Eliminating the Invariance on the Loss Landscape of Linear Autoencoders

no code implementations • ICML 2020 • Reza Oftadeh, Jiayi Shen, Zhangyang Wang, Dylan Shell

For this new loss, we characterize the full structure of the loss landscape in the following sense: we establish analytical expression for the set of all critical points, show that it is a subset of critical points of MSE, and that all local minima are still global.

Neural Networks for Principal Component Analysis: A New Loss Function Provably Yields Ordered Exact Eigenvectors

no code implementations • 25 Sep 2019 • Reza Oftadeh, Jiayi Shen, Zhangyang Wang, Dylan Shell

In this paper, we propose a new loss function for performing principal component analysis (PCA) using linear autoencoders (LAEs).