We propose a new method based on sparse optimal discriminant clustering (SODC), incorporating a penalty term into the scoring matrix based on convex clustering. With the addition of this penalty term, it is expected to improve the accuracy of cluster identification by pulling points within the same cluster closer together and points from different clusters further apart. When the estimation results are visualized, the clustering structure can be depicted more clearly. Moreover, we develop a novel algorithm to derive the updated formula of this scoring matrix using a majorizing function. The scoring matrix is updated using the alternating direction method of multipliers (ADMM), which is often employed to calculate the parameters of the objective function in the convex clustering. In the proposed method, as in the conventional SODC, the scoring matrix is subject to an orthogonal constraint. Therefore, it is necessary to satisfy the orthogonal constraint on the scoring matrix while maintaining the clustering structure. Using a majorizing function, we adress the challenge of enforcing both orthogonal constraint and the clustering structure within the scoring matrix. We demonstrate numerical simulations and an application to real data to assess the performance of the proposed method.

翻译：本文提出了一种基于稀疏最优判别聚类（SODC）的新方法，该方法在评分矩阵中引入了基于凸聚类的惩罚项。通过添加此惩罚项，旨在将同一簇内的点拉得更近，并将不同簇的点推得更远，从而提高簇识别的准确性。当可视化估计结果时，聚类结构可以更清晰地展现。此外，我们开发了一种新算法，利用主化函数推导该评分矩阵的更新公式。评分矩阵使用交替方向乘子法（ADMM）进行更新，该方法常用于计算凸聚类中目标函数的参数。在所提出的方法中，与传统的SODC一样，评分矩阵受到正交约束。因此，需要在保持聚类结构的同时满足评分矩阵的正交约束。通过使用主化函数，我们解决了在评分矩阵中同时施加正交约束和保持聚类结构的难题。我们通过数值模拟和实际数据应用来评估所提方法的性能。