With the development of a series of Galaxy sky surveys in recent years, the observations increased rapidly, which makes the research of machine learning methods for galaxy image recognition a hot topic. Available automatic galaxy image recognition researches are plagued by the large differences in similarity between categories, the imbalance of data between different classes, and the discrepancy between the discrete representation of Galaxy classes and the essentially gradual changes from one morphological class to the adjacent class (DDRGC). These limitations have motivated several astronomers and machine learning experts to design projects with improved galaxy image recognition capabilities. Therefore, this paper proposes a novel learning method, ``Hierarchical Imbalanced data learning with Weighted sampling and Label smoothing" (HIWL). The HIWL consists of three key techniques respectively dealing with the above-mentioned three problems: (1) Designed a hierarchical galaxy classification model based on an efficient backbone network; (2) Utilized a weighted sampling scheme to deal with the imbalance problem; (3) Adopted a label smoothing technique to alleviate the DDRGC problem. We applied this method to galaxy photometric images from the Galaxy Zoo-The Galaxy Challenge, exploring the recognition of completely round smooth, in between smooth, cigar-shaped, edge-on and spiral. The overall classification accuracy is 96.32\%, and some superiorities of the HIWL are shown based on recall, precision, and F1-Score in comparing with some related works. In addition, we also explored the visualization of the galaxy image features and model attention to understand the foundations of the proposed scheme.
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