Theoretical analysis of learning local anchors for classification

In this paper, we present a theoretical analysis on learning anchors for local coordinate coding (LCC), which is a method to model functions for data lying on non-linear manifolds. In our analysis several local coding schemes, i.e., orthogonal coordinate coding (OC-C), local Gaussian coding (LGC), local Student coding (LSC), are theoretically compared, in terms of the upper-bound locality error on any high-dimension data; this provides some insight to understand the local coding for classification tasks. We further give some interesting implications of our results, such as tradeoff between locality and approximation ability in learning anchors.