Unsupervised Feature Extraction Inspired by Latent Low-Rank Representation

Latent Low-Rank Representation (LatLRR) has the empirical capability of identifying "salient" features. However, the reason behind this feature extraction effect is still not understood. Its optimization leads to non-unique solutions and has high computational complexity, limiting its potential in practice. We show that LatLRR learns a transformation matrix which suppresses the most significant principal components corresponding to the largest singular values while preserving the details captured by the components with relatively smaller singular values. Based on this, we propose a novel feature extraction method which directly designs the transformation matrix and has similar behavior to LatLRR. Our method has a simple analytical solution and can achieve better performance with little computational cost. The effectiveness and efficiency of our method are validated on two face recognition datasets.