||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
elds, 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
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.