One-step multi-view kernel clustering based on topological manifold

Many existing multi-view graph-based or kernel-based clustering methods focus on constructing either affinity graphs or consensus kernels from data, often neglecting the underlying topological manifold structure within the data. This oversight compromises the quality of the constructed affinity graphs and consensus kernels. Moreover, most of these methods typically involve multi-step clustering processes , which impair the reliability of the final results. To mitigate these drawbacks, we propose OS-MVKC-TM, a one-step clustering method based on multi-view kernel learning that explicitly models the data's manifold structure. OS-MVKC-TM leverages the data's topological relationships to form an affinity graph and guide the learning of kernel matrices. By jointly optimizing these two components within a unified framework and reinforcing their interaction, the resulting affinity graph and kernel matrices more accurately reflect the intrinsic data structure , thus ensuring higher quality. Furthermore, a block-diagonal representation is employed to directly induce the affinity graph suitable for one-step clustering. Additionally, an iterative algorithm consisting of three stages is developed to address the optimization challenge. Finally, this method demonstrates its effectiveness on eight data sets, outperforming twelve recently proposed counterparts. The code of OS-MVKC-TM is released at https://github.com/mathchen-git/OS-MVKC-TM .