<p>Matrix-object data are common in real-world applications, where each object consists of multiple vectors of varying lengths. However, existing clustering methods for categorical matrix-object data have several limitations: they cannot distinguish between matrix-objects that share identical values but differ in distribution, they ignore the varying contributions of attributes within each cluster, and they fail to consider the distributions of matrix-objects when assigning them to clusters. To address these issues, we propose an innovative weighted clustering algorithm tailored for categorical matrix-object data in this paper. Firstly, we define a novel distance measure that enables the distinction of matrix-objects with the same values but different distributions. Additionally, we propose a new representation method for cluster centers. Based on this new distance, we incorporate distributions of matrix-objects into the clustering process to enhance the clustering outcomes. Furthermore, by assigning a weight to each attribute within every cluster and optimizing the objective function, we ensure that attributes with greater contributions receive higher weights. In addition, since different numbers of vectors form a matrix-object, it is equivalent to a small cluster. This makes the representation and computation of matrix-objects more complex. During the clustering process, not only the distribution of clusters but also the distribution of matrix-objects must be considered. Therefore, high-performance computing is necessary. Experimental results clearly demonstrate the advantages and effectiveness of the proposed algorithm.</p>