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.

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