1 information extraction from large scale sensor networks network data collection dimensionality...

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Information extraction from large scale sensor networks

Network data collection Dimensionality reduction dwMDS cooperative self-localization GEM anomaly detection Conclusions

Alfred HeroUniversity of Michigan, Ann Arbor MI, USA

IPAM Jan. 2007

IPAM, Jan. 2007 © 2007 Alfred Hero Slide 2

Acknowledgements Those past and present in my networking group:

(PG) Raviv Raich, Neal Patwari, Jose Costa, Doron Blatt,Clyde Shih, Derek Justice

(G) Raghu Rangarajan, Kevin Carter, Xing Zhou (UG) Adam Pocholsky, Jionglin Wu, Bobby Li (K12) Panna Felsen, Abiola Adatero

Networking sponsors NSF ITR program (John Cozzens) DARPA ISP program (Doug Cochran, Carey Schwartz) AFOSR MURI program (John Tagney) Motorola (Jim Correal) Raytheon (Harry Schmitt)

Networking collaborators: Rob Nowak, Eric Kolaczyk, Mark Crovella, Paul Barford,

Demos Teneketzis, Stephane Lafortune, Mark Coates, Mike Rabat, Randy Moses, Bin Yu …


I. Network data collection: active/passive

Sensor pair (active, ping)

Single sensor (passive, netflow)

0 500 1000 1500 2000 2500 3000 35000

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120

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160Three node network pairwise RSS

time (sec 2)

Rec

eiv

ed

Sig

nal

Str

en

gth


Sensor network information processing challenges

Collected data is frequently of high dimension Response variables Y:

8 x 1,000,000 samples of an rf field 8 x 10242 pixels of a projected image on IR cameras

Latent variables X: 25 targets, 6 dimensional states, one of 10 labels 10243 image volume

Limited collection, aggregation and computation infrastructure Memory constraints Bandwidth constraints Inadequate training data for refined model fitting

Energy constraints limit SNR Limited transmission power on sensor Limited computation power on sensor

Real-time computation is often required


Enabling hypothesis

Most signals exhibit strong correlation across inputs.

snapshots do not carry independent information

8x1000 sa/sec spatio-temporal time series evolves in lower dimension than: t=1 t=2

t=3t=4


Dimensionality reduction 101

n points in d-dimensional linear subspace of RD

Objective: discover intrinsic structure (dimension, hyperplane) Multidimensional scaling (MDS) – Richardson38,

Young&Householder42,Torgerson 51 Our focus: dimensionality reduction in a networked setting

x1

x2 x4

x3

x5

x

y

z


x

y

z

Dimensionality reduction 101

In MDS we observe distances between points

n x n interpoint Euclidean distance matrix:

Can recover X up to rotation/translation by solving

x1

x2 x4

x3

x5


Application to cooperative self-localization

Use measurements made between pairs of unknown-location devices to self localize

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A B

C

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Unknown Location

Wireless Sensors

Known Location

Time-of-Arrival (TOA)

Angle-of-Arrival (AOA)

Received Signal Strength (RSS)

Connectivity (Proximity)

Quantized RSS (QRSS)

Passive spatial correlation Decentralized computation: scalable


Pairwise measurement modes For TOA probing measurements are

while for RSS probing measurements are

where path loss exponent is

PatwariHPCO:03


MDS for sensor self localization

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Sensor field

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MDS data-passage graph


Scalable version of MDS?

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Sensor field Local data passage graph

yiyi


Distributed weighted MDS (CostaPH:06)

LOESS approximation to MDS with weighting w

dwMDS with anchor node regularization


Stress criterion is non-quadratic

However, it has locally additive decomposition

and each summand has “local data passage” property. Optimization transfer optimization algorithm:

Implementation issues for dwMDS


Iterative/distributed dwMDS algorithm

For each local stress can define quadratic surrogate function Q

Monotone iteration

-10 -8 -6 -4 -2 0 2 4 6 8 100

1000

2000

3000

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6000

x-coordinate of one sensor

Cos

t fun

ctio

nCost functions and Surrogate for various iterations

Cost function at iteration kSurrogate at iteration kOriginal cost function


dwMDS simulation: RSS measurements

EstimatorCRB

1- uncertainty ellipses Actual LocationEstimator Mean

Reference Device

Key:

When initialized with NN oracle dwMDS is unbaised and comes close to CRB

Without oracle NNs are estimated by in-range neighbors. First stage dwMDS location estimates have high bias.

Two stage dwMDS attains similar performance as single stage dwMDS with NN oracle

Data simulated with path loss exponent 2.3 and log normal measurement model.


dwMDS experiments

Challenging outdoor propagation environment

Experiment 1 (no freq hopping) Experiment 3 (freq hopping)


dwMDS embedded implementation PHY: 915 MHz FSK transceivers MAC: Carrier sense (unscheduled)

Path Loss integer recorded w/ each reception•Network: Token-passing in a cycle

–Node k transmits to node k+1 to pass token–All nodes in range timestamp any token passing

•(Node id, timestamp of most recent token)

–Fairness passing: Token is passed to the neighbor which hasn’t had it for the longest time. –Low energy passing: In case of tie, choose lowest-path-loss link.

•Transport (cycle reliability): Retransmission ensures continuation of the cycle

•Application: dwMDS3–Nodes update their own coordinate estimate when they have the token.–Random hopping among 16 frequencies (requires coarse sync)

Task 1

Robust Token

Passing

Task 2

dwMDS calculation


Experiment 2 and 3 Results

Experiment 2 RMSE = 25.6 cm

Experiment 3 RMSE = 55.3 cm

Key: Reference / Anchor NodesActual Node Coordinate

Final Estimated Node Coordinate

Key: Reference / Anchor NodesActual Node Coordinate

Final Estimated Node Coordinate


GEM activity detection

• 14 Mica2 motes randomly distributed inside and outside lab• 14*13=182 pairs of RSSI measurements over 30 minute period• 1 sample acquired every ½ sec.• TDMA broadcast of 24 measurements every 12 secs• Students walk into and out of lab at random times over period• Positions of motes unknown• Webcam recorded activity for ground truth

Experiment


Traces of 182 RSSI signals

0 500 1000 1500 2000 2500 3000 35000

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100

150

200

250Intersensor RSS measurements. Top: ground truth anomaly indicator

Time sample/0.5sec

RS

S i

nte

ger


RSS pairwise scatterN

om

inal

(n

o a

ctiv

ity)

No

min

al (

no

act

ivit

y)

Sen

sor

pai

r

Sensor pair

2D projections of nominal 282D RSS

60 70 8080 100 12060 80 10050 100 15070 80 9060

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8080

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12060

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10050

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15070

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Anomaly detection and level sets

Nominal probability density function Thresholded density function

Prob =

Upper Epigraph = acceptance region

Lower Epigraph = rejection region


GEM

Level set is equivalent to Minimum volume set of specified probability Minimum entropy set of specified probability

Geometric entropy minimization (GEM) provides estimation of epigraphs using minimal graphs Density estimation not required K-point MST K-point kNNG

Asymptotic performance analysis of GEM


GEM anomaly detection algorithm

GEM anomaly detection: Training: for a large set of training samples

construct a k-MST for k=(1-)n points, 0<<1, over training samples (assumed nominal).

Test: for a singleton test sample merge test and training samples together Declare anomaly at level if k-MST does not

“capture” test sample

Example: nominal bivariate Gaussian mixture density

New point X is is in capture region of k-MST


GEM vs. UMP test


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sample number

sco

re =

n/m

ax i(

i)L1O kNN scores. rho=0.99751, Pf=0.0046247 , detection rate=0.090186

Experimental results: Pfa=0.25%

Training segment


Experimental results: Pfa=1%

500 1000 1500 2000 2500 3000

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sample number

sco

re =

n/m

ax i(

i)L1O kNN scores. rho=0.9901, Pf=0.017088 , detection rate=0.20424


Conclusions

Non-parametric framework for reliable extraction of information from high dimensional data Model free algorithms Robust performance Scalability through local implementation

dwMDS – dimensionality reduction GEM – anomaly detection


References J. Costa, N. Patwari and A. O. Hero, "Distributed multidimensional

scaling with adaptive weighting for node localization in sensor networks", (.pdf) , ACM Journal on Sensor Networking. vol. 2, No. 1, pp 39-64, Feb. 2006.

N. Patwari, A. O. Hero and J. Costa, "Learning Sensor Location from Signal Strength and Connectivity," in Secure Localization and Time Synchronization for Wireless Sensor and Ad Hoc Networks , Eds. Radha Poovendran, Cliff Wang, and Sumit Roy, Advances in Information Security series, Vol. 30, Springer, Dec. 2006, ISBN 978-0-387-32721-1. (.pdf) .

N. Patwari and A. O. Hero III, "Demonstrating Distributed Signal Strength Location Estimation", in Proceedings of the 4th ACM Conference on Embedded Networked Sensor Systems (SenSys06), Boulder, CO, November 1-3, 2006 (.pdf)

N. Patwari and A.O. Hero, "Manifold learning visualization of network traffic data," SIGCOMM 2005 Workshop on Mining Network Data, Philadelphia, Aug. 2005. (.pdf)

N. Patwari, A.O. Hero, M. Perkins, N.S. Correal and R.J. O’Dea, “Relative Location Estimation in Wireless Sensor Networks,” IEEE Trans. on Signal Processing, vol. 51, no. 8, pp. 2137–2148, Aug. 2003.

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