张量线性判别分析算法研究

摘要

Aiming at problems of small sample existed in the traditional linear discriminant analysis and two projection matrixes of Ten-sorLDA algorithms cannot calculate,low-dimensional feature extraction is not sufficient,study and implement TensorLDA based on ten-sor subspace. And the It-TensorLDA algorithm is presented,which first initializes with unit matrix,then uses the optimized criterion to get another projection matrix,carrying on many times iteration. Apply ORL human dataset to test the performance of algorithm. The ex-periments show that in ORL dataset It-TensorLDA is 1. 88% higher than TensorLDA and 3. 03% compared with Fisherfaces. So,the al-gorithm avoids the small sample problem,enhances the efficiency of face recognition.%针对传统线性判别分析中存在的小样本问题及对TensorLDA算法中两个投影矩阵不能同时计算、低维特征提取不充分的问题，文中研究并实现了张量子空间下的张量线性判别分析( TensorLDA)算法。并且提出了It-TensorLDA算法，即先用单位矩阵初始化，再利用优化准则求另一个投影矩阵，并进行多次迭代的改进方法。采用ORL数据库测试算法的性能，在ORL人脸数据库上It-TensorLDA比TensorLDA的平均识别率高1.88%，比Fisherfaces的平均识别率高3.03%。因此，文中算法有效避免了小样本问题，提高了人脸识别效果。