N-ary Error Correcting Coding Scheme

The coding matrix design plays a fundamental role in the prediction performance of the error correcting output codes (ECOC)-based multi-class task. In many-class classification problems, e.g., fine-grained categorization, it is difficult to distinguish subtle between-class differences under existing coding schemes due to a limited choices of coding values. In this paper, we investigate whether one can relax existing binary and ternary code design to N -ary code design to achieve better classification performance. In particular, we present a novel N -ary coding scheme that decomposes the original multi-class problem into simpler multi-class subproblems, which is similar to applying a divide-and-conquer method. The two main advantages of such a coding scheme are as follows: (i) the ability to construct more discriminative codes and (ii) the flexibility for the user to select the best N for ECOC-based classification. We show empirically that the optimal N (based on classification performance) lies in [3, 10] with some trade-off in computational cost. Moreover, we provide theoretical insights on the dependency of the generalization error bound of an N -ary ECOC on the average base classifier generalization error and the minimum distance between any two codes constructed. Extensive experimental results on benchmark multi-class datasets show that the proposed coding scheme achieves superior prediction performance over the stateof-the-art coding methods.