Topology: A Theory of a Pseudometric-Based Clustering Model and Its Application in Content-Based Image Retrieval

The clustering problem has been extensively studied over the last 50 years; however, it still has the attention of researchers. This paper presents a topological basis of a pseudometric-based clustering model which takes into account the local and global topological properties of the data to be clustered, as per the definition of homogeneity measurement. The proposed approach takes into account the homogeneity effect produced when a new particle is added to a group. The additional element can be accumulated in the group if its local homogeneity is not altered and, therefore, it is not necessary to carry out tests in another group. A new group needs to be generated if the threshold of the local homogeneity of the group exceeds. Theoretical results, their implementation, and their application to the problem of Content Based Image Retrieval (CBIR) are presented. The tests were performed using three image databases widely used in the literature, which are “Vogel and Shiele,” “Oliva and Torralba,” and “L. Fei- Fei, R. Fergus and P. Perona.” The results are presented and compared with the most competitive methods available in the literature.