一种无参数的局部线性判别分析方法

A Parameter-Free Local Linear Discriminant Analysis Method

摘要: 为了解决因引入局部化思想的线性判别分析(Linear Discriminant Analysis, LDA)方法需要人工设置邻居个数而无法以自适应的方式挖掘数据的局部结构问题，提出了一种无参数的局部线性判别分析(Parameter-free Local Linear Discriminant Analysis, Pf-LLDA)方法。该方法首先建立了一个关于权重矩阵和变换矩阵的统一优化模型。然后，通过使用交替方向的方法迭代求解出了与数据局部结构相关的权重矩阵和与判别分析相关的变换矩阵。从而使得Pf-LLDA在无需人为设定邻居个数的情况下，自适应地挖掘出了数据的局部结构并最终实现了局部线性判别分析的能力。在仿真数据集和手写体真实数据集上的实验结果表明，Pf-LLDA挖掘出数据局部结构的同时实现了更优的判别分析结果。

Abstract: For the Linear Discriminant Analysis (LDA) method which utilized the idea of localization and setting the number of neighbors by hand, it cannot mine the local structure embedded in the data adaptively. In order to solve this problem, this paper proposes a Parameter-free Local Linear Discriminant Analysis (Pf-LLDA) method. This method first establishes a unified optimization model about the weight matrix and the transformation matrix. Then, by using the alternating direction method, the solution of the weight matrix, which is associated with the local structure embedded in the data, and the transformation matrix, which is associated with the discriminant analysis are iteratively well found. Thus, Pf-LLDA adaptively mines the local structure of the data and finally achieves the capability of local linear discriminant analysis without artificially setting the number of neighbors. Experimental results on both synthetic and handwritten real datasets show that Pf-LLDA achieves better discriminant analysis results while mining the local structure of the data.