L-PCA算法下的高维图像降维算法研究

摘要

文中借鉴经典凸技术聚类算法中的全局线性降维算法PCA与LDA聚类算法思想,提出了一种改进型的PCA降维算法L-PCA,该算法在保证原有样本协方差结构不变的前提下,获取变换矩阵中最重要的主分量进行赋权,通过调节类内与类间离散矩阵,使得类内距离最小化、类间聚类最大化,来搜索一个合适的映射子空间来实现不同类别数据之间的划分.通过典型数据集下的实验结果很好的验证了L-PCA算法在一阶最近近邻分类器泛化误差、准确性以及目标数据表达连续性等方面的良好性能.%Based on the idea of global linear dimensionality reduction algorithm named PCA from classical convex clustering algorithm and LDA,an improved PCA method called L-PCA was introduced.The algorithm retained the covariance structure of the original samples,chose the most important principal component from transformation matrix for empowerment.By adjusting the discrete matrixes for inner-class and inter-class,the distances in the same class were minimized and the ones for inner-class were maximized to search for a suitable mapping subspace to separate the data between different categories.The results show that L-PCA performs well regarding generalization errors of 1-NN classifiers,accuracy and continuity.