Clustering is a fundamental technique in unsupervised learning, grouping unlabeled data based on similarity metrics. Nevertheless, the Clustering by Fast Search and Find of Density Peaks (CFSFDP) algorithm requires manual selection of cluster centers, limiting its automation. To address this issue, this paper proposes an Adaptive Density Peak Clustering Algorithm optimized using an N-ary Bézier inverse curve to achieve automatic cluster center determination. By performing data point inversion, the method enhances the distinction between cluster centers and non-center points, simplifying their identification. Additionally, the algorithm integrates gamma processing and information entropy weighting significantly reducing computational complexity. The results demonstrate that the proposed algorithm outperforms other automatic clustering methods in terms of AMI, ARI, FMI, and the number of automatically selected cluster centers. Furthermore, the findings validate its effectiveness in clustering accuracy while enhancing the robustness of density peak-based clustering.