- Research Article
2
- 10.1016/j.patcog.2025.111878
Making clustering methods workable for shapes using the ordinary Procrustes sum of squares
- Jan 01, 2026
- Pattern Recognition
- Kazunori Iwata + 2 more +2
In the last few decades, a number of clustering methods for vectorial data have matured. Occasionally, researchers are interested in making them workable for data of other types, such as an object’s shape. The current difficulty in applying them to shape clustering is that clustering must be invariant to several similarity transformations of shapes. Therefore, we use the ordinary Procrustes sum of squares (OSS) in Procrustes analysis, which refers to analysis that is invariant to the similarity transformations between shapes. Thus, in this study, we aim to make mature methods workable in shape clustering. To achieve this, the essential points that we need to address are to rewrite the optimization problem associated with each method and to present a feasible method for computing the solution to the problem. As a result, we base the method on the OSS, its derivative, or a symmetric matrix concerning the OSS. Another aim of this study is to identify specific applications of shape clustering. We demonstrate the applications through experiments using datasets that contain skewed line drawings, American football formations, and baseball pitch trajectories. We examine the OSS-based methods by considering shape classification and determining the best method for implementing the OSS. As a result, regardless of the dataset, we demonstrate that the OSS in every method is more effective than other shape distances and that the convex clustering method incorporating the OSS is best performed in several ways. • Revisiting some mature clustering methods for processing shapes. • Using the ordinary Procrustes sum of squares to formulate object functions in optimization. • Comparing the revisited clustering methods in shape classification.
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