  Clustering is a representative unsupervised method widely applied in
multi-modal and multi-view scenarios. Multiple kernel clustering (MKC) aims to
group data by integrating complementary information from base kernels. As a
representative, late fusion MKC first decomposes the kernels into orthogonal
partition matrices, then learns a consensus one from them, achieving promising
performance recently. However, these methods fail to consider the noise inside
the partition matrix, preventing further improvement of clustering performance.
We discover that the noise can be disassembled into separable dual parts, i.e.
N-noise and C-noise (Null space noise and Column space noise). In this paper,
we rigorously define dual noise and propose a novel parameter-free MKC
algorithm by minimizing them. To solve the resultant optimization problem, we
design an efficient two-step iterative strategy. To our best knowledge, it is
the first time to investigate dual noise within the partition in the kernel
space. We observe that dual noise will pollute the block diagonal structures
and incur the degeneration of clustering performance, and C-noise exhibits
stronger destruction than N-noise. Owing to our efficient mechanism to minimize
dual noise, the proposed algorithm surpasses the recent methods by large
margins.
