Error-Correcting Output Codes (ECOC) is widely used in the field of multiclass classification. As an optimal codematrix is key to the performance of an ECOC algorithm, this paper proposes a genetic programming (GP) based ECOC algorithm (GP-ECOC). In the design of individual of our GP, each terminal node represents a class, and nonterminal nodes combine the classes in their child nodes. In this way, an individual is a class combination tree, and represents an ECOC codematrix. A legality checking process is embedded in our algorithm to check each codematrix, so as to ensure each codematrix satisfying ECOC constraints. Those violating the constraints will be corrected by a proposed Guided Mutation operator. Before fitness evaluation, a local optimization algorithm is proposed to append new columns for tough classes, so as to improve the generalization ability of each individual and accelerate the evolutionary speed. In this way, our GP can evolve optimal codematrices through the evolutionary process. Experiments show that compared with other ensemble algorithms, our algorithm can achieve stable and high performances with relatively small ensemble scales on various UCI data sets. To the best of our knowledge, it is the first time that GP has been applied to implement the ECOC encoding algorithm. Our Python code is available at https://github.com/samuellees/gpecoc.

纠错输出代码（ECOC）在多类分类领域中被广泛使用。由于最优码矩阵是ECOC算法性能的关键，因此本文提出了一种基于遗传编程（GP）的ECOC算法（GP-ECOC）。在我们GP的个人设计中，每个终端节点代表一个类，非终端节点在其子节点中组合这些类。这样，一个人就是一个类别组合树，并代表一个ECOC代码矩阵。我们的算法中嵌入了合法性检查过程，以检查每个码矩阵，以确保每个码矩阵都满足ECOC约束。违反约束条件的对象将由拟议的引导突变算子纠正。在进行适应度评估之前，提出了一种局部优化算法，以针对困难类别添加新列，从而提高每个人的泛化能力，加快进化速度。这样，我们的GP可以通过进化过程来进化最佳码矩阵。实验表明，与其他集成算法相比，在各种UCI数据集上，我们的算法可以以较小的集成比例实现稳定和高性能。据我们所知，这是GP首次用于实现ECOC编码算法。我们的Python代码可从https://github.com/samuellees/gpecoc获得。我们的算法可以在各种UCI数据集上以相对较小的整体规模实现稳定和高性能。据我们所知，这是GP首次用于实现ECOC编码算法。我们的Python代码可从https://github.com/samuellees/gpecoc获得。我们的算法可以在各种UCI数据集上以相对较小的整体规模实现稳定和高性能。据我们所知，这是GP首次用于实现ECOC编码算法。我们的Python代码可从https://github.com/samuellees/gpecoc获得。