论文标题
构图立方体：多因素构图的新概念
Compositional Cubes: A New Concept for Multi-factorial Compositions
论文作者
论文摘要
组成数据通常称为携带相对信息的多元观测值。即使文献中已经很好地描述了向量或什至两因素组成数据（组成表）的情况，但仍然需要一种综合方法来分析多因素相对价值数据。因此，这种贡献围绕当前关于组成数据的知识建立在k-factorial组成数据的一般工作理论中。作为一个主要发现，事实证明，类似于组成表的情况也可以正交分解为独立和几个交互部分，而且可以构建允许通过标准分析方法进行单独分析的坐标表示。为了简单起见，这些特征是针对三因素组成（组成立方体）的详细说明的，然后是涵盖一般情况的轮廓。在两个实际示例中对三维结构进行了深入分析，以涉及空间和依赖时间的组成立方体。该方法是在R软件包robcompositions中实现的。
Compositional data are commonly known as multivariate observations carrying relative information. Even though the case of vector or even two-factorial compositional data (compositional tables) is already well described in the literature, there is still a need for a comprehensive approach to the analysis of multi-factorial relative-valued data. Therefore, this contribution builds around the current knowledge about compositional data a general theory of work with k-factorial compositional data. As a main finding it turns out that similar to the case of compositional tables also the multi-factorial structures can be orthogonally decomposed into an independent and several interactive parts and, moreover, a coordinate representation allowing for their separate analysis by standard analytical methods can be constructed. For the sake of simplicity, these features are explained in detail for the case of three-factorial compositions (compositional cubes), followed by an outline covering the general case. The three-dimensional structure is analysed in depth in two practical examples, dealing with systems of spatial and time dependent compositional cubes. The methodology is implemented in the R package robCompositions.
