A common criterion for seriation of asymmetric matrices is the maximization of the dominance index, which sums the elements above the main diagonal of a reordered matrix. Similarly, a popular seriation criterion for symmetric matrices is the maximization of an anti-Robinson gradient index, which is associated with the patterning of elements in the rows and columns of a reordered matrix. Although perfect dominance and perfect anti-Robinson structure are rarely achievable for empirical matrices, we can often identify a sizable subset of objects for which a perfect structure is realized. We present and demonstrate an algorithm for obtaining a maximum cardinality (i.e. the largest number of objects) subset of objects such that the seriation of the proximity matrix corresponding to the subset will have perfect structure. MATLAB implementations of the algorithm are available for dominance, anti-Robinson and strongly anti-Robinson structures.

中文翻译：

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一种用于提取具有完美支配或反罗宾逊结构的最大基数子集的算法。

不对称矩阵的序列化的一个通用标准是优势指数的最大化，该指数将重新排序的矩阵的主对角线上方的元素相加。类似地，对称矩阵的一种流行的锯齿准则是反鲁宾逊梯度指数的最大化，该指数与重新排序矩阵的行和列中的元素构图有关。尽管对于经验矩阵而言，极少数的优势和理想的反罗宾逊结构是很难实现的，但我们经常可以识别出可实现理想结构的相当大的对象子集。我们提出并证明了一种用于获得对象的最大基数（即，最大数量的对象）子集的算法，以使与该子集相对应的邻近矩阵的锯齿状具有完美的结构。