Designing LDPC Codes for ECOC Classification Systems Claudio Marrocco and Francesco Tortorella Department of Electrical and Information Engineering Universit`a degli Studi di Cassino e del L.M. Via G. Di Biasio 43, 03043 Cassino (FR), Italia {c.marrocco,tortorella}@unicas.it Abstract. In this paper we analyze a framework for an ECOC clas- sification system founded on the use of LPDC codes, a class of codes well-known in Coding Theory. Such approach provides many advantages over traditional ECOC codings. First, codewords are generated in an al- gebraic way without requiring any selection of rows and columns of the coding matrix. Second, the decoding phase can be improved by exploit- ing the algebraic properties of the code. In particular, it is possible to detect and recover possible errors produced by the dichotomizers through an iterative mechanism. Some experiments have been accomplished with the focus on the parity-check matrix used to define the codewords of the LDPC code, so as to determine how the code parameters influence the performance of the proposed approach. Keywords: ECOC, LDPC codes, Ensemble Methods. 1 Introduction To face a classification problem with several possible classes the most immediate way is to build a single monolithic classifier capable of producing multiple outputs. However, over the last years, a widely diffused technique consists in decomposing the original problem into a set of two-class problems that can be faced through an ensemble of two-class classifiers. The rationale of this approach relies on the stronger theoretical roots characterizing dichotomizers and makes it possible to employ some very effective classifiers, such as AdaBoost or Support Vector Ma- chines, which are not capable to directly perform multiclass classification. In this context, the most simple approach is One-vs-All that subdivides an n- class problem into n two-class problems each one isolating a class from the others. Another approach, suggested by [11], is One-vs-One that defines as many binary problems as the possible pairs of different classes so dividing the n-class problem into a set of n(n - 1)/2 two-class problems. A further technique that emerged for its good generalization capabilities is the Error Correcting Output Coding (ECOC) [5]. ECOC is commonly used for many applications in the field of Pattern Recognition and Data Mining such as text classification [10] or face recognition and verification [20,13]. A bit string P. Fr¨anti et al. (Eds.): S+SSPR 2014, LNCS 8621, pp. 454–463, 2014. c  Springer-Verlag Berlin Heidelberg 2014