# Beyond Neighbourhood-Preserving Transformations for Quantization-Based Unsupervised Hashing

arXiv: https://arxiv.org/abs/2110.00216 · HTML: https://mlsanity.com/paper/2110.00216/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 42 references that are in the map.
- First posted on arXiv 1 Oct 2021.

## Builds on (most cited first, 11 of 11)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [A Survey of Quantization Methods for Efficient Neural Network Inference](https://mlsanity.com/paper/2103.13630/) (2021)
- [Return of the Devil in the Details: Delving Deep into Convolutional Nets](https://mlsanity.com/paper/1405.3531/) (2014)
- [A Survey on Learning to Hash](https://mlsanity.com/paper/1606.00185/) (2016)
- [Can We Gain More from Orthogonality Regularizations in Training Deep CNNs?](https://mlsanity.com/paper/1810.09102/) (2018)
- [Learning to Hash with Binary Deep Neural Network](https://mlsanity.com/paper/1607.05140/) (2016)
- [Hashing with binary autoencoders](https://mlsanity.com/paper/1501.00756/) (2015)
- [Bit-Scalable Deep Hashing with Regularized Similarity Learning for Image Retrieval and Person Re-identification](https://mlsanity.com/paper/1508.04535/) (2015)
- [Simultaneous Compression and Quantization: A Joint Approach for Efficient Unsupervised Hashing](https://mlsanity.com/paper/1802.06645/) (2018)
- [A non-alternating graph hashing algorithm for large scale image search](https://mlsanity.com/paper/2012.13138/) (2020)

## Abstract (arXiv)

An effective unsupervised hashing algorithm leads to compact binary codes preserving the neighborhood structure of data as much as possible. One of the most established schemes for unsupervised hashing is to reduce the dimensionality of data and then find a rigid (neighbourhood-preserving) transformation that reduces the quantization error. Although employing rigid transformations is effective, we may not reduce quantization loss to the ultimate limits. As well, reducing dimensionality and quantization loss in two separate steps seems to be sub-optimal. Motivated by these shortcomings, we propose to employ both rigid and non-rigid transformations to reduce quantization error and dimensionality simultaneously. We relax the orthogonality constraint on the projection in a PCA-formulation and regularize this by a quantization term. We show that both the non-rigid projection matrix and rotation matrix contribute towards minimizing quantization loss but in different ways. A scalable nested coordinate descent approach is proposed to optimize this mixed-integer optimization problem. We evaluate the proposed method on five public benchmark datasets providing almost half a million images. Comparative results indicate that the proposed method mostly outperforms state-of-art linear methods and competes with end-to-end deep solutions.