Abstract
Error correcting output codes (ECOCs) is a powerful framework to solve the multi-class problems. Finding the optimal partitions with maximum class discrimination efficiently is a key point to improve its performance. In this paper, we propose an alternative and efficient approach to obtain the partitions which are discriminative in the class space. The main idea of the proposed method is to transform the partition in the class space into the cut for an undirected graph using spectral clustering. In addition to measuring the class similarity, the confusion matrix with a pre-classifier is used. Our method is compared with the classical ECOC and DECOC over a synthetic dataset, a set of UCI machine learning repository datasets and one face recognition application. The results show that our proposal is able to obtain comparable or even better classification accuracy while reducing the computational complexity in comparison with the state-of-the-art coding methods.






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References
Mathias M, Timofte R, Benenson R, Gool LV (2013) Traffic sign recognition—how far are we from the solution? International joint conference on neural networks (IJCNN), ESAT-PSI/iMinds, University of Leuven, Leuven, Belgium, pp 1–8
Dehzangi O, Ma B, Chng ES, Li H (2012) Discriminative feature extraction for speech recognition using continuous output codes. Pattern Recogn Lett 33:1703–1709
Windeatt T, Ardeshir G (2003) Boosted ECOC ensembles for face recognition. Pattern Recogn 35(4):165–168
Yu J, Rui Y, Tang YY, Tao D (2014) High-order distance-based multiview stochastic learning in image classification. IEEE Trans Cybern 44(12):2431–2442. doi:10.1109/TCYB.2014.2307862
Yu J, Rui Y, Chen B (2014) Exploiting click constraints and multi-view features for image re-ranking. IEEE Trans Multimed 16(1):159–168. doi:10.1109/TMM.2013.2284755
Yu J, Rui Y, Tao D (2014) Click prediction for web image reranking using multimodal sparse coding. IEEE Trans Image Process 23(5):2019–2032. doi:10.1109/TIP.2014.2311377
Tao D, Lin X, Jin L, Li X (2015) Principal component 2-D long short-term memory for font recognition on single Chinese characters. IEEE Trans Cybern. doi:10.1109/TCYB.2015.2414920
Tao D, Li X, Wu X, Maybank SJ (2007) General tensor discriminant analysis and gabor features for gait recognition. IEEE Trans Pattern Anal Mach Intell 29(10):1700–1715. doi:10.1109/TPAMI.2007.1096
Anand R, Mehrotra K, Mohan CK, Ranka S (1995) Efficient classification for multiclass problems using modular neural networks. IEEE Trans Neural Netw 6(1):117–124
Clark P, Boswell R (1991) Rule induction with CN2: Some recent improvements. In: Kodratoff Y (ed) Machine LEARNING—EWSL-91, vol 482., Lecture Notes in Computer ScienceSpringer, Berlin, pp 151–163
Dietterich T, Bakiri G (1995) Solving multiclass learning problems via error-correcting output codes. J Artif Intell Res 2(1):263–268
Pujol O, Radeva P, Vitria J (2006) Discriminant ECOC: a heuristic method for application dependent design of error correcting output codes. IEEE Trans Pattern Anal Mach Intell 28(6):1007–1012
Escalera S, Tax DMJ, Pujol O, Radeva P, Duin RPW (2008) Subclass problem-dependent design for error-correcting output codes. IEEE Trans Pattern Anal Mach Intell 30(6):1041–1053. doi:10.1109/TPAMI.2008.38
Ali-Bagheri M, Ali-Montazer G, Kabir E (2013) A subspace approach to error correcting output codes. Pattern Recogn Lett 34:176–184
Angel-Bautista M, Escalera S, Baro X, Pujol O (2014) On the design of an ECOC-Compliant Genetic Algorithm. Pattern Recogn 47:865–884
Crammer K, Singer Y (2002) On the learnability and design of output codes for multiclass problems. Mach Learn 47:201–233
Masulli F, Valentini G (2003) Effectiveness of error correcting output coding methods in ensemble and monolithic learning machines. Pattern Anal Appl 6:285–300. doi:10.1007/s10044-003-195-9
Garcia-Pedrajas N, Fyfe C (2008) Evolving output codes for multiclass problems. IEEE Trans Evol Comput 12(1):93–106. doi:10.1109/TEVC.2007.894201
Ali-Bagheri M, Gao Q, Escalera S (2013) A genetic-based subspace analysis method for improving error-correcting output coding. Pattern Recogn 46:2830–2839
Valentini G (2000) Upper bounds on the training error of ECOC SVM ensembles. Technical Report DISI-TR-00-17, Dipartimento di Informatica e Science dell’ Informazione, Universita di Genova
Kong E, Dietterich TG (1995) Error-correcting output coding correct bias and variance. In: The XII international conference on machine learning, San Francisco, CA, pp. 313–321
Zhang X, Liang L, Shum HY (2009) Spectral error correcting output codes for efficient multiclass recognition. In: IEEE 12th international conference on computer vision (ICCV)
Duda RO, Hart PE, Stork DG (2001) Pattern classification. Wiley, New York
Luxburg UV (2007) A tutorial on spectral clustering. Stat Comput 17(4):395–416. doi:10.1007/s11222-007-9033-z
Wang X, Yao X, Zhou J (2012) An approach of constructing ECOC adaptively based on confusion matrix. In: 2nd international conference on computer science and network technology, ChangChun, China
Asuncion A, Newman D (2007) UCI machine learning repository. University of California, Irvine, School of Information and Computer Sciences
Samaria F, Harter A (1994) Parameterization of a stochastic model for human face identification. In: IEEE workshop on applications of computer vision. Sarasota (Florida)
Escalera S, Pujol O, Radeva P (2010) ECOCs library. J Mach Learn Res 11:661–664
Griffin P, Holub G, Perona AD The Caltech 256, Caltech Technical Report. http://www.vision.caltech.edu/Image_Datasets/Caltech256
The ImageNet. http://www.image-net.org
Demsar J (2006) Statistical comparisons of classifiers over multiple data sets. J Mach Learn Res 7:1–30
Weiss GM, Provost F (2003) Learning when training data are costly: the effect of class distribution on tree induction. J Artif Intell Res 19:315–354
Duin RPW, Juszczak P, Paclik P, Pekalska E, de Ridder D, Tax DMJ, Verzakov S (2007) PRTools4.1, a matlab toolbox for pattern recognition. Delft University of Technology
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Xue, A., Wang, X., Song, Y. et al. Discriminant error correcting output codes based on spectral clustering. Pattern Anal Applic 20, 653–671 (2017). https://doi.org/10.1007/s10044-015-0523-x
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DOI: https://doi.org/10.1007/s10044-015-0523-x