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Convex clustering method for compositional data modeling.
- Source :
-
Soft Computing - A Fusion of Foundations, Methodologies & Applications . Feb2021, Vol. 25 Issue 4, p2965-2980. 16p. - Publication Year :
- 2021
-
Abstract
- Compositional data refer to a vector with parts that are positive and subject to a constant-sum constraint. Examples of compositional data in the real world include a vector with each entry representing the weight of a stock in an investment portfolio, or the relative concentration of air pollutants in the environment. In this study, we developed a Convex Clustering approach for grouping Compositional data. Convex clustering is desirable because it provides a global optimal solution given its convex relaxations of hierarchical clustering. However, when directly applied to compositions, the clustering result offers little interpretability because it ignores the unit-sum constraint of compositional data. In this study, we discuss the clustering of compositional variables in the Aitchison framework with an isometric log-ratio (ilr) transformation. The objective optimization function is formulated as a combination of a L 2 -norm loss term and a L 1 -norm regularization term and is then efficiently solved using the alternating direction method of multipliers. Based on the numerical simulation results, the accuracy of clustering ilr-transformed data is higher than the accuracy of directly clustering untransformed compositional data. To demonstrate its practical use in real applications, the proposed method is also tested on several real-world datasets. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 14327643
- Volume :
- 25
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- Soft Computing - A Fusion of Foundations, Methodologies & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 148754262
- Full Text :
- https://doi.org/10.1007/s00500-020-05355-z