People often use qualitative relations to describe locations or directional information, especially in written communication, such as ‘the restaurant is located at the southeast corner of the square’. However, when a large number of spatial entities are involved, qualitative relations alone are not intuitive enough for people to understand a spatial configuration. In fact, many applications, e.g. pertaining to sharing travel experiences, use sketch maps, i.e. maps focusing on the main features of an area whilst abstracting exact scale measurements, to help demonstrate abstract qualitative relations with more intuitive geometric points. Current approaches for generating point sketch maps from qualitative spatial relations require a high level of expertise, face inherent difficulties with efficiently processing large-scale data in bulk, and are vulnerable to inaccurate or conflicting information contained in qualitative data. To address these limitations, by incorporating machine learning techniques, we propose to translate the problem into an optimization problem of data reconstruction, enabling a novel end-to-end approach for generating point sketch maps from qualitative directional relations in bulk. Experiments on real-world datasets show that the proposed approach has very high accuracy and is robust even with a large portion of inaccurate or incomplete information.

Co-clustering methods make use of the correlation between samples and attributes to explore the co-occurrence structure in data. These methods have played a significant role in gene expression analysis, image segmentation, and document clustering. In bipartite graph partition-based co-clustering methods, the relationship between samples and attributes is described by constructing a diagonal symmetric bipartite graph matrix, which is clustered by the philosophy of spectral clustering. However, this not only has high time complexity but also the same number of row and column clusters. In fact, the number of categories of rows and columns often changes in the real world. To address these problems, this paper proposes a novel fast flexible bipartite graph model for the co-clustering method (FBGPC) that directly uses the original matrix to construct the bipartite graph. Then, it uses the inflation operation to partition the bipartite graph in order to learn the co-occurrence structure of the original data matrix based on the inherent relationship between bipartite graph partitioning and co-clustering. Finally, hierarchical clustering is used to obtain the clustering results according to the set relationship of the co-occurrence structure. Extensive empirical results show the effectiveness of our proposed model and verify the faster performance, generality, and flexibility of our model.

This paper develops a new mechanism to efficiently compute and compactly store qualitative spatial relations between spatial objects, focusing on topological and directional relations for large datasets of region objects. The central idea is to use minimum bounding rectangles (MBRs) to approximately represent region objects with arbitrary shape and complexity and only store spatial relations that cannot be unambiguously inferred from the relations of corresponding MBRs. We demonstrate, both in theory and practice, that our approach requires considerably less construction time and storage space, and can answer queries more efficiently than the state-of-the-art methods.

In this article we show that the Voronoi-based nine-intersection (V9I) model proposed by Chen et al. (2001, A Voronoi-based 9-intersection model for spatial relations. International Journal of Geographical Information Science, 15 (3), 201–220) is more expressive than what has been believed before. Given any two spatial entities A and B, the V9I relation between A and B is represented as a 3 × 3 Boolean matrix. For each pair of types of spatial entities that is, points, lines, and regions, we first show that most Boolean matrices do not represent a V9I relation by using topological constraints and the definition of Voronoi regions. Then, we provide illustrations for all the remaining matrices. This guarantees that our method is sound and complete. In particular, we show that there are 18 V9I relations between two areas with connected interior, while there are only nine four-intersection relations. Our investigations also show that, unlike many other spatial relation models, V9I relations are context or shape sensitive. That is, the existence of other entities or the shape of the entities may affect the validity of certain relations.