Learning with spectral representations and use of MDL principles

Posted in Science on October 20, 2008


Learning with spectral representations and use of MDL principles

Lecture slides:

  • Recent Progress on Learning with Graph Representations
  • Outline
  • Motivation
  • Problem
  • Measuring similarity of graphs
  • Viewed from the perspective of learning
  • Learning with graphs (circa 2000)
  • Why is structural learning difficult
  • Structural Variations
  • Contributions
  • Spectral Methods
  • Graph (structural) representations of shape
  • Delaunay Graph
  • MOVI Sequence
  • Shock graphs
  • Graph characteristics
  • Pairwise clustering
  • Embeddings
  • Generative model
  • Spectral Generative Model
  • Algebraic graph theory (PAMI 2005)
  • ….joint work with Richard Wilson
  • Spectral Representation
  • Properties of the Laplacian
  • Eigenvalue spectrum
  • Eigenvalues are invariant to permutations of the Laplacian.
  • Why
  • Symmetric polynomials
  • Power symmetric polynomials
  • Symmetric polynomials on spectral matrix
  • Spectral Feature Vector
  • …extend to weighted attributed graphs.
  • Complex Representation
  • Spectral analysis
  • Pattern Spaces
  • Manifold learning methods
  • Separation under structural error
  • Variation under structural error (MDS)
  • CMU Sequence
  • MOVI Sequence
  • YORK Sequence
  • Visualisation (LLP+Laplacian Polynomials)
  • Cospectrality problem for trees
  • Cospectral trees
  • Overcome using quantum random walk\t
  • The positive support of a matrix
  • Cospectral Trees
  • Stongly regular graphs
  • Generative Tree Union Model
  • ..work with Andrea Torsello
  • Ingredients
  • Illustration
  • Cluster structure
  • Model
  • Union as tree distribution
  • Generative Model
  • Max-likelihood parameters
  • Description length
  • Expectation on observation density
  • Tree Union
  • Simplified Description Cost
  • Description Length Gain
  • Unattributed
  • Future

Author: Edwin Hancock, University Of York

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