1. A K-Main Routes Approach to Spatial Network Activity Summarization(SNAS) Group 8

2. Outline  Motivation  Key Concepts  Problem Statement  Challenges  Related Work  Contributions  Algorithm  Validation  Assumption and Future Work

3. Motivation  Pedestrian Fatalities  Crime Activities

4. Key Concepts  Activity Set  Summary Path  Activity Coverage  Active Edge, Active Node, Inactive Node  Active Node Ratio

5. Problem Statement  Given: A spatial network G = (N, E) with weight function w(u, v) ≥ 0 for each edge A set of activities and their locations A desired number of summary paths, called K  Find: A summary path set of size K, called P A partitioning of activities across these summary paths  Objective: Maximize the activity coverage of each summary path for the group it represents.  Constraints: Each summary path is a shortest path between its end-nodes.

6. Challenges  Computational Complexity SNAS is computationally challenging because of the large number of K subsets of shortest paths in a spatial network.  If disjoint paths ? Less computation  If overlapping paths ? NP-complete Problem

7. Related Work  Previous work has focused on either geometry or subgraph-based approaches (only one path), and cannot summarize activities using multiple paths.  Geometry-based K-means  Network-Based Variable-Distance Clumping Method (NT-VCM)

8. Contributions  It shows that SNAS is NP-complete.  It proposes new techniques for improving the performance of K Main Routes: Network Voronoi activity Assignment and Divide and conquer Summary Path Re-computation. Their correctness are demonstrated. The computation cost of KMR can be calculated.  It presents a case study comparing KMR with geometry-based summarization techniques on pedestrian fatality data.  It tests the performance and scalability of KMR using both synthetic and real world data sets and demonstrates the computational efficiency of the performance-tuning strategies.

9. K-Main Routes (KMR) Algorithm  Select K paths as initial summary paths Repeat:  Phase 1 Form K clusters by assigning each activity to its closest summary path  Phase 2 Re-compute summary path of each cluster When summary paths do not change, terminate. Using performance-tuning decisions:  Inactive node pruning  1 Network Voronoi Activity assignment (NOVA_TKDE)  2 Divide and Conquer Summary Path Re-computation (D-SPAE_TKDE)

10. K-Main Routes (KMR) Algorithm

11. Validation  Use the real and synthetic data  Compare and optimize the computational cost in performance- tuning decisions such as Network Voronoi Activity assignment and Divide and Conquer Summary Path Re-computation  Observe the trends about number of nodes, routes, activities and active node ratio on seven versions of KMR  Use one case study – Orlando Crime stat

12. Effect of Number of Nodes  Computational savings increase as the number of nodes  Real data Number of routes K= 30 Number of activities = 602 for 60000 nodes Active node ratio = 0.07  Synthetic data Number of routes K= 2 Number of activities =1200 Active node ratio = 0.2

13. Effect of the Number of Routes  Computational savings increase as the number of routes  Real data Number of nodes = 15000 Number of activities = 369 Active node ratio = 0.005  Synthetic data Number of nodes = 1000 Number of activities =1200 Active node ratio = 0.2

14. Effect of the Number of Activities and Active Node Ratio  Computational savings increase with number of activities and active node ratio.  Synthetic data Number of nodes = 1000 Number of routes K= 2 Number of activities =1200 Active node ratio = 0.2

15. Case Study

16. Assumption and Further Work  The performance which activities are around the nodes  Handle the accidents in height (overpass)  Can be applied to more domains (disaster)  Distance based instead of coverage based  The accidents from static to dynamic  Overlapping paths