Georeferenced compositional data are prominent in many scientific fields and in spatial statistics. This work addresses the problem of proposing models and methods to analyze and predict, through kriging, this type of data. To this purpose, a novel class of $\alpha$-transformations, named the Isometric $\alpha$-transformation ($\alpha$-IT), is proposed, which encompasses the traditional Isometric Log-Ratio (ILR) transformation. Similarly to other $\alpha$-transformations existing in the literature, it is shown that the ILR is the limit case of the $\alpha$-IT as $\alpha$ tends to 0 and that $\alpha =1$ corresponds to a linear transformation of the data. Unlike the ILR, the proposed transformation accepts 0s in the compositions when $\alpha >0$. Maximum likelihood estimation of the parameter $\alpha$ is established. Prediction using kriging on $\alpha$-IT transformed data is validated on synthetic spatial compositional data, using prediction scores computed either in the geometry induced by the $\alpha$-IT, or in the simplex. Application to land cover data shows that the relative superiority of the various approaches w.r.t. a prediction objective depends on whether the compositions contained any zero component. When all components are positive, the limit cases (ILR or linear transformations) are optimal for none of the considered metrics. An intermediate geometry, corresponding to the $\alpha$-IT with maximum likelihood estimate, better describes the dataset in a geostatistical setting. When the amount of compositions with 0s is not negligible, some side-effects of the transformation gets amplified as $\alpha$ decreases, entailing poor kriging performances both within the $\alpha$-IT geometry and for metrics in the simplex.

地理参考成分数据在许多科学领域和空间统计中都很突出。这项工作解决了提出模型和方法以通过克里金法分析和预测此类数据的问题。为此，一个新的类$\alpha$- 变换，命名为等距 $\alpha$-转型 （$\alpha$-IT)，它包含传统的等距对数比 (ILR) 变换。与其他类似$\alpha$- 文献中存在的变换，表明 ILR 是 $\alpha$-它作为 $\alpha$ 趋于 0 并且 $\alpha =1$对应于数据的线性变换。与 ILR 不同，提议的转换在组合中接受 0，当$\alpha >0$. 参数的最大似然估计$\alpha$成立。使用克里金法进行预测$\alpha$- IT 转换的数据在合成空间成分数据上进行验证，使用在由 $\alpha$-IT，或在单纯形。对土地覆盖数据的应用表明，与预测目标相关的各种方法的相对优势取决于成分是否包含任何零成分。当所有分量都为正时，极限情况（ILR 或线性变换）对于所有考虑的指标都不是最佳的。一个中间几何体，对应于$\alpha$- 具有最大似然估计的 IT，可以更好地描述地质统计设置中的数据集。当带有 0 的组合的数量不可忽略时，转换的一些副作用被放大为$\alpha$ 减少，导致克里金法表现不佳 $\alpha$-IT 几何和单纯形中的度量。