The higher-order correlation clustering problem is an expressive model, and recently, local search heuristics have been proposed for several applications. Certifying optimality, however, is NP-hard and practically hampered already by the complexity of the problem statement. Here, we focus on establishing partial optimality conditions for the special case of complete graphs and cubic objective functions. In addition, we define and implement algorithms for testing these conditions and examine their effect numerically, on two datasets.

翻译：高阶相关聚类问题是一种表达力丰富的模型，近年来，针对若干应用场景已提出了局部搜索启发式算法。然而，最优性证明不仅自身是NP难题，且在实际中已因问题表述的复杂性而受阻。在此，我们聚焦于完全图与三次目标函数这一特例，建立部分最优性条件。此外，我们定义并实现了用于检验这些条件的算法，并在两个数据集上对其效果进行了数值分析。