Knowledge Vault 5 /33 - CVPR 2018
Deep Learning of Graph Matching
Andrei Zanfir, Cristian Sminchisescu
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graph LR classDef graph_matching fill:#f9d4d4, font-weight:bold, font-size:14px classDef applications fill:#d4f9d4, font-weight:bold, font-size:14px classDef affinity_matrix fill:#d4d4f9, font-weight:bold, font-size:14px classDef deep_learning fill:#f9f9d4, font-weight:bold, font-size:14px classDef challenges fill:#f9d4f9, font-weight:bold, font-size:14px A[Deep Learning of
Graph Matching] --> B[Graph matching:
node correspondences. 1] A --> C[Applications: geometric
and semantic. 2] C --> D[Geometric matching:
same object,
different views.] C --> E[Semantic matching:
different objects,
same category.] A --> F[Affinity matrix: encodes
node similarities. 3] F --> G[Node similarities:
affinity matrix
encodes.] F --> H[Edge similarities:
affinity matrix
encodes.] A --> I[Relaxation: drops
constraints. 4] I --> J[Solution: leading
eigenvector.] A --> K[Deep learning:
deep features. 5] K --> L[Represents matrix
using features.] K --> M[Trains model
to predict truth.] A --> N[Challenges: gradients
and solver. 6] N --> O[Propagating gradients
through layers.] N --> P[Graph matching
solver.] A --> Q[Matrix backpropagation:
computes gradients. 7] Q --> R[Through matrix
functions.] A --> S[Factorization: reduces
complexity. 8] S --> T[Matrix operation
complexity reduced.] A --> U[Bi-stochastic layer:
mapping constraints. 9] U --> V[One-to-one
mapping.] A --> W[Loss function:
measures deviation. 10] W --> X[Deviation from
ground truth.] A --> Y[Results: competitive
performance. 11] Y --> Z[Sintel: geometric
dataset.] Y --> AA[PascalVOC/CUB:
semantic datasets.] A --> AB[Potential applications:
deep feature problems. 12] AB --> AC[Deep feature
hierarchies.] AB --> AD[Graph models:
text corpora,
social networks.] class A,B graph_matching class C,D,E applications class F,G,H affinity_matrix class I,J challenges class K,L,M deep_learning class N,O,P challenges class Q,R affinity_matrix class S,T challenges class U,V challenges class W,X challenges class Y,Z,AA results class AB,AC,AD potential_applications


1.- Graph matching: computing correspondences between nodes in two graphs under structural constraints.

2.- Applications: geometric matching (same object, different viewpoints) and semantic matching (different objects, same category).

3.- Affinity matrix: encodes node and edge similarities between graphs; used to find correspondences.

4.- Relaxation: drops binary and one-to-one constraints; solution is leading eigenvector of affinity matrix.

5.- Deep learning framework: represents affinity matrix using deep features; trains model to predict ground truth correspondences.

6.- Challenges: propagating gradients through matrix functional layers and graph matching solver.

7.- Matrix backpropagation: enables gradient computation through matrix functions in affinity matrix factorization.

8.- Factorization: reduces computational complexity of matrix operations from quartic to cubic/quadratic.

9.- Bi-stochastic operation layer: enforces one-to-one mapping constraints in final assignment matrix.

10.- Loss function: measures deviation between predicted and ground truth correspondences for training.

11.- Results: competitive performance on Sintel (geometric) and PascalVOC/CUB (semantic) datasets.

12.- Potential applications: problems involving deep feature hierarchies and graph models (e.g. text corpora, social networks).

Knowledge Vault built byDavid Vivancos 2024