tri-Factorization Hashing (MTFH), is proposed to work seamlessly in various settings including paired or unpaired multi-modal data, and equal or varying hash length encoding scenarios. More specifically, MTFH exploits an efficient objective function to flexibly learn the modality-specific hash codes with different length settings, while synchronously learning two semantic correlation matrices to semantically correlate the different hash representations for heterogeneous data comparable. As a result, the derived hash codes are more semantically meaningful for various challenging cross-modal retrieval tasks. Extensive experiments evaluated on public benchmark datasets highlight the superiority of MTFH under various retrieval scenarios and show its competitive performance with the state-of-the-arts.