# Projected Hamming Dissimilarity for Bit-Level Importance Coding in Collaborative Filtering

arXiv: https://arxiv.org/abs/2103.14455 · HTML: https://mlsanity.com/paper/2103.14455/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 35 references that are in the map.
- First posted on arXiv 26 Mar 2021.

## Builds on (most cited first, 17 of 17)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Ups and Downs: Modeling the Visual Evolution of Fashion Trends with One-Class Collaborative Filtering](https://mlsanity.com/paper/1602.01585/) (2016)
- [Variational Autoencoders for Collaborative Filtering](https://mlsanity.com/paper/1802.05814/) (2018)
- [Neural Collaborative Filtering vs. Matrix Factorization Revisited](https://mlsanity.com/paper/2005.09683/) (2020)
- [Compressing Word Embeddings via Deep Compositional Code Learning](https://mlsanity.com/paper/1711.01068/) (2017)
- [Content-aware Neural Hashing for Cold-start Recommendation](https://mlsanity.com/paper/2006.00617/) (2020)
- [Variational Deep Semantic Hashing for Text Documents](https://mlsanity.com/paper/1708.03436/) (2017)
- [NASH: Toward End-to-End Neural Architecture for Generative Semantic Hashing](https://mlsanity.com/paper/1805.05361/) (2018)
- [Learning K-way D-dimensional Discrete Codes for Compact Embedding Representations](https://mlsanity.com/paper/1806.09464/) (2018)
- [Discrete Factorization Machines for Fast Feature-based Recommendation](https://mlsanity.com/paper/1805.02232/) (2018)
- [Recurrent Binary Embedding for GPU-Enabled Exhaustive Retrieval from Billion-Scale Semantic Vectors](https://mlsanity.com/paper/1802.06466/) (2018)
- [Compositional Coding for Collaborative Filtering](https://mlsanity.com/paper/1905.03752/) (2019)
- [Unsupervised Semantic Hashing with Pairwise Reconstruction](https://mlsanity.com/paper/2007.00380/) (2020)
- [Unsupervised Neural Generative Semantic Hashing](https://mlsanity.com/paper/1906.00671/) (2019)
- [Document Hashing with Mixture-Prior Generative Models](https://mlsanity.com/paper/1908.11078/) (2019)
- [Query-adaptive Image Retrieval by Deep Weighted Hashing](https://mlsanity.com/paper/1612.02541/) (2016)

## Built on by (most cited first, 4 of 4)

- [Representation Learning for Efficient and Effective Similarity Search and Recommendation](https://mlsanity.com/paper/2109.01815/) (2021)
- [Sequential Modelling with Applications to Music Recommendation, Fact-Checking, and Speed Reading](https://mlsanity.com/paper/2109.06736/) (2021)
- [Learning Similarity Preserving Binary Codes for Recommender Systems](https://mlsanity.com/paper/2204.08569/) (2022)
- [Federated Hash Projected Latent Factor Learning](https://mlsanity.com/paper/2606.26192/) (2026)

## Abstract (arXiv)

When reasoning about tasks that involve large amounts of data, a common approach is to represent data items as objects in the Hamming space where operations can be done efficiently and effectively. Object similarity can then be computed by learning binary representations (hash codes) of the objects and computing their Hamming distance. While this is highly efficient, each bit dimension is equally weighted, which means that potentially discriminative information of the data is lost. A more expressive alternative is to use real-valued vector representations and compute their inner product; this allows varying the weight of each dimension but is many magnitudes slower. To fix this, we derive a new way of measuring the dissimilarity between two objects in the Hamming space with binary weighting of each dimension (i.e., disabling bits): we consider a field-agnostic dissimilarity that projects the vector of one object onto the vector of the other. When working in the Hamming space, this results in a novel projected Hamming dissimilarity, which by choice of projection, effectively allows a binary importance weighting of the hash code of one object through the hash code of the other. We propose a variational hashing model for learning hash codes optimized for this projected Hamming dissimilarity, and experimentally evaluate it in collaborative filtering experiments. The resultant hash codes lead to effectiveness gains of up to +7% in NDCG and +14% in MRR compared to state-of-the-art hashing-based collaborative filtering baselines, while requiring no additional storage and no computational overhead compared to using the Hamming distance.