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• Replace hard codematrix with soft codematrix. • Use the regression outputs of the base classifiers to replace the traditional classification outputs. • Iteratively softens codematrix elements using global loss tuning. • Conveniently merge the proposed algorithm into other ECOC algorithms to further improve performance. The technique of error-correcting output codes (ECOC) has been proven to be of high discriminative ability in many classification applications. However, most algorithms on the ECOC were designed based on the binary or ternary codes (referred to as the hard codes), which might fail to precisely correct errors in dealing with tough tasks. In this study, a Soft-Recoding strategy based on a self-adaptive algorithm is proposed, which replaces the traditional hard codes with the real-value elements to better fit the output distribution of the base learners. This is achieved by minimizing the ratio of two distances: the distance of the output vector to the ground-truth class, and the average distance of the output vector to the remaining classes. Extensive experiments using five different hard ECOC algorithms and the corresponding softened versions on twenty datasets with diversified numbers of features and classes confirm the effectiveness of our Soft-Recoding strategy in promoting the performance of the original ECOC algorithms. Our source code and additional results are available at: github.com/MLDMXM2017/SA-soft-recoding. [ABSTRACT FROM AUTHOR]

Highlights • We proposed a novel ECOC algorithm for multiclass microarray data classification based on the data complexity theory. • Various data complexity measures are deployed to detect the intrinsic characteristics of microarray data sets, so as to produce diverse coding matrices. • A new data complexity measure, named as C1, is designed to evaluate data distribution. It benefits the optimization process of our class partition. • The proposed ECOC algorithm performs more stably in most multiclass microarray data sets compared with other popular ECOC algorithms. Abstract Nowadays, a lot of new classification and clustering techniques have been proposed for microarray data analysis. However, the multiclass microarray data classification is still regarded as a tough task because of the small sample size problem and the class imbalance problem. In this paper, we propose a novel error correcting output code (ECOC) algorithm for the classification of multiclass microarray data based on the data complexity (DC) theory. In this algorithm, an ECOC coding matrix is generated based on a hierarchical partition of the class space with the aim of Minimizing Data Complexity (named as ECOC-MDC). As the partition process can be mapped as a binary tree, a compact ensemble with high discrimination power is produced. The performance of ECOC-MDC is compared with some state-of-art ECOC algorithms on six multiclass microarray data sets, and it is found that the proposed algorithm can obtain better results in most cases. The correlation between DC measures and the dichotomizers' performances is checked, and the observations confirm that high complexity in data usually leads to high error rates of the connected dichotomizers. But the error correcting mechanism in the ECOC framework can effectively improve our algorithm's generalization ability. In short, ECOC-MDC can produce a compact ensemble system with high error correction capability through the application of diverse DC measures. Our Matlab code is available at: github.com/MLDMXM2017/ECOC-MDC. [ABSTRACT FROM AUTHOR]