Recent studies have highlighted interesting properties of empirical cultural states—collections of cultural trait sequences of real individuals. Matrices of similarity between individuals may be constructed from these states, allowing for more insights to be gained using random matrix techniques, approach first exploited in this study. We propose a null model that enforces, on average, the empirical occurrence frequency of each possible trait. With respect to this null model, the empirical matrices show deviating eigenvalues, which may be signatures of subtle cultural groups. However, they can conceivably also be artifacts of arbitrary redundancies between cultural variables. We study this possibility in a highly simplified setting, allowing for a side-by-side mathematical comparison of the two scenarios (groups and redundancies). The scenarios are shown to be completely indistinguishable in terms of deviating eigenvalues, confirming that the latter can in general be signatures of either redundancies or groups. The scenarios can be distinguished after evaluating the eigenvector uniformities and the associated deviations from null model expectations. This provides a uniformity-based validation criterion, which is reliable when searching for groups that are internally uniform, but fails when these exhibit significant internal non-uniformity. For empirical data, all the relevant eigenvector uniformities are compatible with the null model, indicating the absence of any internally uniform groups. Although there are various indications that some of the deviating eigenvalues could correspond to internally non-uniform groups, a generic procedure for distinguishing such groups from redundancy artifacts requires further research.

最近的研究强调了经验文化状态的有趣特性——真实个体的文化特征序列的集合。可以从这些状态构建个体之间的相似矩阵，从而允许使用随机矩阵技术获得更多见解，这是本研究中首次利用的方法。我们提出了一个空模型，该模型平均强制每个可能特征的经验发生频率。关于这个空模型，经验矩阵显示出偏离的特征值，这可能是微妙文化群体的特征。然而，它们也可能是文化变量之间任意冗余的产物。我们在高度简化的环境中研究这种可能性，允许对两种场景（组和冗余）进行并排的数学比较。就偏离特征值而言，这些场景被证明是完全无法区分的，这证实了后者通常可以是冗余或组的签名。在评估特征向量均匀性和与空模型期望的相关偏差后，可以区分这些场景。这提供了一个基于一致性的验证标准，当搜索内部一致的组时它是可靠的，但当这些组表现出显着的内部非均匀性时会失败。对于经验数据，所有相关的特征向量均匀性都与空模型兼容，表明不存在任何内部均匀组。尽管有各种迹象表明一些偏离的特征值可能对应于内部非均匀组，