# Outer Product-based Neural Collaborative Filtering

arXiv: https://arxiv.org/abs/1808.03912 · HTML: https://mlsanity.com/paper/1808.03912/

## Key facts

- Cited by 41 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Aug 2018.

## Built on by (most cited first, 30 of 41)

- [Recommendation Unlearning](https://mlsanity.com/paper/2201.06820/) (2022)
- [A Survey on Accuracy-oriented Neural Recommendation: From Collaborative Filtering to Information-rich Recommendation](https://mlsanity.com/paper/2104.13030/) (2021)
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- [FedRecAttack: Model Poisoning Attack to Federated Recommendation](https://mlsanity.com/paper/2204.01499/) (2022)
- [Deep Exploration for Recommendation Systems](https://mlsanity.com/paper/2109.12509/) (2021)
- [Rethinking Collaborative Metric Learning: Toward an Efficient Alternative without Negative Sampling](https://mlsanity.com/paper/2206.11549/) (2022)
- [Poisoning Deep Learning Based Recommender Model in Federated Learning Scenarios](https://mlsanity.com/paper/2204.13594/) (2022)
- [The Minority Matters: A Diversity-Promoting Collaborative Metric Learning Algorithm](https://mlsanity.com/paper/2209.15292/) (2022)
- [Improved Diversity-Promoting Collaborative Metric Learning for Recommendation](https://mlsanity.com/paper/2409.01012/) (2024)
- [Multi-annotator Deep Learning: A Probabilistic Framework for Classification](https://mlsanity.com/paper/2304.02539/) (2023)
- [Learning Heterogeneous Temporal Patterns of User Preference for Timely Recommendation](https://mlsanity.com/paper/2104.14200/) (2021)
- [Multi-Sample based Contrastive Loss for Top-k Recommendation](https://mlsanity.com/paper/2109.00217/) (2021)
- [Dynamic Sparse Learning: A Novel Paradigm for Efficient Recommendation](https://mlsanity.com/paper/2402.02855/) (2024)
- [Local Collaborative Autoencoders](https://mlsanity.com/paper/2103.16103/) (2021)
- [Knowledge Sharing via Domain Adaptation in Customs Fraud Detection](https://mlsanity.com/paper/2201.06759/) (2022)
- [FedGRec: Federated Graph Recommender System with Lazy Update of Latent Embeddings](https://mlsanity.com/paper/2210.13686/) (2022)
- [Bilateral Self-unbiased Learning from Biased Implicit Feedback](https://mlsanity.com/paper/2207.12660/) (2022)
- [Multi-target prediction for dummies using two-branch neural networks](https://mlsanity.com/paper/2104.09967/) (2021)
- [Collaborative Reflection-Augmented Autoencoder Network for Recommender Systems](https://mlsanity.com/paper/2201.03158/) (2022)
- [Graph Based Long-Term And Short-Term Interest Model for Click-Through Rate Prediction](https://mlsanity.com/paper/2306.10028/) (2023)
- [Dual-embedding based Neural Collaborative Filtering for Recommender Systems](https://mlsanity.com/paper/2102.02549/) (2021)
- [A Systematic Analysis on the Impact of Contextual Information on Point-of-Interest Recommendation](https://mlsanity.com/paper/2201.08150/) (2022)
- [Simultaneous Learning of the Inputs and Parameters in Neural Collaborative Filtering](https://mlsanity.com/paper/2203.07463/) (2022)
- [Meta-Wrapper: Differentiable Wrapping Operator for User Interest Selection in CTR Prediction](https://mlsanity.com/paper/2206.14647/) (2022)
- [InterMulti:Multi-view Multimodal Interactions with Text-dominated Hierarchical High-order Fusion for Emotion Analysis](https://mlsanity.com/paper/2212.10030/) (2022)
- [Automatic Feature Fairness in Recommendation via Adversaries](https://mlsanity.com/paper/2309.15418/) (2023)
- [Tuning-Free LLM Can Build A Strong Recommender Under Sparse Connectivity And Knowledge Gap Via Extracting Intent](https://mlsanity.com/paper/2505.10900/) (2025)
- [Personalized Recommendations via Active Utility-based Pairwise Sampling](https://mlsanity.com/paper/2508.14911/) (2025)
- [BCFNet: A Balanced Collaborative Filtering Network with Attention Mechanism](https://mlsanity.com/paper/2103.06105/) (2021)
- [A Comprehensive Review on Non-Neural Networks Collaborative Filtering Recommendation Systems](https://mlsanity.com/paper/2106.10679/) (2021)

## Abstract (arXiv)

In this work, we contribute a new multi-layer neural network architecture named ONCF to perform collaborative filtering. The idea is to use an outer product to explicitly model the pairwise correlations between the dimensions of the embedding space. In contrast to existing neural recommender models that combine user embedding and item embedding via a simple concatenation or element-wise product, our proposal of using outer product above the embedding layer results in a two-dimensional interaction map that is more expressive and semantically plausible. Above the interaction map obtained by outer product, we propose to employ a convolutional neural network to learn high-order correlations among embedding dimensions. Extensive experiments on two public implicit feedback data demonstrate the effectiveness of our proposed ONCF framework, in particular, the positive effect of using outer product to model the correlations between embedding dimensions in the low level of multi-layer neural recommender model. The experiment codes are available at: https://github.com/duxy-me/ConvNCF