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Why Data Fusion in Sensor Networks needs a new Champion ?. Kalyan Veeramachaneni Evo-Design Group CSAIL, Yumm Eye Tee Work done at D evelopment and R esearch in E volutionary A lgorithms for M ultisensor S mart Net works ( DreamsNet ) Syracuse University. - PowerPoint PPT Presentation
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Why Why Data Fusion in Sensor Networks Data Fusion in Sensor Networks needs a needs a newnew ChampionChampion? ?
Kalyan VeeramachaneniKalyan Veeramachaneni
Evo-Design GroupEvo-Design Group
CSAIL, Yumm Eye Tee CSAIL, Yumm Eye Tee
Work done at Work done at DDevelopment and evelopment and RResearch in esearch in EEvolutionary volutionary AAlgorithms for lgorithms for MMultisensor ultisensor SSmart mart NetNetworks works (DreamsNet)(DreamsNet)
Syracuse University Syracuse University
Evo-Design Group, CSAIL, MIT, September 3, 2009
AcknowledgementsAcknowledgements
Lisa Osadciw, Syracuse University Lisa Osadciw, Syracuse University Kai Goebel, NASA Ames Research Kai Goebel, NASA Ames Research Arun Ross, West Virginia University Arun Ross, West Virginia University Weizhong Yan, GE Global Research CenterWeizhong Yan, GE Global Research Center Vishwanath Avasarala, GE Global Research CenterVishwanath Avasarala, GE Global Research Center Nisha Srinivas, Syracuse University Nisha Srinivas, Syracuse University
22
Sensor Network Projects Sensor Network Projects
Biometric Security System Biometric Security System Wind Turbine Diagnostics and Prognostics Wind Turbine Diagnostics and Prognostics First Responders Sensor Network First Responders Sensor Network Pipeline Crack Detection System Pipeline Crack Detection System Airport Ground Surveillance System Airport Ground Surveillance System
33
Sensors : How big are they?Sensors : How big are they?
44
55
What are we detecting?What are we detecting?
Modern day society relies on detection or Modern day society relies on detection or determining the meaning of the presence or determining the meaning of the presence or absence of a signal absence of a signal
Digital CommunicationsDigital Communications Pipeline/Bridges crack detection Pipeline/Bridges crack detection Genuine User detection using Genuine User detection using
biometrics biometrics Presence of aircraft, ships, or motor Presence of aircraft, ships, or motor
vehicles vehicles Locating emergency personnelLocating emergency personnel Weather PhenomenaWeather Phenomena Building SecurityBuilding Security
Sensors are located in remote areas making Sensors are located in remote areas making decisions using a variety of criteriadecisions using a variety of criteria
Maximum A-Posteriori CriterionMaximum A-Posteriori Criterion Maximum Likelihood CriterionMaximum Likelihood Criterion Minimum Error CriterionMinimum Error Criterion
Systems Level View (1) Systems Level View (1) Signal Processing Signal Processing
66
Model the Probability Density Functions
Design a DetectorUsing a Likelihood Ratio
Test (LRT)
Measure PerformanceBayesian or Neyman
Pearson
Implement the detector on Hardware
Collect Experimental Data (Design of Experiments)
Da
ta
Model Operations
Per
form
ance
Hardware drives the design Ideally we would want a simple threshold on the incoming data
Systems Level View (2) Systems Level View (2) Machine Learning Machine Learning
77
Collect Data Classifier Design
Neural Networks, SVM, Decision Trees, Several other techniques
Data
Measure Performance
Code Implement on
Software
We do not have control on collection of dataData drives the entire design
Applications Applications
Signal ProcessingSignal Processing Digital communications Digital communications Wireless communications Wireless communications RadarsRadars Surveillance systemsSurveillance systems Locationing and GPS Locationing and GPS
88
Machine LearningMachine Learning Online diagnostic tools (aircrafts, Online diagnostic tools (aircrafts,
turbines etc. )turbines etc. ) Medical Diagnostics ( Cancer, Medical Diagnostics ( Cancer,
Neurological disorders, seizures Neurological disorders, seizures etc.) etc.)
Fraud detection on online systems Fraud detection on online systems
Inferencing in Sensor NetworksInferencing in Sensor Networks A mix of both problems A mix of both problems Seamless interaction of hardware and software Seamless interaction of hardware and software Applications are a mix as wellApplications are a mix as well Seamless interaction of system entities as wellSeamless interaction of system entities as well Biometrics is a classic example !! Biometrics is a classic example !!
Likelihood Ratio Test (1) Likelihood Ratio Test (1) Traditional Traditional “digital communications” “digital communications” example example Decide either a bit ‘0’ or ‘1’ has been sent Decide either a bit ‘0’ or ‘1’ has been sent Additive white Gaussian noise (AWGN) Additive white Gaussian noise (AWGN) Likelihood Ratio Test (maximizes posterior probability) Likelihood Ratio Test (maximizes posterior probability)
Optimal for Bayesian Cost Function Optimal for Bayesian Cost Function
99-3 -2 -1 0 1 2 3 4 50
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
score
Lik
elih
ood P
robabili
ty
)|( 0HzP )|( 1HzPNoise only
Signal +noise
)|()|( 1
1
0
0 zHP
H
H
zHP
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H
H
|z)P(H 1
1
0
0
)()|0()()|1( 11010010 HPHbPCHPHbPCR
)(
)(
)|(
)|(
010
101
1
0
1
0
HPC
HPC
H
H
HzP
HzP
Notice this is a linear cost function
Likelihood Ratio Test (2) Likelihood Ratio Test (2)
The ratio for the The ratio for the digital communications digital communications gives us a neat gives us a neat threshold detector threshold detector
As long as As long as standard deviation standard deviation under both the Hypothesis is the same under both the Hypothesis is the same It makes the LRT It makes the LRT linearlinear and very simple to implement and very simple to implement
After taking logarithm on both sides and solving After taking logarithm on both sides and solving
1010
t
H
H
e
e
mz
mz
1
0
2
1
2
0
21
21
20
20
2
1
2
1
1
1
0
t
H
H
z
Likelihood Ratio Test (3)Likelihood Ratio Test (3)
What happens when it is not digital communications ?What happens when it is not digital communications ? For example, unknown signal buried in noiseFor example, unknown signal buried in noise Standard Deviation under both the hypotheses is different Standard Deviation under both the hypotheses is different LRT becomes LRT becomes quadraticquadratic and requires two thresholds and requires two thresholds Note: Still Note: Still Gaussian Gaussian under both the Hypothesis under both the Hypothesis Solving for the roots of the quadratic we get decision regions as: Solving for the roots of the quadratic we get decision regions as:
Decide HDecide H00 : :
Decide HDecide H11 : :
1111
),( 21 ttz
],[ 21 ttz
Likelihood Ratio Test (4) Likelihood Ratio Test (4)
What about when under HWhat about when under H00 is is GaussianGaussian and under H and under H11 it is it is
ExponentialExponential, will the ratio still result in a simple detector? , will the ratio still result in a simple detector? Multimodal distributions with multiple peaks?Multimodal distributions with multiple peaks?
Summary: Summary:
When you have a When you have a linear cost functionlinear cost function, , linear system operations linear system operations (additive noise) (additive noise) you will have neat you will have neat linear operations in the detectorlinear operations in the detector. . Can we design detectors for more complicated models? Can we design detectors for more complicated models?
What happens when we have What happens when we have multiple detectors multiple detectors helping us make a helping us make a decision?decision?
1212
1313
Data Fusion (1) Data Fusion (1)
Binary Binary hypothesis testinghypothesis testing problem problem HH00 : Indicates an absence : Indicates an absence
HH11: Indicates the presence of the phenomena : Indicates the presence of the phenomena
Decisions rendered by Decisions rendered by multiple classifiers (matchers) are fusedmultiple classifiers (matchers) are fused to generate to generate a global decision a global decision
In bandwidth constrained remote processing, decisions are made locally by In bandwidth constrained remote processing, decisions are made locally by the classifier before sending them to the central nodethe classifier before sending them to the central node
1,
0,i i
ii i
xu i
x
1414
Data Fusion (2) Data Fusion (2)
Let Let xxii be the match score generated by the ibe the match score generated by the ithth classifier classifier
Each classifier applies its own threshold, , to determine if xEach classifier applies its own threshold, , to determine if x ii is a genuine or is a genuine or an impostor scorean impostor score
The variable The variable uuii records the decision made by the local classifier. records the decision made by the local classifier.
Let Let [u] [u] = (= (uu11, u, u22, …u, …unn) be the set of decisions rendered by multiple classifiers) be the set of decisions rendered by multiple classifiers The variable The variable uuff denotes the global decision as a consequence of fusing local denotes the global decision as a consequence of fusing local
decisions (udecisions (uff is 0, or u is 0, or uff is 1) is 1)
1,
0,i i
ii i
xu i
x
i
1515
Bandwidth Constrained Detection Networks Bandwidth Constrained Detection Networks
1
2
Sensor1
Sensor2
X1
X2
Fusion Rule
u1
u2
fu
Second Classifier Only
OR
AND
First SensorOnlyLikelihood density model for
a sensor
Noise only
Event
1616
Errors to be minimizedErrors to be minimized
Goal : Two errors need to be minimized. Goal : Two errors need to be minimized.
Bayesian risk function is minimized Bayesian risk function is minimized
0( 1| )AR fF P u H
0 0[ ]
( 1 | [ ], ) ([ ] | )fu
P u u H P u H
1( 0 | )RR fF P u H 1 1
[ ]( 0 | [ ], ) ([ ] | )f
uP u u H P u H
0 0 1 1( 1| )+ ( 0 | )FA f FR fR P C P u H PC P u H
1717
Independent Decisions Independent Decisions The errors can be estimated using The errors can be estimated using
1( 0 | )RR fF P u H
1 1[ ]
( 0 | [ ], ) ([ ] | )fu
P u u H P u H
1 1[ ] 1
( 0 | [ ], ) ( | )n
f iu i
P u u H P u H
1818
Correlated DecisionsCorrelated Decisions
Estimation of 2Estimation of 2nn-1 joint probabilities for n classifiers-1 joint probabilities for n classifiers
Numerical integration is done to estimate the joint probability integralsNumerical integration is done to estimate the joint probability integrals Bahadur-lazarfeld expansion reduces computational burdenBahadur-lazarfeld expansion reduces computational burden
0 1 1[ ]
( 0 | [ ], ) ([ ] | )RRu
F P u u H P u H
1 1[ ] 1
( 0 | [ ], ) ( | ) 1 ......h h h h h h h
n
RR f i ij i j ijk i j ku i j i j ki
F P u u H P u H z z z z z
Correlation between normalized decisions Normalized Decisions
1919
What is the Problem?What is the Problem? Joint optimization of thresholds and fusion rule (decision level)Joint optimization of thresholds and fusion rule (decision level) The objective function is the Bayesian risk function:The objective function is the Bayesian risk function:
We incorporate the thresholds as the search variables, the search is a NP We incorporate the thresholds as the search variables, the search is a NP Complete problemComplete problem11
11 John N Tsitsiklis, Michael Athans, “On Complexity of Decentralized Decision making John N Tsitsiklis, Michael Athans, “On Complexity of Decentralized Decision making and detection problems” 23and detection problems” 23 rdrd IEEE Conference on Decision and Control, 1984 IEEE Conference on Decision and Control, 1984
0 0 1 1( 1| )+ ( 0 | )FA f FR fR P C P u H PC P u H
1 1[ ] 1
( 0 | [ ], ) ( | ) 1 ......h h h h h h h
n
RR f k ij i j ijk i j ku i j i j kk
F P u u H P u H z z z z z
Effect of fusion rule designEffect of threshold design
2020
Bandwidth Constrained Detection NetworksBandwidth Constrained Detection Networks
Two types of Errors need to be reducedTwo types of Errors need to be reduced If the entire observation value is transmitted to a central processing node, an efficient If the entire observation value is transmitted to a central processing node, an efficient machine machine
learning technique learning technique can be designed to achieve better accuracycan be designed to achieve better accuracy Shown below are 20000 samples of observations, 10000 belong to events, 10000 to noise. Shown below are 20000 samples of observations, 10000 belong to events, 10000 to noise.
9 to 32 bits required per sample if all bits are transmitted 9 to 32 bits required per sample if all bits are transmitted Reduces to 1 bit decision if decision is transmitted insteadReduces to 1 bit decision if decision is transmitted instead
Misses: Fail to detect an event
False Alarms: detecting an event that did not occur
Threshold on Sensor 1
Threshold on Sensor 2
Event is declared only in this quadrant, i.e. AND rule
Noise * Event
2121
What has been happening in this area?What has been happening in this area?
Amount of Research and Publications on Topic Indicates ComplexityAmount of Research and Publications on Topic Indicates Complexity Quick Check Research PublicationsQuick Check Research Publications
120 Journal Articles with Approximately 45 Discussing Similar Design Issues120 Journal Articles with Approximately 45 Discussing Similar Design Issues 48 Textbooks At Least Currently On Sale In This Area 48 Textbooks At Least Currently On Sale In This Area 5 Dissertations deal with same problem and provide human developed designs5 Dissertations deal with same problem and provide human developed designs
Paper Published that Addresses the Difficulty Paper Published that Addresses the Difficulty John N Tsitsiklis, Michael Athans, “On Complexity of Decentralized Decision making John N Tsitsiklis, Michael Athans, “On Complexity of Decentralized Decision making
and detection problems” 23rd IEEE Conference on Decision and Control, 1984and detection problems” 23rd IEEE Conference on Decision and Control, 1984 Optimizing Distributed Detection for 2 SensorsOptimizing Distributed Detection for 2 Sensors
Independent sensors: Intractable Independent sensors: Intractable Correlated sensors: NP Complete Correlated sensors: NP Complete --
Researchers are reluctant to use EAs Researchers are reluctant to use EAs A simple architectural or a parameter change can give you literally 10 pages A simple architectural or a parameter change can give you literally 10 pages
worth of equations, fancy !! worth of equations, fancy !! Failure modes of gradient descent and other approaches are not identified Failure modes of gradient descent and other approaches are not identified
2222
Likelihood Ratio Test Based Design Likelihood Ratio Test Based Design Decouple the two problems: optimize thresholds and fusion rule separatelyDecouple the two problems: optimize thresholds and fusion rule separately
Identify optimal individual threshold that minimizes the Bayesian ErrorIdentify optimal individual threshold that minimizes the Bayesian Error
Optimal fusion rule for independent decisions Optimal fusion rule for independent decisions
Optimal fusion rule for correlated decisions Optimal fusion rule for correlated decisions
0
0
1 1
1
1log 1 log log
(2 )1
j j
j j
NFAFR FR
j jFAj FA FA
HP P P C
u uP P CP
H
1 1 1 1 1 1 1
0 0 0 0 0 0 0
0
0
)1
1
1 ........
log log1 ...... (1
ij i j ijk i j kFAi j i j k
FAij i j ijk i j ki j i j k
Hz z z z z
P C
z z z z z P C
H
arg mini
ii R
Gradient Descent Approach Gradient Descent Approach Use gradient information to simultaneously optimize fusion rule and thresholdsUse gradient information to simultaneously optimize fusion rule and thresholds
where where
Threshold for a sensor is the solution of the likelihood ratio test given by Threshold for a sensor is the solution of the likelihood ratio test given by
where where
0 10 0 0 0 10 0
1 01 0 1 1 01 1
( 1| [ ], 0, ) ( 1| )
( 0 | [ ], 0, ) ( 1| )
i ii i
i ii i
R P C P u u u H P C P u H A
PC P u u u H B PC P u H
0 0 0 0( 1| [ ], 1, ) ( 1| [ ], 0, )i i ii iA P u u u H P u u u H
0 1 0 1( 0 | [ ], 0, ) ( 0 | [ ], 1, )i i ii iB P u u u H P u u u H
01,
1
01
1,
0 ( ) ( | )( / )
( / )( ) ( | )
1
i
i
Nii
FA kk k iu
iN
iiD k
k k iui
u C D u P u HP x H
P x HC D u P u H
u
0 0( ) ( 1| [ ], 1) ( 1| [ ], 0)i i ii iD u P u u u P u u u
1 2 1 1[ ] , , . . . , ,...Ti
i i nu u u u u u
2424
Particle Swarm Optimization Particle Swarm Optimization
1 2( , .......... )i i i inX Each particle is a solution
Particles are randomly initialized in the search space
Particle are moved in the search space using
( 1) tidV
( ) ( ) ( )1
( ) ( )2
[0,1] ( )
[0,1] ( )
t t tid id id
t tgd id
V U p x
U p x
( 1) ( ) ( 1)t t tiq iq iqX X V
Demonstration on a test problem
2525
PSO Based Design PSO Based Design
Random Initialization of Particles
Velocity and Position Updates
Cost Evaluation
Save the best solution so far
Update Particles Memory
i<n
PSO parameters
CFA
Training Data
Output the best
solution
Convergence
PSO : Binary Search SpacesPSO : Binary Search Spaces
Using a sigmoid transformation on the velocity, the probability of Using a sigmoid transformation on the velocity, the probability of a binary variable can be determined ( Kennedy et al.)a binary variable can be determined ( Kennedy et al.)
Position update is changed toPosition update is changed to
Velocity update equation is not changed and the learning Velocity update equation is not changed and the learning
behavior of swarm is preservedbehavior of swarm is preserved
1( )
1 idid id VS sig V
e
( [0,1])id idX u S U
( 1) tidV
( ) ( ) ( )1
( ) ( )2
[0,1] ( )
[0,1] ( )
t t tid id id
t tgd id
V U p x
U p x
PSO : Binary Search SpacesPSO : Binary Search Spaces
Transition is now probabilisticTransition is now probabilistic
Particles try to position themselves in the velocity space such that they Particles try to position themselves in the velocity space such that they have maximum probability of having a value ‘1’, in case they have have maximum probability of having a value ‘1’, in case they have evidence from multiple neighbors/iterations about the goodness of being evidence from multiple neighbors/iterations about the goodness of being at value ‘1’ for a variable at value ‘1’ for a variable
PSO : Discrete Search Spaces PSO : Discrete Search Spaces
Many problems in real world optimization are binary, discreteMany problems in real world optimization are binary, discrete
For example, in sensor management, sensor selection, i.e., the sensor For example, in sensor management, sensor selection, i.e., the sensor
number is discrete variablenumber is discrete variable
Increased complexity due to binary transformation of a discrete variableIncreased complexity due to binary transformation of a discrete variable
The Hamming distance between two discrete values undergoes a non-The Hamming distance between two discrete values undergoes a non-linear transformation when an equivalent binary representation is used linear transformation when an equivalent binary representation is used insteadinstead
The range of the discrete variable often does not match the upper limit of The range of the discrete variable often does not match the upper limit of the equivalent binary representationthe equivalent binary representation
For example, a discrete variable of range [0,1,2,3,4,5] requires a three bit binary For example, a discrete variable of range [0,1,2,3,4,5] requires a three bit binary representation, which ranges between [0-7]representation, which ranges between [0-7]
PSO : Discrete Search Spaces PSO : Discrete Search Spaces
Modify the Sigmoid Transformation, for a M-ary system Modify the Sigmoid Transformation, for a M-ary system
The sigmoid gives the parameters of the distribution from which The sigmoid gives the parameters of the distribution from which the discrete value is generated, i.e., the discrete value is generated, i.e.,
Particles try to position themselves in the velocity space such Particles try to position themselves in the velocity space such that the probability of one or the other discrete variable is highthat the probability of one or the other discrete variable is high
1 idid V
MS
e
Using normal distribution here, Other distributions can be used
if
( ( 1) (1))id idX round S M randn
1 1id idX M then X M 0 0id idX then X if
Boundary Conditions, due to infinite support of the normal distribution
PSO : Discrete Search SpacesPSO : Discrete Search Spaces
( ( 1) (1))id idX round S M randn
1 1id idX M then X M 0 0id idX then X if
Boundary Conditions, due to infinite support of the normal distribution
0.5 0.1
3131
1
2
Sensor1
Sensor2
X1
X2
Fusion Rule
u1
u2
Human Design Solution: Likelihood Ratio Test (LRT) DesignHuman Design Solution: Likelihood Ratio Test (LRT) Design
fu
Optimize thresholds individually by keeping other thresholds and fusion rule constant
Use LRT for independent or correlated deriving fusion rule
Human Design Solution: Person-by-Person Optimal (PBPO) for Independent SensorsHuman Design Solution: Person-by-Person Optimal (PBPO) for Independent Sensors Human Competitive Result: Particle Swarm Optimization (PSO) Based DesignHuman Competitive Result: Particle Swarm Optimization (PSO) Based Design
Joint optimization of thresholds and Fusion RuleNo closed form solution exists
Sensor Suites : Homogeneous NetworkSensor Suites : Homogeneous Network
All sensors are identical in performanceAll sensors are identical in performance
Sensor Suites: Heterogeneous Network Type 1 Sensor Suites: Heterogeneous Network Type 1
Different sensors have different separation of means between the Different sensors have different separation of means between the two hypothesis two hypothesis
Sensor Suite : Heterogeneous Network Type 2 Sensor Suite : Heterogeneous Network Type 2
Different standard deviations under both hypothesis and different separation Different standard deviations under both hypothesis and different separation
of means,of means, solution to LRT is quadraticsolution to LRT is quadratic
Results- Independent Observations, Results- Independent Observations, Homogeneous NetworkHomogeneous Network
Number of Sensors PBPO PSO
% Improvements
3 0.22684 0.226843 0
6 0.15613 0.15613 0
9 0.11254 0.109758 2.4720
12 0.083829 0.079862 4.7322
15 0.060243 0.0586917 2.575
Probability of Error Achieved for Different AlgorithmsAveraged over 100 Trials
Results- Independent Observations, Homogeneous Results- Independent Observations, Homogeneous NetworkNetwork
Counting the evaluations to measure “time”Counting the evaluations to measure “time”
Evaluation Counts for PBPO vs. PSO Across Different Number of Sensors
0.00E+005.00E+021.00E+031.50E+032.00E+032.50E+033.00E+033.50E+034.00E+03
3 8 13
Number of Sensors
Nu
mb
er
of
Err
or
Fu
nc
tio
n E
va
lua
tio
ns
PBPO EvaluationCounts
2*exp(N/2)
N^3
PSO EvaluationCounts
Results : Independent Observations, Heterogeneous Type 1Results : Independent Observations, Heterogeneous Type 1
Number of Sensors PBPO PSO
% Improvements
3 0.0564834 0.055501 1.7384
5 0.0023426 0.0014518 38.0250
7 7.022446e-006 1.97107e-006 71.9317
9 3.539055e-009 5.2906e-011 98.5050
Probability of Error Achieved for Different AlgorithmsAveraged over 100 Trials
Preliminary Results : Independent Observations, Preliminary Results : Independent Observations, Heterogeneous Type 2 Heterogeneous Type 2
Number of Sensors
PBPO PSO(Single
Threshold)
% Benefits
3 1.4350e-004 2.7207e-005 81.04
4 8.9807e-006 7.9398e-006 11.59
Probability of Error Achieved for Different AlgorithmsAveraged over 100 Trials
3939
Result: Independent SensorsResult: Independent Sensors
Number of Number of Sensors Sensors PBPOPBPO PSOPSO
% % Improvements in Improvements in accuracy accuracy
33 0.05648340.0564834 0.0555010.055501 1.73841.7384
55 0.00234260.0023426 0.00145180.0014518 38.025038.0250
77 7.022446e-0067.022446e-006 1.97107e-0061.97107e-006 71.931771.9317
99 3.539055e-0093.539055e-009 5.2906e-0115.2906e-011 98.505098.5050
Human Design Accuracy
PSO Resulting Accuracy
PBPO-Person-By-Person Optimal
PSO – Particle Swarm Optimization
4040
Result: Correlated Sensors Result: Correlated Sensors
Probability of Error
0.00E+00
1.00E-03
2.00E-03
3.00E-03
4.00E-03
5.00E-03
6.00E-03
7.00E-03
8.00E-03
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Correlation Factor
Pro
ba
bili
ty o
f E
rro
r
LRT Based
PSO Based
Human Design
54% 13%
2.5%
Data Driven Design Data Driven Design
4141
no
yes
4242
Correlated Sensors: Designs for 0.1 Correlation Correlated Sensors: Designs for 0.1 Correlation For one specific cost structure For one specific cost structure
LRT (Human) Based Design: 2 thresholds on each sensor 2 Sensor only fusion rule
Region where an event is declared
PSO Based Design:Simple 1 Threshold for each sensor AND fusion ruleVery few errors
Region where an eventis declared
4343
Correlated Sensors: Designs for 0.9 Correlation Correlated Sensors: Designs for 0.9 Correlation
LRT (Human) Based Design: 2 thresholds on each sensor 2 Sensor only fusion rule
Region where an event is declared
PSO Based Design:Simple 1 Threshold for each sensor AND fusion ruleHigher number of errors, but still better
Region where an eventis declared
Comparison of Data Driven PSO Design with Other Comparison of Data Driven PSO Design with Other Approaches and Single Sensor Performance Approaches and Single Sensor Performance
4444
Varying the costs in the Bayesian Risk function and generating the designs gives the entire Receiver operating characteristic curve
Discrete Version of the Problem Discrete Version of the Problem Vendors only allow you to have access to multiple points on the ROC Vendors only allow you to have access to multiple points on the ROC The problem then becomes a The problem then becomes a combinatorial optimization combinatorial optimization problem problem Design problem is then:Design problem is then:
Operating point for each sensor Operating point for each sensor Fusion rule ( can still be solved by LRT) Fusion rule ( can still be solved by LRT)
Suppose we have three classifiers and each classifier can operate on any of Suppose we have three classifiers and each classifier can operate on any of the ‘N’ operating points, there are the ‘N’ operating points, there are 33NN choices for this problem choices for this problem
Discrete version of PSO or GA is used to identify the operating point sets. Discrete version of PSO or GA is used to identify the operating point sets. No alternative approaches existNo alternative approaches exist
4545
Multi-Objective Design Multi-Objective Design
Allows system designer to make trade-offs Allows system designer to make trade-offs Makes the Makes the fused system ROC fused system ROC available to the system designer available to the system designer
Adding a sensor, how much does it help?Adding a sensor, how much does it help? Since Since fused system ROC fused system ROC is available, area under the curve gives a metric to is available, area under the curve gives a metric to
evaluate the system evaluate the system Allows system designers to make choices when acquiring sensors from multiple Allows system designers to make choices when acquiring sensors from multiple
vendors vendors
If I have to use sensors incrementally, which ones should I focus If I have to use sensors incrementally, which ones should I focus on ? on ?
If I want to add sensors to my detection system, which sensors should I add to If I want to add sensors to my detection system, which sensors should I add to improve performance improve performance
4646
Multi-Objective Design Multi-Objective Design Homogeneous Sensor Suite Homogeneous Sensor Suite
4747
Multi-Objective Design Multi-Objective Design Heterogeneous Sensor Suite Heterogeneous Sensor Suite
4848
Multi-Objective Design Multi-Objective Design Results for Sensor Suites with 4,5 Sensors Results for Sensor Suites with 4,5 Sensors
4949
Algorithm design for generating non-dominated solutions (close to Pareto set)
• Non-Dominated Sorting PSO instead of a cost function • Continuous PSO for thresholds• Binary PSO for fusion rule, cannot use LRT for fusion rule
Multi-Objective Design Multi-Objective Design
5050
Distributed Detection Networks : Parallel and Serial Distributed Detection Networks : Parallel and Serial
S1
S3
S4
S2
S5S6
b2
b5u0
S1
S3 S4S2
Fusion Center
2 Sensor Serial Network Example 2 Sensor Serial Network Example
1
1 1
1
1
0
u
x
u
1 1
2 2
0 12 2 2 2
2 2
1 1
or
0 0
b b
b b
x x
b b
fu
Sensor2 X2
Sensor1 X1 b1
Organization of Serial Networks: Organization of Serial Networks: Who reports to Whom?Who reports to Whom?
For a homogeneous network with all the For a homogeneous network with all the sensors having same statistics, this is not sensors having same statistics, this is not a problem a problem
For a Heterogeneous network, the For a Heterogeneous network, the sequence affects the performance sequence affects the performance
As the number of sensors increase, the As the number of sensors increase, the number of possible sequences increase number of possible sequences increase exponentiallyexponentially
# Sensors # Sequences
5 120
6 720
8 40320
10 3628800
Serial Networks: Coupled Problem Serial Networks: Coupled Problem
The algorithm design for optimization and control of a distributed The algorithm design for optimization and control of a distributed serial detection network involves two steps:serial detection network involves two steps:
1:Identify the optimal sequence of sensors, ‘who reports to whom?’1:Identify the optimal sequence of sensors, ‘who reports to whom?’ 2:Identify the optimal local decision rules for sensors.2:Identify the optimal local decision rules for sensors.
A hybrid of PSO –ABC is used to control the sequence and identify A hybrid of PSO –ABC is used to control the sequence and identify the thresholds for a given sequencethe thresholds for a given sequence
Ants Identify the SequenceThe minimum error that is achieved by the sequence,
given by PSO, is used to move in the search space locating
better sequences
PSO Identifies the optimal thresholds for a sequence and feeds the minimum possible error for a given sequence
The
con
figur
atio
n
Receiver Operating Characteristic Curve: 10 Sensor Test Receiver Operating Characteristic Curve: 10 Sensor Test Bed Bed
Best PerformingSensor
Results: Serial NetworksResults: Serial Networks
% of Unique Evaluations (log plot)
-10
-8
-6
-4
-2
0
2
5 7 9 11 13 15
Number of Sensors
% E
valu
atio
ns
in L
og
Probability of Error Achieved for Different AlgorithmsAveraged over 30 Trials
Sensor Management of a Building Access Control SystemSensor Management of a Building Access Control SystemAdaptation in Real Time Adaptation in Real Time
5757
0 0 1 1( 1| )+ ( 0 | )FA f FR fR P C P u H PC P u H
5858
Thank you!Thank you!
5959
1
2
Sensor1
Sensor2
X1
X2
Fusion Rule
u1
u2
Human Design Solution:Human Design Solution:Likelihood Ratio Test (LRT) DesignLikelihood Ratio Test (LRT) Design
1
11 arg min R
0
0
1 1
1
1log 1 log log
(2 )1j j
j j
NFAM M
j jFAj FA FA
H
P P P Cu u
P P CPH
LRT based fusion rule for independent sensors
2
22 arg min R
fu
1 1 1 1 1 1 1
0 0 0 0 0 0 0
0
0
)1
1
1 ........
log log1 ...... (1
ij i j ijk i j kFAi j i j k
FAij i j ijk i j ki j i j k
Hz z z z z
P C
z z z z z P C
H
LRT based Fusion Rule for
correlated sensors
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