论文标题
Multiway $ p $ - 光谱图在Grassmann歧管上切割
Multiway $p$-spectral graph cuts on Grassmann manifolds
论文作者
论文摘要
光谱聚类方法的非线性重新构造由于其数值增长和坚实的数学背景而引起了很多最近的关注。 We present a novel direct multiway spectral clustering algorithm in the $p$-norm, for $p \in (1, 2]$. The problem of computing multiple eigenvectors of the graph $p$-Laplacian, a nonlinear generalization of the standard graph Laplacian, is recasted as an unconstrained minimization problem on a Grassmann manifold. The value of $p$ is reduced in a促进较稀疏的解决方案矢量的伪装方式与$ p $相对应，以监测平衡图的单调降低，可确保我们从$ p $ levels中获得最佳的解决方案。提出的方法在平衡图剪切指标方面都获得了高质量的群集，并在标签分配的准确性方面获得了研究。
Nonlinear reformulations of the spectral clustering method have gained a lot of recent attention due to their increased numerical benefits and their solid mathematical background. We present a novel direct multiway spectral clustering algorithm in the $p$-norm, for $p \in (1, 2]$. The problem of computing multiple eigenvectors of the graph $p$-Laplacian, a nonlinear generalization of the standard graph Laplacian, is recasted as an unconstrained minimization problem on a Grassmann manifold. The value of $p$ is reduced in a pseudocontinuous manner, promoting sparser solution vectors that correspond to optimal graph cuts as $p$ approaches one. Monitoring the monotonic decrease of the balanced graph cuts guarantees that we obtain the best available solution from the $p$-levels considered. We demonstrate the effectiveness and accuracy of our algorithm in various artificial test-cases. Our numerical examples and comparative results with various state-of-the-art clustering methods indicate that the proposed method obtains high quality clusters both in terms of balanced graph cut metrics and in terms of the accuracy of the labelling assignment. Furthermore, we conduct studies for the classification of facial images and handwritten characters to demonstrate the applicability in real-world datasets.
