Transcript Uncertainty Processing and Information Fusion for

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: [email protected]
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
Technical Issues
• Uncertainty representation and computation
• Data/information fusion
• Time-critical computation and quality of
service (QoS) issues
• Uncertainty visualization and validation
Information Acquisition and
Fusion Model for Visualization
Mobile
Agent 1
Mobile Agent i
Info. processing &
fusion
HCI and
Visualization
Communication
Network
Command &
Control Center
Info. processing &
fusion
HCI and
Visualization
Mobile
Agent N
• Dynamic network connectivity with varying bandwidths
• Heterogeneous mobile agents in terms of resources and capabilities
Uncertainty Computation and
Visualization
Information
acquisition
Physical
phenomenon
-sensors
-humans
-databases
Transformation
-sampling
-quantization
-compression
Info. processing
& fusion
-computational
algorithms
Uncertainty computation
Uncertainty
visualization
-target deformation
-glyphs
-animation
Analysis
-interaction
-decision
Uncertainty Representation and
Computation
• Sources of uncertainty
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Sensor and human limitations
Noise, clutter, jamming, etc.
Modeling errors
Algorithm limitations
Data compression, interpolation and
approximation
– Communication connectivity and bandwidth
variations
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
Uncertainty Representation and
Computation (continued)
• Unifying theories for uncertainty
representation
– Projective geometry (DuPree and Antonik)
– Random sets (Mahler, Nguyen, Goodman et al)
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)
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)
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
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
The JDL Model
Data Fusion Domain
Source
Pre-Processing
Level One
Level Two
Level Three
Object
Refinement
Situation
Refinement
Threat
Refinement
Human
Computer
Interface
Sources
Database Management System
Level Four
Process
Refinement
Support
Database
Fusion
Database
Fusion Techniques for
Multisensor Inferencing
Tasks
Fusion levels
• Existence of an entity
• Identity, attributes and
location of an entity
• Behavior and
relationships of entities
• Situation Assessment
• Performance
evaluation and
resource allocation
Techniques
• Signal detection/estimation
theory
• Estimation and filtering,
Kalman filters
• Neural networks,
Clustering, Fuzzy logic
• Knowledge-based systems
• Control and optimization
algorithms
Solution of complex fusion problems requires a
multi-disciplinary approach involving integration of
diverse algorithms and techniques
A Decentralized Statistical
Inferencing Problem
• Solution of a target detection problem by a
team of interconnected detectors
Phenomenon
y2
y1
DM 1
u1
DM 2
y3
DM 3
u2
u3
Fusion Center
u0
yN
DM N
uN
A Decentralized Statistical
Inferencing Problem (Continued)
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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 (NPcomplete)
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
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
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
Research Issues (3)
• Development of models
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Data arrival-time dependence models
Agent location dependence models
Human user inputs (prioritization, risk, feedback)
Incorporation of specialized user knowledge
• Development of algorithms
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Sensitivity analysis (decision-critical data & parameters)
Application of utility theory
Rollback algorithms with multiple milestones
Uncertainty updating based on changes in network topology
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