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摘要: 近来, 稀疏表示分类算法已经在模式识别和特征提取领域获得了广泛的关注. 受最近提出的稀疏表示判别投影算法启发, 本文提出了一种新的特征加权组稀疏判别投影算法(Feature weighted group sparse classification steered discriminative projection, FWGSDP). 首先, 提出特征加权组稀疏分类算法(Feature weighted group sparsebased classification, FWGSC)进行稀疏系数编码, 该算法采用带特征加权约束的保局性信息, 能够鲁棒地重构给定的输入数据; 其次, 通过类内重构散度最小、类间重构散度最大为目标计算最优投影判别矩阵, 使得输入数据具有最佳的模式分类效果; 最后, 提出迭代重约束稀疏编码方法并结合特征分解操作进行FWGSDP模型高效求解. 在ExYaleB, PIE和AR三个人脸数据库的实验验证了所提算法在普通数据和带噪数据中的分类效果都优于现存的算法.Abstract: Recently, sparse representation classification (SRC) has attracted more and more attention in pattern recognition and feature extraction. Motivated by the recent developed SRC steered discriminative projection algorithm, a new feature weighted group sparse discriminative projection algorithm (FWGSDP) is proposed in this paper. First, sparse coefficients are produced by a new proposed feature weighted group sparse representation classification algorithm (FWGSC), which can robustly regress a given signal with regularized regression coefficients by introducing the feature weighted locality structure of the data. Second, FWGSDP maximizes the subtraction of inter-class reconstruction residual and intra-class reconstruction residual, and thus enables data-in to achieve better separation. Finally, a sequentially iteratively re-restrained sparse coding and eigen-decomposition strategy is developed to solve the FWGSDP model efficiently. Experimental results on the ExYaleB, the PIE, and the AR database demonstrate that the proposed algorithm is more effective than other feature extraction methods.
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Key words:
- Sparse representation /
- locality-constraint /
- group sparse /
- discriminative projection
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图 2 稀疏型分类器在不同数据库中识别率对比
Fig. 2 The recognition rates of different sparse representation classifiers in ExYaleB and PIE databases
图 4 不同子空间维数的人脸识别率和方差对比
Fig. 4 Comparison of recognition rates and variance under different feature dimensions
图 5 PIE中FWGSC参数λ和τ选择
Fig. 5 The selection of parameter λ and τ of FWGSC in PIE database
表 1 AR数据库有遮挡情形下不同算法的识别率对比
Table 1 Recognition rate by competing algorithms on AR database with occlusion
测试样本 算法 墨镜遮挡（％) 围巾遮挡（％) FWGSC 99.3 95.7 RRC 99.0 94.7 同时期 CESR 95.3 38.0 GSRC 87.3 85.0 SRC 89.3 32.3 FWGSC 89.3 78.3 RRC 89.3 76.3 不同时期 CESR 79.0 20.7 GSRC 45.0 66.0 SRC 57.3 12.7 
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表 2 降维前后FWGSC分类算法的人脸识别对比
Table 2 Comparison of FWGSC performance with and without dimension reduction
唯数 ExYaleB PIE 识别率(%) 测试时间(s) 识别率(%) 测试时间(s) 原始样本1024 97.34 0.9983 95.69 1.4002 FWGSDP 100 95.04 0.1103 93.62 0.4683 FWGSDP200 96.25 0.1170 95.20 0.4896 FWGSDP300 97.44 0.1215 95.80 0.5046 FWGSDP 400 97.61 0.1286 95.89 0.5175 FWGSDP500 97.61 0.1332 95.95 0.5296
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表 3 AR数据库有遮挡情形下不同算法的识别率对比
Table 3 Comparison of competing dimension reduction algorithms on AR database with occlusion
测试样本 算法 墨镜遮挡识别率(%) 墨镜遮挡耗时(s) 围巾遮挡识别率(%) 围巾遮挡耗时(s) PCA 91.0 1.083 85.7 1.184 LPP 92.5 2.810 89.6 2.672 同时期 LFDA 93.4 4.380 91.5 4.253 SRCDP 92.8 21.27 58.4 21.96 FWGSDP 99.5 14.72 96.0 14.03 PCA 84.6 1.079 70.6 1.067 LPP 87.3 2.714 75.1 2.705 不同时期 LFDA 86.5 4.525 75.4 4.361 SRCDP 78.7 22.15 52.4 22.06 FWGSDP 90.8 15.18 79.6 14.98
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