Robust Multiple Flat Projections Clustering With Truncated Distance Maximization Constraints

Recently, interest in flat-type projection clustering methods has grown as they improve learner's performance by exploring multiple projection subspaces. However, solvers used in previous representative works predominantly rely on greedy search strategies, which incur high computational costs and fail to consider interdependencies between projections. Moreover, these methods do not simultaneously guarantee the effective suppression of outliers and noisy data at cluster boundaries, ultimately compromising data discrimination. To address these limitations and discover a more effective subspace for each flat, we propose robust multiple flat projections clustering (RMFPC). This method computes within- and between-cluster distances using the L2,1-norm to enhance robustness against outliers. Furthermore, we propose a truncated distance maximization constraint (TDMC) to eliminate the influence of noisy data on cluster separability. The resulting objective is presented in a ratio form, which is not trivial. We provide a novel formulation to achieve a theoretically equivalent problem. Based on this reformulation, we develop an efficient non-greedy solution algorithm. In addition, a cluster center optimization mechanism is incorporated into the solution process to accurately estimate the distribution of each cluster center. The convergence analysis and proof of the proposed algorithm are provided. Experiments on both toy and real-world datasets demonstrate the effectiveness of the proposed method.