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Significant progress has been made in learning image classification neural networks under long-tail data distribution using robust training algorithms such as data re-sampling, re-weighting, and margin adjustment. Those methods, however, ignore the impact of data imbalance on feature normalization. The dominance of majority classes (head classes) in estimating statistics and affine parameters causes internal covariate shifts within less-frequent categories to be overlooked. To alleviate this challenge, we propose a compound batch normalization method based on a Gaussian mixture. It can model the feature space more comprehensively and reduce the dominance of head classes. In addition, a moving average-based expectation maximization (EM) algorithm is employed to estimate the statistical parameters of multiple Gaussian distributions. However, the EM algorithm is sensitive to initialization and can easily become stuck in local minima where the multiple Gaussian components continue to focus on majority classes. To tackle this issue, we developed a dual-path learning framework that employs class-aware split feature normalization to diversify the estimated Gaussian distributions, allowing the Gaussian components to fit with training samples of less-frequent classes more comprehensively. Extensive experiments on commonly used datasets demonstrated that the proposed method outperforms existing methods on long-tailed image classification.