Implicit ZCA Whitening Effects of Linear Autoencoders for Recommendation
Katsuhiko Hayashi Kazuma Onishi
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.