| Summary: | Imbalanced data exist in many classification problems. The classification of imbalanced data has remarkable challenges in machine learning. The support vector machine (SVM) and its variants are popularly used in machine learning among different classifiers thanks to their flexibility and interpretability. However, the performance of SVMs is impacted when the data are imbalanced, which is a typical data structure in the multi-category classification problem. In this paper, we employ the data-adaptive SVM with scaled kernel functions to classify instances for a multi-class population. We propose a multi-class data-dependent kernel function for the SVM by considering class imbalance and the spatial association among instances so that the classification accuracy is enhanced. Simulation studies demonstrate the superb performance of the proposed method, and a real multi-class prostate cancer image dataset is employed as an illustration. Not only does the proposed method outperform the competitor methods in terms of the commonly used accuracy measures such as the <i>F</i>-score and <i>G</i>-means, but also successfully detects more than 60% of instances from the rare class in the real data, while the competitors can only detect less than 20% of the rare class instances. The proposed method will benefit other scientific research fields, such as multiple region boundary detection.
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