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Binary-class classification algorithm with multiple-access acquired objects based on the SVM
LI Huan, WANG Shitong
School of Digital Media, Jiangnan University, Wuxi 214000, China
Abstract: The binary-class classification algorithm with multiple-access acquired objects based on the SVM is proposed for the purpose of classification of an object given with multiple observations in this paper. In each classification, initially all single observation samples in the multiple observation sample set are restricted to a same class.Two hypotheses are made for the class of the multiple observation sample set, and the class is determined by comparing the optimal values of the different objective functions under different class hypotheses. This method does not require training the classifier or early feature representation of the training set, instead, it takes advantage of the continuity law of the feature space of similar samples with the labeled samples and multiple observation samples as a whole, making the algorithm more accurate for classifications. Experiments show that the proposed method is valid and efficient.
Key words: pattern recognition     multiple observations     similar samples     SVM     binary-class classification

1 多观测样本二分类问题的描述

 图 1 多观测样本形成示意图 Fig. 1 Schematic diagram of producing multiple observations

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2 基于SVM的多观测样本二分类 2.1 支持向量机

SVM最基本的理论是用来解决二分类问题的，SVM的目标就是构造线性最优分类超平面，使其将2类样本完全正确地分开，同时使分类间隔最大。对于给定的样本集，(xi, yi), i=1, 2, …, l, xiRd, yi=±1，当样本集线性可分时，对应的线性判别函数的一般形式为：g(x)=(wTx)+b，其中wbn维向量，对判别函数作归一化处理，使离分类面最近的样本满足，则分类间隔等于, 使分类间隔最大等价于使最小；要求分类面能将所有样本正确分类，也就是要求它满足：

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2.2 基于SVM的多观测样本二分类

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2.3 基于SVM的多观测样本二分类的算法描述

X(l)Y(l)：已标记样本集和它的标签集；

X(u)：多观测样本集；

l:已标记样本的数目；

m:多观测样本数目。

:多观测样本的类别。

1)由X(l)X(u)得到样本矩阵X, XRn×d，由Y(l)得到标签矩阵Y

2)计算样本矩阵X对应的核矩阵K

3)设y=-1, 求解优化问题：max OAAT((YYTK)A/2，得到g1; 设y=+1, 求解优化问题：max OAAT((YYTK)A/2，得到g2

4)若g1>g2, 否则

3 多图像样本集的分类 3.1 手写数字分类

 图 2 在2种手写数字数据库上的识别率 Fig. 2 Classification results measured on two different handwritten digit data sets

3.2 物体图像分类

1)KLD[2](KL-divergence):该方法是典型的基于密度估计的统计方法，把所有样本集看作是独立同分布的高斯随机变量，然后通过计算样本集间KL散度完成多观测样本的分类。实验中，协方差矩阵特征向量的长度按能量的96%来选取。

2)MSM[6](mutual subspace method)：MSM是典型的子空间方法，该方法中的每个图像集用子空间来表示，而子空间通过主成分即协方差矩阵获得，把训练集与测试集之间的主成分角[17]作为相似性度量。实验中，当样本数目小于9时候，协方差矩阵的特征向量长度等于样本数目，否则设为9。

3)KMSM[8](kernel mutual subspace method)：KMSM是MSM在非线性空间的扩展，该方法考虑了图像集的非线性。与MSM不同的是，在用线性子空间建模之前，KMSM需要先把图像样本非线性地映射到高维特征空间。也就是说，KMSM用KPCA来取代PCA，从而获得了数据的非线性。KMSM方法中，使用高斯核函数，其中σ的选取与本文所提的算法相同。

 图 3 ETH-80数据库的样本图像 Fig. 3 Sample images from the ETH-80 database

 /% 算法 KLD MSM KMSM 本文SVM 识别率 85.714 97.500 91.071 98.036

4 基于视频的人脸识别 4.1 实验数据集

4.2 基于VidTIMIT数据库的人脸识别

 图 4 VidTIMIT数据库中的样本图像 Fig. 4 Sample images in the VidTIMIT database

 /% 样本数目m KLD MSM KMSM 本文SVM 4 50.600 72.965 86.157 97.287 8 88.410 89.277 92.229 98.828 12 94.630 95.995 95.496 99.148 16 96.630 96.742 96.244 99.003

 图 5 在VidTIMIT数据库上的识别率 Fig. 5 Recognition results on the VidTIMIT database
4.3 基于Honda/UCSD数据库的人脸识别

 图 6 Honda/UCSD数据库中的样本图像 Fig. 6 Sample images in the Honda/UCSD database

 /% 样本数目m KLD MSM KMSM 本文SVM 4 54.678 63.158 79.825 88.596 8 85.371 85.088 82.164 94.444 12 92.690 90.936 83.333 95.322 16 93.860 92.105 85.673 95.906

 图 7 在Honda/UCSD数据库上的识别率 Fig. 7 Recognition results on the Honda/UCSD database

5 结束语

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DOI: 10.3969/j.issn.1673-4785.201312040

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#### 文章信息

LI Huan, WANG Shitong

Binary-class classification algorithm with multiple-access acquired objects based on the SVM

CAAI Transactions on Intelligent Systems, 2014, 9(4): 392-400
http://dx.doi.org/10.3969/j.issn.1673-4785.201312040