https://github.com/airoldilab/sas

Sort and Smooth Algorithm for Graphon Estimation (Matlab)
https://github.com/airoldilab/sas

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Sort and Smooth Algorithm for Graphon Estimation (Matlab)

• Host: GitHub
• URL: https://github.com/airoldilab/sas
• Owner: airoldilab
• License: gpl-2.0
• Created: 2014-01-10T20:36:47.000Z (about 11 years ago)
• Default Branch: master
• Last Pushed: 2014-01-10T20:42:01.000Z (about 11 years ago)
• Last Synced: 2024-11-06T01:50:48.503Z (2 months ago)
• Language: Matlab
• Size: 2.46 MB
• Stars: 2
• Watchers: 9
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: Readme.txt
  • License: LICENSE

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README

        
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Sort and Smooth (SAS) Algorithm for Consistent Graphon Estimation

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This MATLAB package is a supplement to the paper 

S. H. Chan and E. M. Airoldi, "A Consistent Histogram Estimator for Exchangeable Graph Models", in Proceedings of International Conference on Machine Learning, 2014.

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Content:

1. Construct Graphs from a Graphon

	Method 1: [G P u] = construct_a_graph(w,n,T)

		Input:  w - a Graphon 

			n - number of nodes

			T - number of observations

		Output: G - graph (size nxnxT)

			P - probability of each node

			u - label indices

	Method 2: G = construct_a_graph_from_P(P,n,T)

		Input:  P - probability of each node

			n - number of nodes

			T - number of observations

		Output: G - graph (size nxnxT)

2. Sorting and Smoothing (sort_and_smooth.m)

	Input:  G    - a graph

	Output: west - estimated graphon

	

	Algorithm dependency: ./deconvtv_v1/

3. Results reported in the paper

	Figure1.m - plot a twin graphon

	Figure2.m - display an example of the SAS algorithm

	Figure3.m - results of SAS, USVT and SBA for graphons no. 5 and no. 10

	Figure4.m - runtime plot

	Figure5.m - graphon estimation of soc-Epinion1 and ca-astroph network

	Table2.m  - mean squared error (average and standard deviation) of SAS, USVT and SBA.

4. Compared Methods

	(i)   stochastic_block.m (Stochastic Blockmodel Approximation, Airoldi et al. 2013)

	(ii)  usvt.m             (Universal Singular Value Thresholding, Chatterjee 2012)

	

References

[1] E. M. Airoldi, T. B. Costa, and S. H. Chan, "Stochastic blockmodel approximation of a graphon: Theory and consistent estimation", Advances in Neural Information Processing Systems. ArXiv: 1311.1731. 2013.

[2] S. Chatterjee. Matrix estimation by universal singular value thresholding. ArXiv:1212.1247. 2012.

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COPYRIGHT (C) 2014 Stanley Chan and Edoardo Airoldi

This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program.  If not, see .

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Please report bugs to Stanley Chan [email protected]

Last update: January 10, 2014