Clustering Dynamics on Graphs: From Spectral Clustering to Mean Shift Through Fokker–Planck Interpolation

Craig, Katy; Trillos, Nicolás García; Slepčev, Dejan

doi:10.1007/978-3-030-93302-9_4

Cited by 4 publications

(4 citation statements)

References 31 publications

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“…Wang et al 16 proposed an anisotropic kernel mean shift method, in which the kernels' shape, scale, and orientation are tailored to match the local framework of the image or video, and the segmentation outcomes that align better with human visual saliency. Craig et al 17 introduced the spectral clustering method in graph theory, combined with the mean shift algorithm for segmentation. Tao et al 18 integrated mean shift and NCUT for color image segmentation, reducing the calculation complexity.…”

Section: Introductionmentioning

confidence: 99%

Cluster segmentation algorithm for enhancing edge information

Liu,

Lu,

Zhang

et al. 2024

J. Electron. Imag.

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To solve the blurred image edge segmentation problem and the influence of a complex background on the segmentation accuracy of the clustering algorithm, this paper proposes an edge gravity mean shift (EGMS) image segmentation algorithm. Aiming at the problem of partial edge information loss when the Canny algorithm processes images, the L 0 gradient minimization method is introduced to iteratively optimize the gradient map to extract more edge information, and then the L 0 Canny edge detection algorithm is proposed. Aiming at the problem that the Epanechnikov mean shift algorithm will converge to the local optimum due to the non-smooth Epanechnikov kernel function, the optimal bandwidth is obtained, and the smoothness of the kernel function shape is improved by cross-validation and spline function. Then, the sleek Epanechnikov kernel function is constructed by integrating the weight function, which can reflect the richness of clustering information at the peak so that the kernel function can more accurately reflect the data characteristics of the peak. Based on the sleek Epanechnikov kernel function, the sleek Epanechnikov mean shift (SEMS) clustering algorithm is proposed. The EGMS image segmentation algorithm is constructed by fusing the L 0 Canny and SEMS. The experimental results indicate that EGMS can retain more edge contour information when segmenting images, and it can generate better clustering clusters for clustered datasets. In addition, compared to other clustering segmentation algorithms, the proposed EGMS algorithm demonstrates superior clustering accuracy and convergence on the majority of image datasets. Our code is available at: https://gitee.com/ zhiweilu111/edge-gravity-mean-shift.

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Section: Introductionmentioning

confidence: 99%

Cluster segmentation algorithm for enhancing edge information

Liu,

Lu,

Zhang

et al. 2024

J. Electron. Imag.

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“…This distinction becomes particularly relevant in applications in data science and machine learning. For example, the popular mean-shift algorithm for clustering tasks can be understood in the framework of a continuity equation on a graph [15]. In a nutshell, this method attempts to find clusters in the data depending on the density of the distribution of the point cloud through different regions in space.…”

Section: Introductionmentioning

confidence: 99%

On evolution PDEs on co-evolving graphs

Esposito,

Mikolás

2024

DCDS

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We provide a well-posedness theory for a class of nonlocal continuity equations on co-evolving graphs. We describe the connection among vertices through an edge weight function and we let it evolve in time, coupling its dynamics with the dynamics on the graph. This is relevant in applications to opinion dynamics and transportation networks. Existence and uniqueness of suitably defined solutions is obtained by exploiting the Banach fixed-point theorem. We consider different time scales for the evolution of the weight function: faster and slower than the flow defined on the graph. The former leads to graphs whose weight functions depend nonlocally on the density configuration at the vertices, while the latter induces static graphs. Furthermore, we prove a discrete-to-continuum limit for the PDEs under study as the number of vertices converges to infinity.

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“…In the recent papers [19,20], the analysis is extended to nonlocal cross-interaction systems on graphs with a nonlinear mobility, in the context of nonquadratic Finslerian gradient flows. In [9], dynamics on graphs are shown to be useful for data clustering; indeed, the authors connect the mean shift algorithm with spectral clustering at discrete and continuum levels via Fokker-Planck equations on data graphs.…”

Section: Introductionmentioning

confidence: 99%

On a class of nonlocal continuity equations on graphs

2023

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Motivated by applications in data science, we study partial differential equations on graphs. By a classical fixed-point argument, we show existence and uniqueness of solutions to a class of nonlocal continuity equations on graphs. We consider general interpolation functions, which give rise to a variety of different dynamics, for example, the nonlocal interaction dynamics coming from a solution-dependent velocity field. Our analysis reveals structural differences with the more standard Euclidean space, as some analogous properties rely on the interpolation chosen.

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Clustering Dynamics on Graphs: From Spectral Clustering to Mean Shift Through Fokker–Planck Interpolation

Cited by 4 publications

References 31 publications

Cluster segmentation algorithm for enhancing edge information

Cluster segmentation algorithm for enhancing edge information

On evolution PDEs on co-evolving graphs

On a class of nonlocal continuity equations on graphs

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