Dealing with Distances and Transformations for Fuzzy C-Means Clustering of Compositional Data |
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Authors: | Javier Palarea-Albaladejo Josep Antoni Martín-Fernández Jesús A Soto |
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Institution: | 1. Biomathematics and Statistics Scotland, JCMB, The King??s Buildings, Edinburgh, EH9 3JZ, UK 2. Universitat de Girona, Girona, Spain 3. Universidad Cat??lica San Antonio, Murcia, Spain
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Abstract: | Clustering techniques are based upon a dissimilarity or distance measure between objects and clusters. This paper focuses on the simplex space, whose elements??compositions??are subject to non-negativity and constant-sum constraints. Any data analysis involving compositions should fulfill two main principles: scale invariance and subcompositional coherence. Among fuzzy clustering methods, the FCM algorithm is broadly applied in a variety of fields, but it is not well-behaved when dealing with compositions. Here, the adequacy of different dissimilarities in the simplex, together with the behavior of the common log-ratio transformations, is discussed in the basis of compositional principles. As a result, a well-founded strategy for FCM clustering of compositions is suggested. Theoretical findings are accompanied by numerical evidence, and a detailed account of our proposal is provided. Finally, a case study is illustrated using a nutritional data set known in the clustering literature. |
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