Abstract: In order to improve the orthogonality of discriminant subspace in Fisherface and increase the recognition rate, a new algorithm called matrix symmetry of Fisherface is proposed. The PCA is used for dimensionality reduction to eliminate the small sample size problem. The Fisher criterion is redefined by introducing a symmetric matrix. Some examples are classified by the symmetric matrix. Experimental results on ORL face image database indicate that the proposed method is more effective than the previous ones. And this method is more stable and less affected by the training set.

Key words: principal component analysis, linear discriminant analysis, high-dimensional and small sample size problem, orthogonal discriminant space, face recognition

摘要： 为了改善Fisherface方法中判别特征子空间正交性并提高识别率，提出了矩阵对称性的Fisherface算法。该方法利用PCA进行降维来消除小样本问题，对传统的Fisher准则进行修改使矩阵具有对称性，用构造的对称矩阵进行分类识别。在ORL标准人脸库上进行的实验表明，矩阵对称性方法的识别率明显地高于传统的方法，而且识别结果比较稳定受训练集影响较小，具有很好的实用性。

关键词: 主成分分析, 线性判别分析, 高维小样本问题, 正交判别空间, 人脸识别