K-proximal plane clustering (kPPC) cluster data points to the center points and local k-proximal plane clustering (LkPPC) uses the combination of hyperplane and points as the cluster center to localize the hyperplane. However, the \(l_{2}\) -norm is employed to group the data into corresponding clusters, which is sensitive to outliers because of the square operation. Many previous works chose to use \(l_{1}\) -norm instead of \(l_{2}\) -norm to improve robustness. However, this approach has limited improvement in the robustness of outlier, and the solution of \(l_{1}\) -norm mostly uses a greedy algorithm search strategy, which is easy to fall into local optimization and consumes a long time. In this paper, we propose a clustering method using \(l_{2,1}\) -norm, named RLkPPC. To solve the objective function, we combine an efficient iterative optimization algorithm with the Lagrange multiplier method, and on this basis, propose a non-greedy weighted iterative optimization algorithm for solving the \(l_{2,1}\) -norm minimum problem. Compared to existing methods, the advantage of our method is: (1) similar to LkPPC, it has a clear geometric explanation; (2) it has good robustness and a stronger ability to resist the influence of outliers; (3) it uses a non-greedy weighted iterative optimization algorithm, prevent falling into local optima. The experimental results on some artificial and benchmark datasets indicate that our algorithm has the robustness and clustering accuracy advantages.
