Connected Sub-graph Detection

Jing Qian, Venkatesh Saligrama, Yuting Chen
Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics, PMLR 33:796-804, 2014.

Abstract

We characterize the family of connected subgraphs in terms of linear matrix inequalities (LMI) with additional integrality constraints. We then show that convex relaxations of the integral LMI lead to parameterization of all weighted connected subgraphs. These developments allow for optimizing arbitrary graph functionals under connectivity constraints. For concreteness we consider the connected sub-graph detection problem that arises in a number of applications including network intrusion, disease outbreaks, and video surveillance. In these applications feature vectors are associated with nodes and edges of a graph. The problem is to decide whether or not the null hypothesis is true based on the measured features. For simplicity we consider the elevated mean problem wherein feature values at various nodes are distributed IID under the null hypothesis. The non-null (positive) hypothesis is distinguished from the null hypothesis by the fact that feature values on some unknown connected sub-graph has elevated mean.

Cite this Paper


BibTeX
@InProceedings{pmlr-v33-qian14, title = {{Connected Sub-graph Detection}}, author = {Jing Qian and Venkatesh Saligrama and Yuting Chen}, booktitle = {Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics}, pages = {796--804}, year = {2014}, editor = {Samuel Kaski and Jukka Corander}, volume = {33}, series = {Proceedings of Machine Learning Research}, address = {Reykjavik, Iceland}, month = {22--25 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v33/qian14.pdf}, url = {http://proceedings.mlr.press/v33/qian14.html}, abstract = {We characterize the family of connected subgraphs in terms of linear matrix inequalities (LMI) with additional integrality constraints. We then show that convex relaxations of the integral LMI lead to parameterization of all weighted connected subgraphs. These developments allow for optimizing arbitrary graph functionals under connectivity constraints. For concreteness we consider the connected sub-graph detection problem that arises in a number of applications including network intrusion, disease outbreaks, and video surveillance. In these applications feature vectors are associated with nodes and edges of a graph. The problem is to decide whether or not the null hypothesis is true based on the measured features. For simplicity we consider the elevated mean problem wherein feature values at various nodes are distributed IID under the null hypothesis. The non-null (positive) hypothesis is distinguished from the null hypothesis by the fact that feature values on some unknown connected sub-graph has elevated mean.} }
Endnote
%0 Conference Paper %T Connected Sub-graph Detection %A Jing Qian %A Venkatesh Saligrama %A Yuting Chen %B Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2014 %E Samuel Kaski %E Jukka Corander %F pmlr-v33-qian14 %I PMLR %P 796--804 %U http://proceedings.mlr.press/v33/qian14.html %V 33 %X We characterize the family of connected subgraphs in terms of linear matrix inequalities (LMI) with additional integrality constraints. We then show that convex relaxations of the integral LMI lead to parameterization of all weighted connected subgraphs. These developments allow for optimizing arbitrary graph functionals under connectivity constraints. For concreteness we consider the connected sub-graph detection problem that arises in a number of applications including network intrusion, disease outbreaks, and video surveillance. In these applications feature vectors are associated with nodes and edges of a graph. The problem is to decide whether or not the null hypothesis is true based on the measured features. For simplicity we consider the elevated mean problem wherein feature values at various nodes are distributed IID under the null hypothesis. The non-null (positive) hypothesis is distinguished from the null hypothesis by the fact that feature values on some unknown connected sub-graph has elevated mean.
RIS
TY - CPAPER TI - Connected Sub-graph Detection AU - Jing Qian AU - Venkatesh Saligrama AU - Yuting Chen BT - Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics DA - 2014/04/02 ED - Samuel Kaski ED - Jukka Corander ID - pmlr-v33-qian14 PB - PMLR DP - Proceedings of Machine Learning Research VL - 33 SP - 796 EP - 804 L1 - http://proceedings.mlr.press/v33/qian14.pdf UR - http://proceedings.mlr.press/v33/qian14.html AB - We characterize the family of connected subgraphs in terms of linear matrix inequalities (LMI) with additional integrality constraints. We then show that convex relaxations of the integral LMI lead to parameterization of all weighted connected subgraphs. These developments allow for optimizing arbitrary graph functionals under connectivity constraints. For concreteness we consider the connected sub-graph detection problem that arises in a number of applications including network intrusion, disease outbreaks, and video surveillance. In these applications feature vectors are associated with nodes and edges of a graph. The problem is to decide whether or not the null hypothesis is true based on the measured features. For simplicity we consider the elevated mean problem wherein feature values at various nodes are distributed IID under the null hypothesis. The non-null (positive) hypothesis is distinguished from the null hypothesis by the fact that feature values on some unknown connected sub-graph has elevated mean. ER -
APA
Qian, J., Saligrama, V. & Chen, Y.. (2014). Connected Sub-graph Detection. Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 33:796-804 Available from http://proceedings.mlr.press/v33/qian14.html.

Related Material