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Nearest Descent, In-Tree, and Clustering

Author

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  • Teng Qiu

    (Key Laboratory for Neuroinformation of Ministry of Education, University of Electronic Science and Technology of China, Chengdu 610054, China)

  • Yongjie Li

    (Key Laboratory for Neuroinformation of Ministry of Education, University of Electronic Science and Technology of China, Chengdu 610054, China)

Abstract

Clustering aims at discovering the natural groupings in a dataset, prevalent in many disciplines that involve multivariate data analysis. In this paper, we propose a physically inspired graph-theoretical clustering method, which first makes the data points organized into an attractive graph, called In-Tree, via a physically inspired rule, called Nearest Descent (ND). The rule of ND works to select the nearest node in the descending direction of potential as the parent node of each node, which is fundamentally different from the classical Gradient Descent. The constructed In-Tree proves a very good candidate for clustering due to its particular features and properties. In the In-Tree, the original clustering problem is reduced to a problem of removing the inter-cluster edges from this graph. Pleasingly, those inter-cluster edges are usually so distinguishable that they can be easily determined by different automatic edge-cutting methods. We also propose a visualized strategy to validate the effectiveness of the automatic edge-cutting methods. The experimental results reveal that the proposed method is superior to the related clustering methods. The results also reveal the characteristics of different automatic cutting methods and the meaningfulness of the visualized strategy in increasing the reliability of the clustering results in practice.

Suggested Citation

  • Teng Qiu & Yongjie Li, 2022. "Nearest Descent, In-Tree, and Clustering," Mathematics, MDPI, vol. 10(5), pages 1-37, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:5:p:764-:d:760228
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    References listed on IDEAS

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    1. Giovanna Menardi, 2016. "A Review on Modal Clustering," International Statistical Review, International Statistical Institute, vol. 84(3), pages 413-433, December.
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