Department of Marketing, College of Business, Florida State University, Tallahassee, FL 32306-1110, USA.
Psychol Methods. 2010 Jun;15(2):145-57. doi: 10.1037/a0017738.
Structural balance theory (SBT) has maintained a venerable status in the psychological literature for more than 5 decades. One important problem pertaining to SBT is the approximation of structural or generalized balance via the partitioning of the vertices of a signed graph into K clusters. This K-balance partitioning problem also has more general psychological applications associated with the analysis of similarity/dissimilarity relationships among stimuli. Accordingly, K-balance partitioning can be gainfully used in a wide variety of SBT applications, such as attraction and child development, evaluation of group membership, marketing and consumer issues, and other psychological contexts not necessarily related to SBT. We present a branch-and-bound algorithm for the K-balance partitioning problem. This new algorithm is applied to 2 synthetic numerical examples as well as to several real-world data sets from the behavioral sciences literature.
结构平衡理论（SBT）在心理学文献中已有超过 50 年的历史，地位尊崇。SBT 存在一个重要问题，即通过将有向图的顶点划分为 K 个簇来近似结构或广义平衡。K 平衡划分问题在与刺激之间的相似性/相异性关系分析相关的更广泛的心理学应用中也很重要。因此，K 平衡划分可广泛应用于 SBT 的各种应用中，例如吸引力和儿童发展、群体成员评估、营销和消费者问题，以及其他不一定与 SBT 相关的心理学背景。我们提出了一种 K 平衡划分问题的分支定界算法。该新算法应用于 2 个合成数值示例以及来自行为科学文献的几个真实数据集。
