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.

本篇论文通过精确定义二重噪声、最小化噪声并设计了一个高效的两步迭代策略，提出了一种新的多核聚类算法，能有效地提高聚类性能。

双重噪声最小化的多核聚类

Multiple Kernel Clustering with Dual Noise Minimization

Multiple kernel clustering (MKC) is committed to achieving optimal
information fusion from a set of base kernels. Constructing precise and local
kernel matrices is proved to be of vital significance in applications since the
unreliable distant-distance similarity estimation would degrade clustering
per-formance. Although existing localized MKC algorithms exhibit improved
performance compared to globally-designed competi-tors, most of them widely
adopt KNN mechanism to localize kernel matrix by accounting for {\tau} -nearest
neighbors. However, such a coarse manner follows an unreasonable strategy that
the ranking importance of different neighbors is equal, which is impractical in
applications. To alleviate such problems, this paper proposes a novel local
sample-weighted multiple kernel clustering (LSWMKC) model. We first construct a
consensus discriminative affinity graph in kernel space, revealing the latent
local structures. Further, an optimal neighborhood kernel for the learned
affinity graph is output with naturally sparse property and clear block
diagonal structure. Moreover, LSWMKC im-plicitly optimizes adaptive weights on
different neighbors with corresponding samples. Experimental results
demonstrate that our LSWMKC possesses better local manifold representation and
outperforms existing kernel or graph-based clustering algo-rithms. The source
code of LSWMKC can be publicly accessed from
this https URL.

本文提出了一种新的本地样本加权多核聚类（LSWMKC）模型，它在核空间中构建一个共识判别力亲和力图，揭示了潜在的本地结构，并输出一个最优的邻域核，具有自然稀疏属性和清晰的块对角结构。此外，LSWMKC 隐式地优化了不同邻居在相应样本上的自适应权重，并表现出比现有的基于核或图形的聚类算法更好的本地流形表示。