平均紧性约束下的最坏分离空间平滑判别分析

摘要

Spatially Smooth Linear Discriminant Analysis( SLDA) and IMage Euclidean Distance Discriminant Analysis( IMEDA) combined with spatial structure information of the images are two main discriminant methods to reduce dimension, and the classification performance of SLDA and IMEDA is better than that of LDA. Different from SLDA and IMEDA, the solutions in the proposed algorithms called WSLDA and WIMEDA are obtained by parameterizing projection directions, maintaining an upper bound for average within-class scatter and maximizing the minimal between-class scatter. Also their solution can simply be attributed to solve a well-known eigenvalue optimization problem called minimization for the maximal eigenvalue of a symmetric matrix. It overcomes the shortcoming that many algorithms need to use full eigenvalue decomposition. In addition, experiments on standard face dataset Yale、AR and FERET validate the effectiveness of WSLDA and WIMEDA.%空间平滑的线性判别分析( SLDA)和基于空间平滑欧氏距离的线性判别分析( IMEDA)是目前结合图像特有的空间结构信息进行图像判别降维的两种主要方法，具有比线性判别分析( LDA)更显著的分类效果.与SLDA和IMEDA不同，文中通过参数化投影方向，约束平均类内散度(或紧性)上界和最大化最坏类间散度(或分离度)，产生的降维算法分别称为WSLDA和WIMEDA.它们的求解最终可归结为简单的特征值优化问题，避免使用完整特征值分解的缺点.在Yale、AR和FERET标准人脸集上的实验验证它们的有效性.