Dealing with Distances and Transformations for Fuzzy C-Means Clustering of Compositional Data

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.     

Estrogen action in the male.

Estrogen administration induces a migration of eosinophil leukocytes to ductus deferens.     

水稻光温敏雄性不育基因连锁标记的分离与鉴定

两系法杂交稻是一种利用水稻杂种优势的重要途径，主要依据水稻光温敏雄性不育系在不同条件下的育性转换用于配制杂交种．以培矮64S(PTGMS)与明恢63杂种自交的F2代为供试材料，采用随机放大多态性DNA(RAPD)技术分离与培矮64S的PTGMS基因连锁的分子标记．在F2代2个分别代表可育和不育的群体以及亲本株系中，采用100个RAPD引物扩放基因组DNA筛选多态性DNA片段．RAPD引物S8产生的DNA片段中，除重复顺序外，有一个长度为0．85kb片段为单拷贝．分子杂交表明，这一单拷贝标记与培矮64S的PTGMS基因连锁．