Distributed Principal Component Analysis for Wireless Sensor Networks
Abstract
:1 Introduction
2 Principal component aggregation in wireless sensor networks
2.1 Data aggregation
2.1.1 Aggregation service
2.1.2 Aggregation primitives
- an initializer init which transforms a sensor measurement into a partial state record,
- an aggregation operator f which merges partial state records, and
- an evaluator e which returns, on the basis of the root partial state record, the result required by the application.
2.1.3 Communication costs
D operation
A operation
F operation
2.2 Principal component analysis
2.3 Principal component aggregation
2.4 Applications
2.4.1 Approximate monitoring
2.4.2 Dimensionality reduction
2.4.3 Event detection
2.5 Tradeoffs
3 Computation of the principal components
3.1 Outline
3.2 Centralized approach
3.2.1 Scalability analysis
Highest network load
Computational and memory costs
3.3 Distributed estimation of the covariance matrix
3.3.1 Positive semi-definiteness criterion
3.3.2 Scalability analysis
Highest network load
Computational and memory costs
3.4 Distributed estimation of the principal components
3.4.1 Power iteration method
3.4.2 Computation of subsequent eigenvectors
3.4.3 Implementation in the aggregation service
Computation of Cv
Normalization and orthogonalization
3.4.4 Synchronization
3.4.5 Scalability analysis
Highest network load
Computational and memory costs
3.5 Summary
4 Experimental results
4.1 Dataset description
4.2 Network simulation
4.3 Principal component aggregation
4.4 Communication costs
4.5 Distributed covariance matrix
4.6 Distributed principal component computation
4.7 Summary
5 Related work
Conclusion
Acknowledgments
References
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- *Measurements are centered so that the origin of the coordinate system coincides with the centroid of the set of measurements. This translation is desirable to avoid a biased estimation of the basis {wk}1≤k≤q of ℝp towards the centroid of the set of measurements.
- †The time to first failure is the amount of time at which the first node in the network runs out of energy.
- ‡that contains negative eigenvalues
Operation | Communication | Computation | Memory |
---|---|---|---|
Covariance | |||
Centralized | O(pT) | O(p2T) | O(p2) |
Distributed | |||
Eigenvectors | |||
Centralized | O(qp) | O(p3) | O(p2) |
Distributed |
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Le Borgne, Y.-A.; Raybaud, S.; Bontempi, G. Distributed Principal Component Analysis for Wireless Sensor Networks. Sensors 2008, 8, 4821-4850. https://doi.org/10.3390/s8084821
Le Borgne Y-A, Raybaud S, Bontempi G. Distributed Principal Component Analysis for Wireless Sensor Networks. Sensors. 2008; 8(8):4821-4850. https://doi.org/10.3390/s8084821
Chicago/Turabian StyleLe Borgne, Yann-Aël, Sylvain Raybaud, and Gianluca Bontempi. 2008. "Distributed Principal Component Analysis for Wireless Sensor Networks" Sensors 8, no. 8: 4821-4850. https://doi.org/10.3390/s8084821