Three-way clustering: Foundations, survey and challenges

Wang, Pingxin; Yang, Xibei; Ding, Weiping; Zhan, Jianming; Yao, Yiyu

doi:10.1016/j.asoc.2023.111131

Cited by 9 publications

(4 citation statements)

References 91 publications

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“…In mereotopology, the 3WD paradigm is naturally suitable for accommodating two possible extensions of reasoning with regions. The first is considering regions with areas of indefiniteness ("fringes"), and the second is applying ideas of 3WD to spatial relations [41,88]. Although the cited papers are of a mereological nature, there is no doubt that the ideas are applicable to spatially extended regions (because of the usual domain universe in R n ).…”

Section: On the Three-way Paradigmmentioning

confidence: 99%

“…Ideas towards three-way mereology are a key component of recent approaches to classic classification/decision methods. For example, the two main types of three-way clustering described in [88] would be completely characterized in this paper in the case of clusters characterized as regions (similar analysis could be done in other contexts, as in [90,91]).…”

Section: On the Three-way Paradigmmentioning

confidence: 99%

“…The reinterpretation of the relations on a topological space with pulsation is based on considering the pairs (x, σ(x)) as the intended regions. In three-way clustering [88] (particularly in those inspired by Mathematical Morphology [41]), pulsation can be understood as a natural operation on sets or regions that relates a core set with a fringe set representing indefiniteness in the cluster (Figure 12). Theorem 5.…”

Section: Interpreting With Pulsation/contractionmentioning

confidence: 99%

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A Logical–Algebraic Approach to Revising Formal Ontologies: Application in Mereotopology

Aranda-Corral,

Borrego-Díaz,

Chávez-González

et al. 2024

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In ontology engineering, reusing (or extending) ontologies poses a significant challenge, requiring revising their ontological commitments and ensuring accurate representation and coherent reasoning. This study aims to address two main objectives. Firstly, it seeks to develop a methodological approach supporting ontology extension practices. Secondly, it aims to demonstrate its feasibility by applying the approach to the case of extending qualitative spatial reasoning (QSR) theories. Key questions involve effectively interpreting spatial extensions while maintaining consistency. The framework systematically analyzes extensions of formal ontologies, providing a reconstruction of a qualitative calculus. Reconstructed qualitative calculus demonstrates improved interpretative capabilities and reasoning accuracy. The research underscores the importance of methodological approaches when extending formal ontologies, with spatial interpretation serving as a valuable case study.

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Section: On the Three-way Paradigmmentioning

confidence: 99%

Section: On the Three-way Paradigmmentioning

confidence: 99%

Section: Interpreting With Pulsation/contractionmentioning

confidence: 99%

See 1 more Smart Citation

A Logical–Algebraic Approach to Revising Formal Ontologies: Application in Mereotopology

Aranda-Corral,

Borrego-Díaz,

Chávez-González

et al. 2024

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“…Recently, three-way clustering [39] has garnered widespread research interest, leading to the development of various three-way clustering algorithms within this theoretical framework. Wang and Yao [40] proposed a three-way clustering framework called CE3, derived from mathematical morphology's erosion and dilation concepts.…”

Section: Introductionmentioning

confidence: 99%

Similarity-Based Three-Way Clustering by Using Dimensionality Reduction

Li,

Meng,

Wang

2024

Mathematics

Self Cite

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Three-way clustering uses core region and fringe region to describe a cluster, which divide the dataset into three parts. The division helps identify the central core and outer sparse regions of a cluster. One of the main challenges in three-way clustering is the meaningful construction of the two sets. Aimed at handling high-dimensional data and improving the stability of clustering, this paper proposes a novel three-way clustering method. The proposed method uses dimensionality reduction techniques to reduce data dimensions and eliminate noise. Based on the reduced dataset, random sampling and feature extraction are performed multiple times to introduce randomness and diversity, enhancing the algorithm’s robustness. Ensemble strategies are applied on these subsets, and the k-means algorithm is utilized to obtain multiple clustering results. Based on these results, we obtain co-association frequency between different samples and fused clustering result using the single-linkage method of hierarchical clustering. In order to describe the core region and fringe region of each cluster, the similar class of each sample is defined by co-association frequency. The lower and upper approximations of each cluster are obtained based on similar class. The samples in the lower approximation of each cluster belong to the core region of the cluster. The differences between lower and upper approximations of each cluster are defined as fringe region. Therefore, a three-way explanation of each cluster is naturally formed. By employing various UC Irvine Machine Learning Repository (UCI) datasets and comparing different clustering metrics such as Normalized Mutual Information (NMI), Adjusted Rand Index (ARI), and Accuracy (ACC), the experimental results show that the proposed strategy is effective in improving the structure of clustering results.

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