In this paper, we propose a method to cluster the spacial patterns of the visual field in glaucoma patients to analyze the progression patterns of glaucoma. The degree of progression in the visual field of glaucoma patients can be divided into several regions by straight line boundaries, we call this specific structure Direct Product Structure in this paper. Since we can observe the direct product structure in the visual fields, we propose a bottom-up hierarchical clustering method to embed this structure into the clustering structure. In our method, according to the minimum description length (MDL) principle, we select the best cluster division so that the total code length required for encoding the data as well as the clustering structure is minimum. We can thereby select the clusters that are robust to the noise in the position of the direct product structure for clustering. We demonstrate the effectiveness of our method using an artificial dataset and a real glaucoma dataset. Our proposed method performed better than existing methods for both datasets. For the real glaucoma dataset in particular, our method discovered the characteristic progressive patterns of glaucoma as specific features of clusters. These patterns agree with clinical knowledge. Furthermore, we show that our clusters can be applied to improve the accuracy of predicting glaucoma progression. Thus, our clusters contain rich information of glaucoma, and hence can contribute to further development in glaucoma research.