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For hierarchical classification tasks, label relationships can be represented as a hierarchical structure ranging from coarse-grained to fine-grained. Existing hierarchical classifications typically employ a top-down classification approach, which leads to significant inter-level error propagation. Moreover, none of the existing approaches consider the impact of the path weights of different classes on the classification. In this paper, we propose a Hierarchical Classification method with Exponential Weighting of Multi-granularity Paths (HCEWMP), which combines path weights and hierarchical structure to propose a new hierarchical classification framework. Firstly, HCEWMP decomposes the datasets from coarse-grained to fine-grained based on the hierarchical structure and assigns weights to paths by the data distribution. Secondly, two different weighting strategies, probability weighting, and exponential weighting, are considered to calculate the probability of each class. Thirdly, the fine-grained top k classes are selected based on the probability descending order. Finally, HCEWMP obtains the best-predicted class using a random forest classifier. Compared with eight different algorithms on seven datasets, our experimental results demonstrate that the proposed method is effective in addressing the inter-level error propagation problem. The exponential weighting strategy has superior results among the two strategies, further indicating the significance of path weighting in hierarchical classification. [ABSTRACT FROM AUTHOR]