Abstract Based on the concept of relative density degrees, a density-punished support vector data description method is presented. The relative density degrees are associated with punishing misclassifications. If the relative density degree of the sample is large, it is likely to be a target sample. Thus, a large penalty should be put on its misclassification. Similarly, if the relative densitydegree of the sample is small, it might be a boundary or noise point so that the corresponding penalty for its misclassification should be small as well. The experimental results on UCI datasets show that the proposed method has better performance compared with support vector data description and density-induced support vector data description.
[1] Tax D M J, Duin R P W. Support Vector Domain Description. Pa-ttern Recognition Letters, 1999, 20(11/12/13): 1191-1199 [2] Tax D M J, Duin R P W. Support Vector Data Description. Machine Learning, 2004, 54(1): 45-66 [3] Zhang L, Zhou W D, Jiao L C. Wavelet Support Vector Machine. IEEE Trans on Systems, Man and Cybernetics, 2004, 34(1): 34-39 [4] Sch lkopf B, Burges C, Vapnik V N. Extracting Support Data for a Given Task // Proc of the 1st International Conference on Know-ledge Discovery and Data Mining. Menlo Park, USA, 1995: 252-257 [5] Tax D M J, Duin R W. Data Domain Description by Support Vectors // Proc of the 7th European Symposium on Artificial Neural Network. Bruges, Belgium, 1999: 251-256 [6] Lee K, Kim D W, Lee D, et al. Improving Support Vector Data Description Using Local Density Degree. Pattern Recognition, 2005, 38(10): 1768-1771 [7] Zhang L, Wang B J, Li F Z, et al. Support Vector Novelty Detection in Hidden Space. Journal of Computational Information Systems, 2011, 7(15): 5581-5590 [8] Yu X H, Pu K Q, Koudas N. Monitoring K-Nearest Neighbor Queries over Moving Objects // Proc of the 21st International Conference on Data Engineering. Tokyo, Japan, 2005: 631-642 [9] Xiong X P, Mokbel M F, Aref W G. SEA-CNN: Scalable Processing of Continuous K-Nearest Neighbor Queries in Spatio-Temporal Data-Bases // Proc of the 21st International Conference on Data Engineering. Tokyo, Japan, 2005: 643-654 [10] Markou M, Singh S. Novelty Detection: A Review-Part 1:Statistical Approaches. Signal Processing, 2003, 83(12): 2481-2497 [11] Markou M, Singh S. Novelty Detection: A Review-Part 2:Neural Network Based Approaches. Signal Processing, 2003, 83(12): 2499-2521 [12] Vapnik V N. The Nature of Statistical Learning Theory. New York, USA: Springer-Verlag, 1995 [13] Burges C J C. A Tutorial on Support Vector Machines for Pattern Recognition. Data Mining and Knowledge Discovery, 1998, 2 (2): 121-167 [14] Zhang L. The Research of Support Vector Machine and Kernel Function. Xi′an, China: Xidian University, 2002 (in Chinese) (张 莉.支撑矢量机与核方法研究.博士学位论文.西安:西安电子科技大学, 2002) [15] Campbell C, Bennett K P. A Linear Programming Approach to Novelty Detection // Proc of the Conference on Neural Information Processing Systems: Natural and Synthetic. Vancouver, Canada, 2001: 395-401 [16] Manevitz L M, Yousef M. One-Class SVMs for Document Classification. Journal of Machine Learning Research, 2001, 2: 139-154 [17] Tax D M J, Duin R P W. Uniform Object Generation for Optimizing One-Class Classifiers. Journal of Machine Learning Research, 2001, 2: 155-173 [18] Diehl C P, Hampshire J B II. Real-Time Object Classification and Novelty Detection for Collaborative Video Surveillance // Proc of the International Joint Conference on Neural Networks. Honolulu, USA, 2002, III: 2620-2625 [19] R tsch G, Mika S, Sch lkopf B, et al. Constructing Boosting Algorithms from SVMs: An Application for One-Class Classification. IEEE Trans on Pattern Analysis and Machine Intelligence, 2002, 24(9): 1184-1199 [20] Sch lkopf B, Platt J, Shawe-Taylor J, et al. Estimating the Su-pport of a High-Dimensional Distribution. Neural Computation, 2001, 13(7): 1443-1471 [21] Zhang L, Zhou W D, Lin Y, et al. Support Vector Novelty Detection with Dot Product Kernels for Non-Spherical Data // Proc of the International Conference on Information and Automation. Changsha, China, 2008: 41-46 [22] Lee K, Kim D W, Lee K H, et al. Density-Induced Support Vector Data Description. IEEE Trans on Neural Networks, 2007, 18(1): 284-289 [23] Kwok J T, Tsang I W, Zurada J M. A Class of Single-Class Mi-nimax Probability Machines for Novelty Detection. IEEE Trans on Neural Networks, 2007, 18(3): 778-785
2014, Vol. 27 
