GM problem

[binghao-cai]

Task

base: Graph, GraphSetTaskBase
gm: GMTask

key functions in graphset.base.py

• Graph
  • from_data
• GraphSetTaskBase
  • from_data
• numpy completement of sinkhorn
• numpy completement of hungarian

key functions in graphset.gm.py

• gmtask.build_aff_mat()
• inner_prod_aff_fn()
• gaussian_aff_fn()
• _aff_mat_from_node_edge_aff()
• gmtask.evaluate()
• gmtask.render()

Generator

graphset.base.py
class

• GRAPH_TYPE
• GRAPH_FEATURE_TYPE
• GraphFeatureGenerator
• GraphSetGeneratorBase
  • single graph generate methods
  • _isomorphic_graph_generate()
  • _induced_subgraph_generate()
  • _perturbed_graph_generate()

graphset.gm.py
the function _create_instance() construct gmtask from nx_graphs with aff_mat

Solver

To match the requestment of evaluation and test, hard solutions are added through hungarian(nummpy) affer the soft solutions are given by solvers.

• classical solver for gm
• sm
• ipfp
• rrwm
• astar(torch completement)
• neural solver for gm
• ngm(torch completement)
• gnn_astar(torch completement)

Wrapper

The internal structure of the .txt file
“ edge_index_for_graph1 src1 tgt1 src2 tgt2 $\cdots$"
“ edge_index_for_graph2 src1 tgt1 src2 tgt2 $\cdots$"
“ node_feature_for_graph1 feat1;feat2; $\cdots$"
“ node_feature_for_graph2 feat1;feat2; $\cdots$"
“ edge_feature_for_graph1 feat1;feat2; $\cdots$"
“ edge_feature_for_graph2 feat1;feat2; $\cdots$"
" association_graph_label label1 label2 $\cdots$"
The above is in the same line and feat is joined by " "space

Testdata

gm.task

• gm_er_uniform_ind_task.pkl
  30 nodes , 4-dim node-feat, 4-dim edge-feat for graph1, keep_ratio=0.5
• gm_er_gaussian_ind_task.pkl
  30 nodes , 4-dim node-feat, 4-dim edge-feat for graph1, keep_ratio=0.5
• gm_er_uniform_iso_task.pkl
  30 nodes , 4-dim node-feat, 4-dim edge-feat
• gm_er_gaussian_iso_task.pkl
  30 nodes , 4-dim node-feat, 4-dim edge-feat
• gm_er_uniform_iso_task_astar.pkl
  10 nodes, 4-dim node-feat, 4-dim edge-feat
• gm_er_gaussian_iso_task_astar.pkl
  10 nodes, 4-dim node-feat, 4-dim edge-feat

gm.wrapper

• gm_er_uniform_iso_4ins
  4 nodes ,36-dim node-feat, 36-dim edge-feat
• gm_er_gaussian_iso_4ins
  4 nodes ,36-dim node-feat, 36-dim edge-feat