传统的欠采样方法容易丢失重要的样本信息，且其实验结果的稳定性较差。针对上述问题，提出一种基于类重叠度欠采样的不平衡数据模糊多类支持向量机算法。该算法首先采用LOF局部离群点因子和箱线图的方法清洗训练数据集中的噪声样本，然后根据类重叠度抽取对分类起关键作用的支持向量，并且将代表每个样本点重要程度的类重叠度作为隶属度值，构造模糊多类支持向量机。实验结果表明，该算法克服了随机欠采样的支持向量机容易丢失重要样本信息和实验结果不稳定的缺点，且很好地提升了支持向量机在不平衡且含噪声的数据集上的分类精度，并保持较高的计算效率。
Undersampling is a commonly-used method for data reconstruction. This method is used to solve the problem of imbalanced data classification. However, the traditional undersampling method often loses important sample information, and lacks stabilities of experimental results. To settle these two problems, this paper proposes an imbalanced fuzzy multiclass support vector machine algorithm based on class-overlap degree undersampling. This algorithm combines LOF local outlier factor and box-whisker plot to delete noise samples in the training datasets, then extracts support vectors based on class-overlap degree. Finally, the class-overlap degree of each sample is set as the membership value of this sample, and the fuzzy multiclass support vector machine is constructed. Experimental results show that our algorithm overcomes the disadvantages that the support vector machine with random undersampling often loses the important sample information and the unstabilities of experimental results. In addition, our algorithm improves the classification accuracy of support vector machine in imbalanced and noisy datasets.
[1] Cortes C, Vapnik V. Support-vector networks[J]. Machine Learning, 1995, 20(3):273-297.
[2] 康健,左宪章,唐力伟,等.基于灰色支持向量机的裂纹扩展信息预测研究[J].机械强度, 2010, 32(5):120-123.
[3] Cao L J,Lee H P,Chong W K. Modified support vector novelty detector using training data with outliers[J]. Pattern Recognition Letters, 2003, 24(14):2479-2487.
[4] Wang B X, Japkowicz N. Boosting support vector machines for imbalanced data sets[J]. Knowledge and Information Systems, 2010, 25(1):1-20.
[5] Lin C F, Wang S D. Fuzzy support vector machines[J]. IEEE Transactions on Neural Networks, 2002, 13(2):464-471.
[6] Huang H P, Liu Y H. Fuzzy support vector machine for pattern recognition and data mining[J]. International Journal of Fuzzy Systems, 2002, 4(3):826-835.
[7] Jiang X, Yi Z, Lü J C. Fuzzy SVM with a new fuzzy membership function[J]. Neural Computing & Applications, 2006, 15(3):268-276.
[8] Castillo B, Gennaro S D, Monaco S, et al. On regulation under sampling[J]. IEEE Transactions on Automatic Control, 1997, 42(6):864-868.
[9] 韩家炜. 数据挖掘:概念与技术[M].北京:机械工业出版社, 2012:1-3.
[10] McClave J Y, Benson P G, Sincich T. 商务与经济统计学[M]. 易丹辉,李扬,译.北京:中国人民大学出版社, 2014:67-69.
[11] Chawla N V, Bowyer K W, Hall L O, et al. SMOTE:synthetic minority over-sampling technique[J]. Journal of Artificial Intelligence Research, 2011, 16(1):321-357.
[12] Chen L, Bao L, Li J, et al. An aliasing artifacts reducing approach with random undersampling for spatiotemporally encoded single-shot MRI[J]. Journal of Magnetic Resonance, 2013, 237(6):115-124.
[13] Kubat M, Matwin S. Addressing the curse of imbalanced training sets:one-sided selection[C]//Fisher D H. 14th International Conference on Machine Learning. San Francisco:MorganKaufmann Press, 1997:179-186.
[14] 谢纪刚,裘正定.非平衡数据集Fisher线性判别模型[J].北京交通大学学报, 2006, 30(5):15-18.
[15] 瞿俊,姜青山,翁芳菲. 基于重叠度的层次聚类算法[J].计算机研究与发展, 2007, 44(s2):181-186.
[16] Crammer K, Singer Y. On the algorithmic implementation of multiclass kernel-based vector machines[J]. Journal of Machine Learning Research, 2001, 2(2):265-292.
[17] 浮盼盼.大规模不均衡数据分类方法研究[D]. 大连:辽宁师范大学, 2014.
[18] Veropoulos K, Campbell C, Cristianini N. Controlling the sensitivity of support vector machines[C]//International Joint Conference on Artificial Intelligence. Stockholm:IJCAI Press, 1999:55-60.
[19] Batuwita R, Palade V. FSVM-CIL:fuzzy support vector machines for class imbalance learning[J]. IEEE Transactions on Fuzzy Systems, 2010, 18(3):558-571.
