Since p-spectral clustering has good performance in many practical problems, it has attracted great attention. The Cheeger cut criterion is used in p-spectral clustering to do graph partition. However, due to the improper affinity measure and outliers, the original p-spectral clustering algorithm is not effective in dealing with manifold data. To solve this problem, we propose a manifold p-spectral clustering (M-pSC) using path-based affinity measure. First, we design a path-based affinity function to describe the complex structures of manifold data. This affinity function obeys the clustering assumption that the data pairs within the manifold structure share high affinities, and the data pairs between different manifold structures share low affinities. This will help us construct a good affinity matrix, which carry more category information of the points. Then we propose a M-pSC algorithm using the path-based affinity function. In the Cheeger cut criterion, the p-Laplacian matrix are constructed based on the manifold affinity function, and the final clustering results are obtained by using the eigenvectors of graph p-Laplacian. At last, the proposed algorithm is tested on several public data sets and the experiments show that our algorithm is adaptive to different manifold data. Compared with other popular clustering algorithms, our algorithm has good clustering quality and robustness.

由于p谱聚类在许多实际问题中都有良好的表现，因此引起了极大的关注。Cheeger割准则用于p谱聚类中以进行图划分。然而，由于不适当的亲和力度量和离群值，原始的p谱聚类算法在处理流形数据方面无效。为了解决这个问题，我们提出了流形p使用基于路径的亲和力度量的光谱聚类（M-pSC）。首先，我们设计基于路径的亲和力函数来描述流形数据的复杂结构。此相似性函数遵循以下聚类假设：流形结构内的数据对共享高亲和力，而不同流形结构之间的数据对共享低亲和力。这将帮助我们构建一个良好的亲和力矩阵，该矩阵携带更多点的类别信息。然后，我们提出了一种基于路径的亲和力函数的M-pSC算法。在Cheeger割准则中，基于流形亲和函数构造p -Laplacian矩阵，并使用图p的特征向量获得最终的聚类结果。-拉普拉斯人。最后，该算法在多个公共数据集上进行了测试，实验表明该算法适用于不同的流形数据。与其他流行的聚类算法相比，我们的算法具有良好的聚类质量和鲁棒性。