完备的无参数近邻保持及最大化非近邻算法  

Complete parameter-free local neighborhood preserving and non-local maximization algorithm

作　　者：林玉娥[1] 陈静逸[1] 许光宇[1] 梁兴柱[1] 

机构地区：[1]安徽理工大学计算机科学与工程学院,安徽淮南232001

出　　处：《计算机应用》2015年第8期2244-2248,共5页journal of Computer Applications

摘　　要：无参数保持投影算法无需参数设置且识别性能稳定,但算法不能有效地保持样本的局部结构,且忽略了非局部样本所起的作用,而且存在着小样本(SSS)问题,为此提出了一种完备的无参数近邻保持及最大化非近邻算法。算法以样本间余弦距离0.5为分界点将样本分成近邻及非近邻样本,为了充分利用近邻样本及非近邻样本,分别构造了近邻散度矩阵及非近邻散度矩阵,因此算法的目标函数就是求取能够最小化近邻散度矩阵的同时,最大化非近邻散度矩阵的投影矩阵。对于目标函数的求解,可先将高维样本通过主成分分析(PCA)算法降至一个低维的子空间,并通过两个定理证明了这种处理方法没有损失任何有效的判别信息;然后将目标函数转换为差形式,从而有效地解决了小样本问题。在人脸库及掌纹库上的实验结果表明,与无参数局部保持投影算法相比,所提算法平均识别率更高,验证了算法的有效性。Parameter-free locality preserving projection does not need to set parameters and has stable performance, but the algorithm cannot effectively maintain the local structure of the sample and ignores the role of non-local samples. Moreover, this method exists the Small Size Sample （SSS） problem. A complete parameter-free local neighborhood preserving and non- local maximization algorithm was proposed. In order to make full use of the nearest neighbor samples and non-nearest neighbor samples, which were divided by whether the distance between two samples is no more than O. 5 or not, the neighbor scatter matrix and non-nearest neighbor scatter matrix were constructed. Then, the objective function of the algorithm was to seek a set of projection vectors such that the neighbor scatter matrix was maximized and non-nearest neighbor scatter matrix was minimized simultaneously. As to solve the objective function, the high dimensional samples were projected to a low dimensional subspace by Principal Component Analysis （PCA） algorithm, which was proved without lossing any effective discriminant information according to two theorems. In order to solve the SSS problem, the objective function was converted to differential form. The experimental results on face database and palmprint database illustrate that the proposed method outperforms Parameter-free locality preserving projection with average recognition rate, which proves the effectiveness of the proposed algorithm.

关 键 词：无参数 局部结构 小样本问题 近邻 非近邻 

分 类 号：TP391.4[自动化与计算机技术—计算机应用技术]