Multi-objective soft subspace clustering in the composite kernel space

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.