Two-layers local coordinate coding

Abstract

Extracting informative regularized representations of input signals plays a key role in the field of artificial intelligence, such as machine learning and robotics. Traditional approaches feature ℓ2 norm and sparse inducing ℓp norm (0 ≤ p ≤ 1) based optimization methods, imposing strict regularization on the representations. However, these approaches overlook the fact that signals and atoms in the overcomplete dictionaries usually contain such wealth of structural information that could improves representations. This paper systematically exploits data manifold geometric structure where signals and atoms reside in, and thus presents a principled extension of sparse coding, i.e. two-layers local coordinate coding, which demonstrates a high dimensional nonlinear function could be locally approximated by a global linear function with quadratic approximation power. Moreover, to learn each latent layer, corresponding patterned optimization approaches are developed, encoding distance information between signals and atoms into the representations. Experimental results demonstrate the significance of this extension on improving the image classification performance and its potential applications for object recognition in robot system are also exploited.