Similarity matrix has a significant effect on the performance of the spectral clustering, and how to determine the neighborhood in the similarity matrix effectively is one of its main difficulties. In this paper, a “divide and conquer” strategy is proposed to model the similarity matrix construction task by adopting Multiobjective evolutionary algorithm (MOEA). The whole procedure is divided into two phases, phase I aims to determine the nonzero entries of the similarity matrix, and Phase II aims to determine the value of the nonzero entries of the similarity matrix. In phase I, the main contribution is that we model the task as a biobjective dynamic optimization problem, which optimizes the diversity and the similarity at the same time. It makes each individual determine one nonzero entry for each sample, and the encoding length decreases to O(N) in contrast with the non-ensemble multiobjective spectral clustering. In addition, a specific initialization operator and diversity preservation strategy are proposed during this phase. In phase II, three ensemble strategies are designed to determine the value of the nonzero value of the similarity matrix. Furthermore, this Pareto ensemble framework is extended to semi-supervised clustering by transforming the semi-supervised information to constraints. In contrast with the previous multiobjective evolutionary-based spectral clustering algorithms, the proposed Pareto ensemble-based framework makes a balance between time cost and the clustering accuracy, which is demonstrated in the experiments section.

相似度矩阵对频谱聚类的性能有重要影响，如何有效地确定相似度矩阵中的邻域是其主要困难之一。本文提出了一种“分而治之”的策略，通过采用多目标进化算法（MOEA）对相似性矩阵的构建任务进行建模。整个过程分为两个阶段，第一阶段旨在确定相似性矩阵的非零项，第二阶段旨在确定相似性矩阵的非零项的值。在第一阶段，主要贡献是我们将任务建模为双目标动态优化问题，该问题同时优化了多样性和相似性。它使每个人为每个样本确定一个非零条目，并且编码长度减小为O（N）与非集合多目标谱聚类相反。此外，在此阶段还提出了一种特定的初始化运算符和多样性保存策略。在阶段II中，设计了三种集成策略来确定相似性矩阵的非零值。此外，通过将半监督信息转换为约束，此Pareto集成框架已扩展到半监督聚类。与以前的基于多目标进化的谱聚类算法相比，本文提出的基于Pareto集成的框架在时间成本和聚类精度之间取得了平衡，这在实验部分得到了证明。