1. Data Mining Presentation Learning Patterns in the Dynamics of Biological Networks Chang hun You, Lawrence B. Holder, Diane J. Cook

2. Background – Biological Networks Protein-Protein interaction network  Nodes = proteins  Edges = physical interactions Metabolic network  Nodes = metabolites  Edges = reactions or enzymes Gene regulatory network  Nodes = transcription factors or DNA elements  Edges = physical binding between the two

3. Motivation Interactions are not static. Networks change over time. Party Hubs - usually act inside functional modules Date Hubs - usually connect functional modules to each other

4. Related Work Several studies on static networks. Discovered the global PPI network is scale-free. Work on dynamic graphs quantified the difference between time steps. One group predicted how the dynamic graph changes over time using frequent subgraphs.

5. Paper Goal Given a set of sequential graphs: G 0, G 1,...,G n-1, G n Discover patterns that represent how these graphs change over time.

6. General Overview 1) Learn the 'rewrite rules' between consecutive graphs. Represented by a removal of a subgraph followed by an addition of a subgraph to get to the next graph. 2) Learn the 'transformation rules' throughout the entire dynamic graph. Represented by the same subgraphs being removed and added over time.

7. Step 1: Rewrite Rules (5 + 11) / 27 = 16/27 (5 + 3 + 7) / 27 = 15/27 (11 + 7) / 27 = 18/27

8. Step 2: Transformation Rules

9. Time Complexity Finding maximum common subgraphs is NP- complete. The DiscoverCommonSub method takes a limit parameter which is equal to the number of unique edge and node labels. Running time of algorithm 1 = N dcs x (T-1) Running time of algorithm 2 = O(N dcs ) Running time of N dcs on a graph guaranteed to have unique node labels is quadratic

10. Evaluation Metrics Coverage represents how well the transformation rule describes the total changes in the dynamic graph over time Assume size(R1) = 10 size(A2) = 10, size(BestSub) = 9 Coverage = 9 x (1/10 + 1/10)/2 = 9/10

11. Evaluation Metrics Prediction represents how accurate their predictions is on future transformations. For example: A subgraph is predicted to be present in a removal and then an addition. It is perfect for the first, and ½ for the second. Prediction = (1 +.5) / 2 =.75

12. Results – Artificial Data First created a static graph from one of the KEGG pathways. Copied it 20 times and manually removed/added specific nodes. Repeated 4 times, varying how they added/removed

13. Mathematical Modeling Took mathematical model developed by another group to represent the cell cycle signaling pathway. At each time step, the model determines how abundant a certain protein is. If abundance is over a certain threshold, it is in the graph for that time step. Ran model for 700 seconds, had 10 second intervals leaving them with 51 training points and 20 for testing their predictions. Ran several iterations, perturbing some model parameters each time.

14. Mathematical Modeling

15. Microarray

16. Future Directions Find more complicated transformation rules such as conditional removal/addition, and rules that span multiple consecutive time slices. Compare prediction results to other methods. Have prediction measure take into account temporal accuracy.

17. Conclusions Came up with algorithm to find simple patterns in a dynamic graph They used a different definition for the best subgraph to be used for a pattern, namely best compression subgraph rather than frequent subgraph. They kinda validated their results.

18. Questions?