title: Local Laplacian Coding From Theoretical Analysis of Local Coding Schemes for Locally Linear Classification.
abstract: Local coordinate coding (LCC) is a framework to approximate a Lipschitz smooth function by combining linear functions into a nonlinear one. For locally linear classification, LCC requires a coding scheme that heavily determines the nonlinear approximation ability, posing two main challenges: 1) the locality making faraway anchors have smaller influences on current data and 2) the flexibility balancing well between the reconstruction of current data and the locality. In this paper, we address the problem from the theoretical analysis of the simplest local coding schemes, i.e., local Gaussian coding and local student coding, and propose local Laplacian coding (LPC) to achieve the locality and the flexibility. We apply LPC into locally linear classifiers to solve diverse classification tasks. The comparable or exceeded performances of state-of-the-art methods demonstrate the effectiveness of the proposed method.
authors.forename: Junbiao
authors.initials: J
authors.lastname: Pang
authors.forename: Lei
authors.initials: L
authors.lastname: Qin
authors.forename: Chunjie
authors.initials: C
authors.lastname: Zhang
authors.forename: Weigang
authors.initials: W
authors.lastname: Zhang
authors.forename: Qingming
authors.initials: Q
authors.lastname: Huang
authors.forename: Baocai
authors.initials: B
authors.lastname: Yin