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摘要: 针对特征子集区分度准则(Discernibility of feature subsets, DFS)没有考虑特征测量量纲对特征子集区分能力影响的缺陷, 引入离散系数, 提出GDFS (Generalized discernibility of feature subsets)特征子集区分度准则. 结合顺序前向、顺序后向、顺序前向浮动和顺序后向浮动4种搜索策略, 以极限学习机为分类器, 得到4种混合特征选择算法. UCI数据集与基因数据集的实验测试, 以及与DFS、Relief、DRJMIM、mRMR、LLE Score、AVC、SVM-RFE、VMInaive、AMID、AMID-DWSFS、CFR和FSSC-SD的实验比较和统计重要度检测表明: 提出的GDFS优于DFS, 能选择到分类能力更好的特征子集.Abstract: To overcome the deficiencies of the discernibility of feature subsets (DFS) which cannot take into account the influences from different attribute scales on the discernibility of a feature subset, the generalized DFS, shorted as GDFS, is proposed in this paper by introducing the coefficient of variation. The GDFS is combined with four search strategies, including sequential forward search (SFS), sequential backward search (SBS), sequential forward floating search (SFFS) and sequential backward floating search (SBFS) to develop four hybrid feature selection algorithms. The extreme learning machine (ELM) is adopted as a classification tool to guide feature selection process. We test the classification capability of the feature subsets detected by GDFS on the datasets from UCI machine learning repository and on the classic gene expression datasets, and compare the performance of the ELM classifiers based on the feature subsets by GDFS, DFS and classic feature selection algorithms including Relief, DRJMIM, mRMR, LLE Score, AVC, SVM-RFE, VMInaive, AMID, AMID-DWSFS, CFR, and FSSC-SD respectively. The statistical significance test is also conducted between GDFS, DFS, Relief, DRJMIM, mRMR, LLE Score, AVC, SVM-RFE, VMInaive, AMID, AMID-DWSFS, CFR, and FSSC-SD. Experimental results demonstrate that the proposed GDFS is superior to the original DFS. It can detect the feature subsets with much better capability in classification performance.
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图 1 DFS+SFS算法的5-折交叉验证实验结果
Fig. 1 The 5-fold cross-validation experimental results of DFS+SFS
图 4 DFS+SBFS算法的5-折交叉验证实验结果
Fig. 4 The 5-fold cross-validation experimental results of DFS+SBFS
图 2 DFS+SBS算法的5-折交叉验证实验结果
Fig. 2 The 5-fold cross-validation experimental results of DFS+SBS
图 3 DFS+SFFS算法的5-折交叉验证实验结果
Fig. 3 The 5-fold cross-validation experimental results of DFS+SFFS
图 5 各特征选择算法的Nemenyi检验结果
Fig. 5 Nemenyi test results of 13 feature selection algorithms in terms of performance metrics of ELM built on their selected features
表 1 实验用UCI数据集描述
Table 1 Descriptions of datasets from UCI
数据集 样本个数 特征数 类别数 iris 150 4 3 thyroid-disease 215 5 3 glass 214 9 2 wine 178 13 3 Heart Disease 297 13 3 WDBC 569 30 2 WPBC 194 33 2 dermatology 358 34 6 ionosphere 351 34 2 Handwrite 323 256 2 
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表 2 GDFS+SFS与DFS+SFS算法的5-折交叉验证实验结果
Table 2 The 5-fold cross-validation experimental results of GDFS+SFS and DFS+SFS algorithms
Data sets #原特征 #选择特征 测试准确率 GDFS DFS GDFS DFS iris 4 2.2 3 0.9733 0.9667 thyroid-disease 5 1.4 1.6 0.9163 0.9070 glass 9 2.4 3.2 0.9346 0.9439 wine 13 3.6 3.6 0.9272 0.8925 Heart Disease 13 2.8 3.4 0.5889 0.5654 WDBC 30 3.4 6.2 0.9227 0.9193 WPBC 33 1.8 2 0.7835 0.7732 dermatology 34 4.6 5 0.7151 0.6938 ionosphere 34 4.4 3 0.9029 0.8717 Handwrite 256 7.4 7.2 0.9657 0.9440 平均 43.1 3.4 3.82 0.8630 0.8478
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表 5 GDFS+SBFS与DFS+SBFS算法的5-折交叉验证实验结果
Table 5 The 5-fold cross-validation experimental results of GDFS+SBFS and DFS+SBFS algorithms
Data sets #原特征 #选择特征 测试准确率 GDFS DFS GDFS DFS iris 4 2.4 2.8 0.98 0.9667 thyroid-disease 5 2.4 2.2 0.9395 0.9209 glass 9 5.4 4 0.8979 0.9490 wine 13 9.2 9.4 0.6519 0.6086 Heart Disease 13 5.4 6.4 0.5757 0.5655 WDBC 30 22.8 24.6 0.8911 0.8893 WPBC 33 24.6 25.4 0.7681 0.7319 dermatology 34 28.2 27.2 0.9444 0.9362 ionosphere 34 28.4 26.2 0.9174 0.9087 Handwrite 256 137.4 148 0.9938 0.9722 平均 43.1 26.62 27.62 0.8560 0.8449
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表 3 GDFS+SBS与DFS+SBS算法的5-折交叉验证实验结果
Table 3 The 5-fold cross-validation experimental results of GDFS+SBS and DFS+SBS algorithms
Data sets #原特征 #选择特征 测试准确率 GDFS DFS GDFS DFS iris 4 2.6 3.2 0.9867 0.9733 thyroid-disease 5 2.8 3.2 0.9269 0.9070 glass 9 8.2 6.8 0.9580 0.9375 wine 13 12 11.6 0.6855 0.6515 Heart Disease 13 11.8 11.8 0.5490 0.5419 WDBC 30 28 28.8 0.8981 0.8616 WPBC 33 30.8 31.6 0.7785 0.7633 dermatology 34 31 31 0.9443 0.9303 ionosphere 34 31.8 32.2 0.9031 0.8947 Handwrite 256 245 248.6 1 0.9936 平均 43.1 40.4 40.88 0.8630 0.8455
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表 4 GDFS+SFFS与DFS+SFFS算法的5-折交叉验证实验结果
Table 4 The 5-fold cross-validation experimental results of GDFS+SFFS and DFS+SFFS algorithms
Data sets #原特征 #选择特征 测试准确率 GDFS DFS GDFS DFS iris 4 2.8 3 0.9867 0.9667 thyroid-disease 5 2.2 2.2 0.9395 0.9349 glass 9 4.2 4.4 0.9629 0.9442 wine 13 4.2 4.4 0.9261 0.9041 Heart Disease 13 4.4 4.8 0.5928 0.5757 WDBC 30 11 11.4 0.9385 0.9074 WPBC 33 5.8 4.4 0.7943 0.7886 dermatology 34 16.8 17.4 0.9522 0.9552 ionosphere 34 9.6 10.2 0.9173 0.9231 Handwrite 256 42.2 40.8 0.9907 0.9846 平均 43.1 10.32 10.3 0.8992 0.8885
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表 6 实验使用的基因数据集描述
Table 6 Descriptions of gene datasets using in experiments
数据集 样本数 特征数 类别数 Colon 62 2000 2 Prostate 102 12625 2 Myeloma 173 12625 2 Gas2 124 22283 2 SRBCT 83 2308 4 Carcinoma 174 9182 11
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表 7 各算法在表6基因数据集的5-折交叉验证实验结果
Table 7 The 5-fold cross-validation experimental results of all algorithms on datasets from Table 6
Data sets 算法 特征数 Accuracy AUC recall precision F-measure F2-measure Colon GDFS+SFFS 5.2 0.7590 0.8925 0.9 0.7 0.78 0.4133 DFS+SFFS 5.4 0.7256 0.78 0.8250 0.6856 0.7352 0.2332 Relief 8 0.7231 0.7575 0.9 0.6291 0.7396 0.16 DRJMIM 13 0.7282 0.7825 0.8750 0.6642 0.7495 0.3250 mRMR 5 0.7602 0.7325 0.85 0.6281 0.7185 0.1578 LLE Score 7 0.7577 0.6563 0.8750 0.6537 0.7431 0.2057 AVC 2 0.7256 0.7297 0.86 0.6439 0.7256 0.2126 SVM-RFE 5 0.7577 0.7588 0.75 0.6273 0.6775 0.3260 VMInaive 2 0.7423 1 1 0.6462 0.7848 0 AMID 8 0.7436 0.95 0.95 0.6328 0.7581 0 AMID-DWSFS 2 0.8397 0.9875 0.9750 0.6688 0.7895 0.1436 CFR 3 0.7603 0.95 1 0.6462 0.7848 0 FSSC-SD 2 0.7269 0.9750 0.9750 0.6401 0.7721 0 Prostate GDFS+SFFS 6.4 0.9305 0.9029 0.8836 0.8836 0.8829 0.8818 DFS+SFFS 6.6 0.9105 0.9349 0.8816 0.8818 0.8529 0.8497 Relief 11 0.93 0.8525 0.8255 0.7824 0.7981 0.79 DRJMIM 9 0.94 0.8629 0.7891 0.8747 0.8216 0.83 mRMR 12 0.9414 0.7895 0.7327 0.7816 0.7520 0.7597 LLE Score 26 0.9119 0.6796 0.7291 0.6582 0.6847 0.6616 AVC 12 0.9514 0.8144 0.7655 0.7598 0.7592 0.7573 SVM-RFE 22 0.92 0.8453 0.6927 0.8474 0.7567 0.7824 VMInaive 9 0.9419 0.8605 0.7655 0.7418 0.7481 0.7580 AMID 27 0.9314 0.7929 0.7655 0.7936 0.7690 0.7797 AMID-DWSFS 4 0.9514 0.7251 0.7127 0.7171 0.7011 0.7098 CFR 7 0.9410 0.7840 0.88 0.7430 0.7922 0.7942 FSSC-SD 23 0.9024 0.7796 0.8018 0.8205 0.7892 0.8130 Myeloma GDFS+SFFS 9.6 0.7974 0.6805 0.8971 0.8230 0.8558 0.5463 DFS+SFFS 9.8 0.7744 0.6296 0.8971 0.8047 0.8474 0.3121 Relief 23 0.8616 0.6453 0.8693 0.8225 0.8415 0.4631 DRJMIM 36 0.8559 0.6210 0.8392 0.7881 0.8124 0.2682 mRMR 12 0.8436 0.6332 0.8095 0.8046 0.8067 0.3539 LLE Score 64 0.8492 0.6169 0.9127 0.7909 0.8461 0.2313 AVC 22 0.8329 0.5820 0.8974 0.8098 0.8501 0.3809 SVM-RFE 20 0.8330 0.6270 0.8971 0.7935 0.8416 0.3846 VMInaive 19 0.8383 0.5639 0.8847 0.7902 0.8331 0.2691 AMID 11 0.8325 0.6743 0.8979 0.8282 0.8603 0.5254 AMID-DWSFS 38 0.8381 0.6233 0.8381 0.8197 0.8249 0.5224 CFR 14 0.8504 0.5931 0.9124 0.8014 0.8523 0.3010 FSSC-SD 15 0.8381 0.6662 0.8754 0.8173 0.8438 0.4992 Gas2 GDFS+SFFS 7.4 0.9840 0.9704 0.9051 0.9846 0.9412 0.9474 DFS+SFFS 8.4 0.9429 0.9465 0.9064 0.9212 0.9203 0.9018 Relief 4 0.9763 0.9520 0.8577 0.9316 0.8911 0.9005 DRJMIM 19 0.9750 0.9004 0.8192 0.8848 0.8449 0.8584 mRMR 5 0.9756 0.9358 0.8551 0.9131 0.8815 0.8895 LLE Score 25 0.9769 0.9312 0.8659 0.8748 0.8449 0.8538 AVC 3 0.9840 0.9073 0.8897 0.9390 0.9122 0.9160 SVM-RFE 18 0.9756 0.9009 0.8205 0.9052 0.8503 0.8716 VMInaive 10 0.9763 0.9425 0.7372 0.9778 0.8311 0.8778 AMID 16 0.9833 0.9305 0.9205 0.8829 0.8968 0.9013 AMID-DWSFS 2 0.9840 0.9247 0.8359 0.9424 0.8839 0.8977 CFR 10 0.9917 0.9080 0.9013 0.8236 0.8432 0.8434 FSSC-SD 16 0.9596 0.9095 0.8538 0.8758 0.8555 0.8642 SRBCT GDFS+SFFS 11.6 0.9372 0.9749 0.9567 0.9684 0.9579 0.9573 DFS+SFFS 11.6 0.9034 0.9130 0.9356 0.9449 0.9452 0.9352 Relief 10 0.9631 0.9479 0.9439 0.9589 0.9467 0.9390 DRJMIM 4 0.9389 0.9363 0.9656 0.9511 0.9555 0.9503 mRMR 8 0.9528 0.9479 0.9283 0.9624 0.9275 0.9294 LLE Score 11 0.9271 0.8941 0.9333 0.9332 0.9247 0.9154 AVC 8 0.9042 0.9355 0.9139 0.9544 0.9223 0.9183 SVM-RFE 13 0.8421 0.9149 0.9128 0.9385 0.9159 0.8240 VMInaive 14 0.9409 0.9181 0.9250 0.9429 0.9269 0.9188 AMID 13 0.9387 0.8999 0.9567 0.9335 0.9407 0.9239 AMID-DWSFS 9 0.9167 0.8151 0.8178 0.8516 0.82 0.7466 CFR 8 0.9314 0.6839 0.8994 0.8570 0.8693 0.7150 FSSC-SD 6 0.8806 0.9096 0.9267 0.9422 0.9284 0.9160 Carcinoma GDFS+SFFS 23.4 0.7622 0.9037 0.7872 0.7879 0.7839 0.5570 DFS+SFFS 19.4 0.7469 0.8998 0.7808 0.7869 0.7801 0.6261 Relief 42 0.7351 0.8701 0.7687 0.7785 0.7680 0.5392 DRJMIM 13 0.7757 0.8991 0.6742 0.6621 0.6656 0.4557 mRMR 24 0.8079 0.9188 0.7613 0.7505 0.7533 0.5089 LLE Score 76 0.6682 0.8452 0.6689 0.6702 0.6663 0.4109 AVC 77 0.7227 0.8746 0.7872 0.7790 0.7796 0.5068 SVM-RFE 30 0.7213 0.87 0.7027 0.6933 0.6929 0.4065 VMInaive 33 0.7443 0.8784 0.7487 0.7527 0.7441 0.4731 AMID 42 0.7307 0.8878 0.7295 0.7165 0.7194 0.4841 AMID-DWSFS 38 0.7412 0.6231 0.7558 0.7447 0.7457 0.4255 CFR 33 0.7054 0.6216 0.7514 0.74 0.7410 0.5315 FSSC-SD 21 0.7306 0.8716 0.7039 0.7016 0.6992 0.4344
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表 8 各算法所选特征子集分类能力的Friedman检测结果
Table 8 The Friedman＇s test of the classification capability of feature subsets of all algorithms
Accuracy AUC recall precision F-measure F2-measure ${\chi ^2}$ 23.4094 27.5527 22.1585 29.2936 26.7608 32.5446 df 12 12 12 12 12 12 p 0.0244 0.0064 0.0358 0.0036 0.0084 0.0011
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