Laplacian Eigenmaps Bibtex Bibliography

  • 2018
  • [i22]

    Mikhail Belkin:
    Approximation beats concentration? An approximation view on inference with smooth radial kernels.CoRRabs/1801.03437 (2018)

  • [i21]

    Mikhail Belkin, Siyuan Ma, Soumik Mandal:
    To understand deep learning we need to understand kernel learning.CoRRabs/1802.01396 (2018)

  • [i20]

    Akshay Mehra, Jihun Hamm, Mikhail Belkin:
    Fast Interactive Image Retrieval using large-scale unlabeled data.CoRRabs/1802.04204 (2018)

  • [i19]

    Chaoyue Liu, Mikhail Belkin:
    Parametrized Accelerated Methods Free of Condition Number.CoRRabs/1802.10235 (2018)

  • 2017
  • [c47]

    Siyuan Ma, Mikhail Belkin:
    Diving into the shallows: a computational perspective on large-scale shallow learning.NIPS2017: 3781-3790

  • [i18]

    Siyuan Ma, Mikhail Belkin:
    Diving into the shallows: a computational perspective on large-scale shallow learning.CoRRabs/1703.10622 (2017)

  • [i17]

    Justin Eldridge, Mikhail Belkin, Yusu Wang:
    Unperturbed: spectral analysis beyond Davis-Kahan.CoRRabs/1706.06516 (2017)

  • [i16]

    Siyuan Ma, Raef Bassily, Mikhail Belkin:
    The Power of Interpolation: Understanding the Effectiveness of SGD in Modern Over-parametrized Learning.CoRRabs/1712.06559 (2017)

  • 2016
  • [c46]

    James R. Voss, Mikhail Belkin, Luis Rademacher:
    The Hidden Convexity of Spectral Clustering.AAAI2016: 2108-2114

  • [c45]

    Qichao Que, Mikhail Belkin:
    Back to the Future: Radial Basis Function Networks Revisited.AISTATS2016: 1375-1383

  • [c44]

    Mikhail Belkin, Luis Rademacher, James R. Voss:
    Basis Learning as an Algorithmic Primitive.COLT2016: 446-487

  • [c43]

  • Abstract

    We introduce vector diffusion maps (VDM), a new mathematical framework for organizing and analyzing massive high-dimensional data sets, images, and shapes. VDMis a mathematical and algorithmic generalization of diffusion maps and other nonlinear dimensionality reduction methods, such as LLE, ISOMAP, and Laplacian eigenmaps. While existing methods are either directly or indirectly related to the heat kernel for functions over the data, VDM is based on the heat kernel for vector fields. VDM provides tools for organizing complex data sets, embedding them in a low-dimensional space, and interpolating and regressing vector fields over the data. In particular, it equips the data with a metric, which we refer to as the vector diffusion distance. In the manifold learning setup, where the data set is distributed on a low-dimensional manifold embedded in , we prove the relation between VDM and the connection Laplacian operator for vector fields over the manifold. © 2012 Wiley Periodicals, Inc.

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