Separability of ternary codes for sparse designs of error-correcting output codes

Error-correcting output codes (ECOC) represent a successful framework to deal with multi-class categorization problems based on combining binary classifiers. With the extension of the binary ECOC to the ternary ECOC framework, ECOC designs have been proposed in order to better adapt to distributions of the data. In order to decode ternary matrices, recent works redefined many decoding strategies that were formulated to deal with just two symbols. However, the coding step also is affected, and therefore, it requires to be reconsidered. In this paper, we present a new formulation of the ternary ECOC distance and the error-correcting capabilities in the ternary ECOC framework. Based on the new measure, we stress on how to design coding matrices preventing codification ambiguity and propose a new sparse random coding matrix with ternary distance maximization. The results on a wide set of UCI Machine Learning Repository data sets and in a real speed traffic sign categorization problem show that when the coding design satisfies the new ternary measures, significant performance improvement is obtained independently of the decoding strategy applied.