Multi-view clustering method based on anchor graph has been widely concerned
due to its high efficiency and effectiveness. In order to avoid
post-processing, most of the existing anchor graph-based methods learn
bipartite graphs with connected components. However, such methods have high
requirements on parameters, and in some cases it may not be possible to obtain
bipartite graphs with clear connected components. To end this, we propose a
label learning method based on tensor projection (LLMTP). Specifically, we
project anchor graph into the label space through an orthogonal projection
matrix to obtain cluster labels directly. Considering that the spatial
structure information of multi-view data may be ignored to a certain extent
when projected in different views separately, we extend the matrix projection
transformation to tensor projection, so that the spatial structure information
between views can be fully utilized. In addition, we introduce the tensor
Schatten $p$-norm regularization to make the clustering label matrices of
different views as consistent as possible. Extensive experiments have proved
the effectiveness of the proposed method.

基于锚点图的多视角聚类方法备受关注，为避免后处理，现有的基于锚点图的方法学习到具有连通分量的二部图，然而，这些方法对参数有很高的要求，且在某些情况下可能无法获得具有清晰连通分量的二部图。为了解决这个问题，我们提出了一种基于张量投影的标签学习方法（LLMTP），通过正交投影矩阵将锚点图投影到标签空间中直接得到聚类标签。为了充分利用多视角数据的空间结构信息，我们将矩阵投影转化为张量投影，以便在不同视角的投影中可以充分利用视角之间的空间结构信息。此外，引入了张量 Schatten p - 范数正则化，使不同视角的聚类标签矩阵尽可能一致。通过大量实验证明了该方法的有效性。

基于张量投影的标签学习方法

Label Learning Method Based on Tensor Projection

Although numerous clustering algorithms have been developed, many existing
methods still leverage k-means technique to detect clusters of data points.
However, the performance of k-means heavily depends on the estimation of
centers of clusters, which is very difficult to achieve an optimal solution.
Another major drawback is that it is sensitive to noise and outlier data. In
this paper, from manifold learning perspective, we rethink k-means and present
a new clustering algorithm which directly detects clusters of data without mean
estimation. Specifically, we construct distance matrix between data points by
Butterworth filter such that distance between any two data points in the same
clusters equals to a small constant, while increasing the distance between
other data pairs from different clusters. To well exploit the complementary
information embedded in different views, we leverage the tensor Schatten p-norm
regularization on the 3rd-order tensor which consists of indicator matrices of
different views. Finally, an efficient alternating algorithm is derived to
optimize our model. The constructed sequence was proved to converge to the
stationary KKT point. Extensive experimental results indicate the superiority
of our proposed method.

该论文提出了一种基于流形学习和张量正则化的聚类算法，不同于传统的基于 k-means 的方法，该算法通过构建距离矩阵来直接检测数据簇，同时应用于多视图数据中，证明了其优越性能。