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 [phone]
• Email varshney_at_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

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

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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