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• The first attempt to design a GEP-based codematrix generation algorithm. The individual structure of GEP allows the codematrix to be optimized in a much faster and more effective way. • The feature selection scheme is combined with the design of codematrix, to accomplish the feature selection and codematrix optimization simultaneously. • A greedy strategy-based adaptive optimization method to further improve the individual's quality to deal with hard classes by appending proper columns to the codematrix. The multi-class classification task is one of the most common tasks in machine learning. As a typical solution based on a partitioning strategy, Error-Correcting Output Codes (ECOC) can transform a multi-class classification problem into multiple binary classification problems. The key of ECOC is to construct an effective codematrix to represent a set of class decomposition schemes, which transforms a multiclass problem into a group of binary class problems. Consequently, the design of a fast and effective ECOC codematrix generation method is of great research significance and value for solving multi-class classification problems. In ECOC algorithms, the design of codematrix is treated as a combination problem between different code columns, in which the evolutionary algorithm shows a great advantage. Based on this consideration, the Gene Expression Programming (GEP) is applied to search for the codematrix with high performance because its expressive tree structure makes it well represent codematrcies for subsequent optimization operations. This paper proposes an adaptive ECOC algorithm based on Gene Expression Programming (GEP) and similarity measurement matrix, named GEP-ECOC. In our GEP, each individual represents a set of columns to form a random ECOC codematrix, which is optimized in the evolutionary process. Meanwhile, the crossover and mutation operations are modified to include a legality checking process to ensure that the generated codematrix satisfies the ECOC constraints. The GEP-based ECOC codematrix generation algorithm can quickly produce a codematrix with better performance, which ensures the efficiency of the algorithm to a certain extent. In addition, an adaptive algorithm based on a similarity measurement matrix is proposed to add new columns to the current codematrix, aiming to better handle hard classes. Our algorithm is compared with other algorithms on various data sets, and the experimental results confirm that our GEP-ECOC can balance the efficiency and performance of the algorithm and achieve higher performance. [ABSTRACT FROM AUTHOR]

1 A new ECOC encoding algorithm is proposed, which separates classes into two groups by maximizing the ratio of the inter-group distance to intra-group distance. 2 A novel Soft-Coded (SC) ECOC algorithm is proposed by softening the codewords of the ECOC codematrix by considering the subordination degree of each class to both groups. 3 A new measure coverage is designed to evaluate the subordination degrees of different classes to the positive and the negative groups, and the values are set as the elements of the codematrix. 4 A self-adaptive strategy is designed to adjust codewords, making them better fit the associated learners. Error-Correcting Output Codes (ECOC) algorithms enable multiclass classification by reassigning multiple classes to the positive/negative group with the class reassignment schemes being recorded as binary/ternary hard-coded (HC) codematrices. Different classes tend to get diverse subordination degrees to the positive/negative group, providing clues to correct potential errors. However, the HC codematrices are unable to provide the information in the subordination degrees. In this paper, a Soft-Coded ECOC (SC-ECOC) scheme, namely, the Sequential Forward Floating Selection algorithm, is proposed by filling codematrices with real values instead of hard codes to improve classification performance. This algorithm divides multiple classes into two groups by maximizing the ratio of inter-group distance to intra-group distance. Then a new measure coverage is designed to evaluate the subordination degrees of different classes to both groups, which are set as the elements to form a codematrix. Furthermore, a self-adaptive strategy adjusts the value of each element to fit learners better. Experiments are carried out to verify the performance of our algorithm on various data sets, and results confirm that our algorithm can achieve more balanced results compared with the traditional HC ECOC algorithms. Besides, the values of soft codes correlate with the difficulty level of various classes to improve the multiclass classification ability. [ABSTRACT FROM AUTHOR]

A common way to model multiclass classification problems is by means of Error-Correcting Output Codes (ECOCs). Given a multiclass problem, the ECOC technique designs a code word for each class, where each position of the code identifies the membership of the class for a given binary problem. A classification decision is obtained by assigning the label of the class with the closest code. One of the main requirements of the ECOC design is that the base classifier is capable of splitting each subgroup of classes from each binary problem. However, we cannot guarantee that a linear classifier model convex regions. Furthermore, nonlinear classifiers also fail to manage some type of surfaces. In this paper, we present a novel strategy to model multiclass classification problems using subclass information in the ECOC framework. Complex problems are solved by splitting the original set of classes into subclasses and embedding the binary problems in a problem-dependent ECOC design. Experimental results show that the proposed splitting procedure yields a better performance when the class overlap or the distribution of the training objects conceal the decision boundaries for the base classifier. The results are even more significant when one has a sufficiently large training size. [ABSTRACT FROM AUTHOR]