Local Laplacian Coding From Theoretical Analysis of Local Coding Schemes for Locally Linear Classification
本文从理论上分析了两种简单的局部编码方案，提出局部拉普拉斯编码（LPC），在局部线性分类中平衡了数据重建和局部性，实验表明其性能达到或超过现有方法。
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.