Robust data representation using locally linear embedding guided PCA

Locally Linear Embedding (LLE) is widely used for embedding data on a nonlinear manifold. It aims to preserve the local neighborhood structure on the data manifold. Our work begins with a new observation that LLE has a natural robustness property. Motivated by this observation, we propose to integrate LLE and PCA into a LLE guided PCA model (LLE-PCA) that incorporates both global structure and local neighborhood structure simultaneously while performs robustly to outliers. LLE-PCA has a compact closed-form solution and can be efficiently computed. Extensive experiments on five datasets show promising results on data reconstruction and improvement on data clustering and semi-supervised learning tasks.