# Implicit ZCA Whitening Effects of Linear Autoencoders for Recommendation

arXiv: https://arxiv.org/abs/2308.13536 · HTML: https://mlsanity.com/paper/2308.13536/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 21 references that are in the map.
- First posted on arXiv 15 Aug 2023.

## Builds on (most cited first, 9 of 9)

- [Variational Autoencoders for Collaborative Filtering](https://mlsanity.com/paper/1802.05814/) (2018)
- [Whitening Sentence Representations for Better Semantics and Faster Retrieval](https://mlsanity.com/paper/2103.15316/) (2021)
- [Optimal whitening and decorrelation](https://mlsanity.com/paper/1512.00809/) (2015)
- [Embarrassingly Shallow Autoencoders for Sparse Data](https://mlsanity.com/paper/1905.03375/) (2019)
- [Item2Vec: Neural Item Embedding for Collaborative Filtering](https://mlsanity.com/paper/1603.04259/) (2016)
- [WhiteningBERT: An Easy Unsupervised Sentence Embedding Approach](https://mlsanity.com/paper/2104.01767/) (2021)
- [Deep Item-based Collaborative Filtering for Top-N Recommendation](https://mlsanity.com/paper/1811.04392/) (2018)
- [Towards a Better Understanding of Linear Models for Recommendation](https://mlsanity.com/paper/2105.12937/) (2021)
- [It's Enough: Relaxing Diagonal Constraints in Linear Autoencoders for Recommendation](https://mlsanity.com/paper/2305.12922/) (2023)

## Abstract (arXiv)

Recently, in the field of recommendation systems, linear regression (autoencoder) models have been investigated as a way to learn item similarity. In this paper, we show a connection between a linear autoencoder model and ZCA whitening for recommendation data. In particular, we show that the dual form solution of a linear autoencoder model actually has ZCA whitening effects on feature vectors of items, while items are considered as input features in the primal problem of the autoencoder/regression model. We also show the correctness of applying a linear autoencoder to low-dimensional item vectors obtained using embedding methods such as Item2vec to estimate item-item similarities. Our experiments provide preliminary results indicating the effectiveness of whitening low-dimensional item embeddings.