Abstract
Error-correcting output codes (ECOC) can effectively reduce the multiclass to the binary and is attracting close attention, in which the construction of coding matrix based on data is the key to use ECOC to solve multiclass problems. An approach to the hierarchical error-correcting output codes based on support vector data description is presented in this paper. The main idea of the work is to construct the data-driven coding matrix with the help of support vector data description and binary tree. The support vector data description is used to measure the class separability quantitatively to obtain the inter-class separability matrix. And, a binary tree is built based on the matrixes from bottom to top. Then, each node of each layer is encoded to get the final hierarchical error-correcting output code. The independence of base classifiers trained by different encoding methods is compared in experiments. The results show that the proposed technique can promote the diversity of the base classifiers and enhance the classification accuracy.


References
Dietterich TG, Bakiri G (1995) Solving: multi-class learning problems via error-correcting output codes. J Artif Intell Res 34(2):263–286
Crammer K, Singer Y (2000) On the learnability and design of output codes for multiclass problems. In: Proceedings of the thirteenth annual conference on computational learning theory. Kluwer Academic Publishers, Boston, pp 896–909
Pujol O, Radeva P, Vitria J (2006) Discriminate ECOC: a heuristic method for application dependent design of error correcting output codes. IEEE Trans Pattern Anal Mach Intell 28(6):1001–1007
Escalera S, Tax DMJ, Pujol O, Duin RPW (2008) Subclass problem-dependent design for error-correcting output codes. IEEE Trans Pattern Anal Mach Intell 30(6):1041–1054
Escalera S, Masip D, Puertas E, Radeva P, Pujol O (2011) Online error correcting output codes. Pattern Recognit Lett 32:458–467
Simeone P, Marrocco C, Tortorella F (2012) Design of reject rules for ECOC classification systems. Pattern Recognit 2:863–875
Hatami N (2012) Thinned-ECOC ensemble based on sequential code shrinking. Expert Syst Appl 39(1):936–947
Escalera S, Pujol O (2013) Re-coding ECOCs without re-training. Pattern Recognit Lett 31(5):555–562
Wang Y, Chen S, Xue H (2012) Can under-exploited structure of original-classes help ECOC-based multi-class classification. Eeurocomputing 89(15):158–167
Masulli F, Valentini G (2003) Effectiveness of error correcting output coding methods in ensemble and monolithic learning machines. Pattern Anal Appl 6:285–300
Zhou J, Wang X (2010) Designing of output codes based on minimal k nearest neighbor classifying error and its application in multi-class classification. Control Decis 26(9):1296–1302
Tax David MJ, Duin Robert PW (1999) Support vector domain description: proceedings of the 1999 pattern recognition in practice. Pattern Recognit Lett 20(11–13):1191–1199
Tax David MJ, Duin Robert PW (2004) Support vector data description. Mach Learn 54(1):45–66
Liu Z, Li D et al. (2004) Hierarchical multi-category support vector machines based inter-class separability in feature space. Geomat Inf Sci Wuhan Univ 29(4):324–328
Garcia-Pedrajas N, Ortiz-Boyer D (2011) An empirical study of binary classifier fusion methods for multi-class classification. Inf Fus 12(2011):111–130
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This work is supported by National Science Foundation of China under grant 61273275 and 60975026.
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Lei, L., Xiao-dan, W., Xi, L. et al. Hierarchical error-correcting output codes based on SVDD. Pattern Anal Applic 19, 163–171 (2016). https://doi.org/10.1007/s10044-015-0455-5
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DOI: https://doi.org/10.1007/s10044-015-0455-5