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Volume Corrected Affinity on Graph Laplacian

A volume corrected affinity on graph Laplacian approximates the optimal Parzen window or kernel bandwidth that leads to point wise convergence to its respective Laplace-Beltrami operator.

How to use?

Run nldr_interactive.m file to open the interactive window.

Results on synthetic dataset

References

  1. Manifold Regularization: a Geometric Framework for Learning from Examples, M. Belkin, P. Niyogi, V. Sindhwani, University of Chicago Computer Science Technical Report TR-2004-06, 2004, http://manifold.cs.uchicago.edu/manifold_regularization/manifold.html
  2. Nonlinear dimensionality reduction by locally linear embedding, Sam Roweis & Lawrence Saul, Science, v.290 no.5500 , Dec.22, 2000. pp.2323--2326, https://cs.nyu.edu/~roweis/lle/code.html
  3. A global geometric framework for nonlinear dimensionality reduction, Tenenbaum, J., de Silva, V., Langford, J., Science 290, 2319-2323, 2000, http://web.mit.edu/cocosci/isomap/code/Isomap.m
  4. Principal Manifolds and Nonlinear Dimension Reduction via Local Tangent Space Alignment, Zhang, Zhenyue, Hongyuan Zha, SIAM Journal on Scientific Computing, 26 (1), 313–338, 2004, https://arxiv.org/abs/cs/0212008
  5. Self-tuning spectral clustering, Zelnik-Manor, L., Perona, P, Advances in neural information processing systems, pp. 1601-1608, 2005, https://papers.nips.cc/paper/2619-self-tuning-spectral-clustering.pdf
  6. Adaptive kernel density-based anomaly detection for nonlinear systems, Zhang, L., Lin, J., Karim, R, Knowledge-Based Systems 139, 50-63, 2018, https://www.sciencedirect.com/science/article/pii/S0950705117304707

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Variable Parzen Window

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