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