增量式正交局部判别投影法

Orthogonal locally discriminant projection algorithm for incremental data

针对现有投影分析算法随着输入数据量的增加计算复杂度急剧增长这一问题,通过子块优化策略构建了目标投影模型,称之为增量的局部判别投影(ILDP)算法。算法兼顾样本的类间离散度和类内紧凑性,求得的投影矩阵还具有正交性;通过子块叠加和奇异值升级算法对模型的求解进行了增量式扩展,计算过程中并无出现矩阵逆操作,即规避了小样本问题。在COIL图像库、USPS手写字体库和ExYaleB人脸库中的实验表明,对比经典的ILDA、LSDA、MMP等降维算法,ILDP具有更高的识别率,尤其在USPS数据库中,ILDP的识别率接近于90%,而其它的算法识别率都低于85%。与此同时,ILDP的计算量也明显少于对比算法,在USPS数据库中仅需要少于0.5s的时间即可完成最优投影矩阵计算。

The standard implementation of traditional projection algorithms takes all the training samples as the input data, which scales badly with the dataset size and makes computations for large samples application infeasible. We introduce a block optimization and batch alignment strategy to propose a novel locally discriminant projection （LDP） algorithm for solving this problem. The advantages of the proposed algorithm are：Firstly,it preserves the intra class structure of the manifold and maximizes margins between the data of different classes;Secondly, the final projection matrix of the proposed algorithm has the orthogonality property;Thirdly, there is no small sample size problem in this algorithm; Finally, LDP can be easily extended to the incremental LDP （ILDP） for learning the locally discriminant subspace with the newly inserted data by employing the singular value decomposition updating algorithm. The experimental data by employing the singular value decomposition updating algoirthm. The experimental results on COIL image database, USPS hand written digit database on ExYaleB face database demonstrate that ILDP has higher recognition rate compared with the classical ILDA, LSDA and MMP algorithms. Especially in the USPS database, ILDP reaches recognition rate of 90% while the others are all below 85%. Meanwhile, ILDP bears less computational cost, which needs only less than 0. 5 s for training USPS database.