Conventional subspace clustering algorithms group the data samples by optimizing the objective function which aggregates different clustering criteria using the linear combination. However, the performance is sensitive to the user-defined coefficients. Besides, the widely used Euclidean distance metric falls short of handling the linear indivisible problems. Some composite kernel metrics are proposed to overcome this drawback, but it is still difficult to determine the proper weight of base kernels. To address these problems, a novel multi-objective soft subspace clustering model is proposed. The novel model simultaneously optimizes three clustering criteria without setting coefficients. The distance between data points is measured in a composite kernel space. The weight of base kernels is optimized by a multi-objective evolutionary algorithm. A decomposition-based local search strategy is developed to enhance the performance of the proposed algorithm. The experimental results indicate that the proposed algorithm can achieve better solutions.

传统的子空间聚类算法通过优化目标函数对数据样本进行分组，该目标函数使用线性组合来聚合不同的聚类标准。但是，性能对用户定义的系数很敏感。此外，广泛使用的欧几里德距离度量标准不能解决线性不可分的问题。提出了一些复合内核度量标准来克服此缺点，但是仍然难以确定基本内核的适当权重。为了解决这些问题，提出了一种新颖的多目标软子空间聚类模型。新模型同时优化了三个聚类标准，而无需设置系数。数据点之间的距离是在复合内核空间中测量的。基本内核的权重通过多目标进化算法进行了优化。开发了一种基于分解的局部搜索策略，以增强所提出算法的性能。实验结果表明，该算法可以取得较好的解决方案。