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Applying Hyperspectral Reflectance Imaging to Investigate the Palettes and the Techniques of Painters
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Multiway p-spectral graph cuts on Grassmann manifolds.

Dimosthenis Pasadakis1, Christie Louis Alappat2, Olaf Schenk1

  • 1Institute of Computing, Faculty of Informatics, Università della Svizzera italiana, Lugano, Switzerland.

Machine Learning
|April 11, 2022
PubMed
Summary

We introduce a new nonlinear spectral clustering algorithm using p-Laplacian for multiway graph partitioning. This method enhances numerical efficiency and accuracy in clustering tasks, including image and character classification.

Keywords:
Direct multiway cutsGraph clusteringGraph p-LaplacianManifold optimization

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Area of Science:

  • Machine Learning
  • Graph Theory
  • Numerical Analysis

Background:

  • Spectral clustering methods are popular for data partitioning.
  • Nonlinear reformulations offer improved numerical benefits and mathematical rigor.
  • Existing methods may lack efficiency or robustness in multiway partitioning.

Purpose of the Study:

  • To develop a novel direct multiway spectral clustering algorithm.
  • To leverage the p-Laplacian for enhanced graph partitioning.
  • To achieve sparser solutions and optimal graph cuts.

Main Methods:

  • Recasting eigenvector computation for the graph p-Laplacian as a Grassmann manifold minimization problem.
  • Employing a pseudocontinuous reduction of 'p' to promote sparsity.
  • Monitoring balanced graph cut decrease for solution quality.

Main Results:

  • Demonstrated effectiveness and accuracy on artificial datasets.
  • Achieved high-quality clusters using balanced graph cut metrics.
  • Showcased superior performance compared to state-of-the-art methods in labelling accuracy.
  • Validated applicability on real-world facial image and handwritten character classification.

Conclusions:

  • The proposed nonlinear spectral clustering algorithm offers significant improvements in efficiency and accuracy.
  • The method effectively handles multiway graph partitioning and real-world classification tasks.
  • The p-Laplacian approach provides a robust framework for advanced clustering.