Brusco Michael J, Stahl Stephanie
Department of Marketing, College of Business, Florida State University, Tallahassee, FL 32306, USA.
Br J Math Stat Psychol. 2007 Nov;60(Pt 2):377-93. doi: 10.1348/000711006X107872.
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.
非对称矩阵序列化的一个常见标准是优势指数最大化，该指数对重新排序矩阵主对角线以上的元素求和。类似地，对称矩阵常用的序列化标准是反罗宾逊梯度指数最大化，它与重新排序矩阵的行和列中的元素模式相关。尽管对于经验矩阵来说，很少能实现完美的优势和完美的反罗宾逊结构，但我们通常可以识别出一个能实现完美结构的可观对象子集。我们提出并演示了一种算法，用于获得对象的最大基数（即最大数量的对象）子集，使得与该子集对应的邻近矩阵的序列化具有完美结构。该算法的MATLAB实现可用于优势、反罗宾逊和强反罗宾逊结构。
