Uncertainty Processing and Information Fusion for Visualization

1. Uncertainty Processing and Information Fusion for Visualization Pramod K. Varshney Electrical Engineering and Computer Science Dept. Syracuse University Syracuse, NY 13244 Phone: (315) 443-4013 Email: varshney@syr.edu

2. Key Personnel • Pramod K. Varshney • Ph.D. in EE, Illinois, 1976 • Data/information fusion, signal and image processing, communication theory and communication networks • Kishan G. Mehrotra • Ph.D. in Statistics, Wisconsin, 1970 • Probability and statistics, neural networks and genetic algorithms • C. K. Mohan • Ph.D. in Computer Science, SUNY at Stony Brook, 1988 • Expert systems, evolutionary algorithms, neural networks

3. Technical Issues • Uncertainty representation and computation • Data/information fusion • Time-critical computation and quality of service (QoS) issues • Uncertainty visualization and validation

4. Information Acquisition andFusion Model for Visualization • Dynamic network connectivity with varying bandwidths • Heterogeneous mobile agents in terms of resources and capabilities

5. Uncertainty Computation and Visualization

6. Uncertainty Representation and Computation • Sources of uncertainty • Sensor and human limitations • Noise, clutter, jamming, etc. • Modeling errors • Algorithm limitations • Data compression, interpolation and approximation • Communication connectivity and bandwidth variations

7. Uncertainty Representation and Computation (continued) • Uncertainty formalisms used by the fusion community • Probability • Dempster-Shafer evidence theory • Fuzzy sets and possibility theory • Uncertainty representation in visualization research • Confidence intervals • Estimation error • Uncertainty range

8. Uncertainty Representation and Computation (continued) • Unifying theories for uncertainty representation • Projective geometry (DuPree and Antonik) • Random sets (Mahler, Nguyen, Goodman et al)

9. Random Sets • Random sets are mathematically isomorphic to Dempster-Shafer bodies of evidence. (Guan and Bell 1992, Smets 1992, Hestir et al 1991) • Many methods are available to convert a given probability distribution to a possibility distribution and vice-versa. (de Cooman et al 1995, Klir and Yuan 1995, Sudkamp 1992)

10. Random Sets (continued) • “Possibility theory and Probability theory arise in Dempster-Shafer evidence theory as fuzzy measures defined on random sets; and their distributions are both fuzzy sets” (Joslyn 1997) • Projective Geometry Approach Dempster-Shafer theory and Probability theory can be combined by using information theoretic approach and projective geometry (DuPree and Antonik, 1998)

11. Research Issues (1) • Practical applications of theory of random sets • Transformation of uncertainty among different formalisms • Development of integrated uncertainty measures based on random set theory and other formalisms for visualization applications. • Computational algorithms for uncertainty measures for visualization

12. Information Fusion • Theory, techniques, and tools for exploiting the synergy in the information acquired from multiple sources: sensors, databases, intelligence sources, humans, etc. • Three levels of fusion: • Data-level • Feature-level • Decision-level

13. The JDL Model Data Fusion Domain Source Pre-Processing Level One Object Refinement Level Two Situation Refinement Level Three Threat Refinement Sources Human Computer Interface Database Management System Support Database Fusion Database Level Four Process Refinement

14. Fusion Techniques for Multisensor Inferencing Tasks Techniques • Existence of an entity • Identity, attributes and location of an entity • Behavior and relationships of entities • Situation Assessment • Performance evaluation and resource allocation • Signal detection/estimation theory • Estimation and filtering, Kalman filters • Neural networks, Clustering, Fuzzy logic • Knowledge-based systems • Control and optimization algorithms Fusion levels Solution of complex fusion problems requires a multi-disciplinary approach involving integration of diverse algorithms and techniques

15. Fusion Center A Decentralized Statistical Inferencing Problem • Solution of a target detection problem by a team of interconnected detectors Phenomenon y2 y3 y1 yN DM 1 DM 2 DM 3 DM N u1 u2 u3 uN u0

16. A Decentralized Statistical Inferencing Problem (Continued) • Fixed parallel network topology • Limited channel bandwidths • Optimization criterion • Under the conditional independence assumption, optimum decision rules are likelihood ratio tests (LRTs) • A computationally intensive problem especially for the dependent observations case (NP-complete)

17. Research Issues (2) • Information fusion algorithms for dynamic distributed networks • Intermittent connectivity, varying bandwidths, mobility, changing link quality • Information fusion and uncertainty analysis • Uncertainty definition and evaluation for different fusion tasks • Information exchange among different system blocks for uncertainty evaluation • Uncertainty evaluation for different network topologies • Uncertainty-aware fusion algorithms

18. Time Critical Computation and QoS • Uncertainty computation in a dynamic distributed environment requires extensive computational effort, conflicting with the requirement of immediate response • Tradeoffs possible between amount of computation and user needs • Intelligent recomputation strategies needed in the context of time-varying inputs from multiple sources • User's input in the visualization process can be exploited to modify consequences of uncertainty computations

19. Time Critical Computation and QoS (Continued) • Data arrives continually, requiring constant recomputation • Complete probabilistic calculations require exponential time • Older results less reliable than newer data • Results may be more sensitive to inputs received from certain sources • Recomputation needed when topology/network connectivity change • Fast yet imprecise answers may sometimes be preferred

20. Research Issues (3) • Development of models • Data arrival-time dependence models • Agent location dependence models • Human user inputs (prioritization, risk, feedback) • Incorporation of specialized user knowledge • Development of algorithms • Sensitivity analysis (decision-critical data & parameters) • Application of utility theory • Rollback algorithms with multiple milestones • Uncertainty updating based on changes in network topology

21. Concluding Remarks • Uncertainty handling is a challenging problem due to heterogeneity of uncertainty sources, their models and characterization • Updating of data and associated uncertainty is crucial in dynamic mobile environments • Joint consideration of information fusion and visualization is expected to yield • greater efficiency • enhanced system performance • responsiveness to user needs