Distributed Gram-Schmidt orthogonalization based on dynamic consensus

Slučiak, Ondrej; Straková, Hana; Rupp, Markus; Gansterer, Wilfried N.

doi:10.1109/acssc.2012.6489213

Cited by 8 publications

(4 citation statements)

References 16 publications

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“…There exist many variations of the algorithm, e.g., [ 27 – 33 ]. Comparing the proposed DS-CGS algorithm with a dynamic consensus algorithm from [ 30 , 32 ], we observe an interesting resemblance.…”

Section: Distributed Classical Gram-schmidt With Simultaneous Elementmentioning

confidence: 89%

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Distributed Gram-Schmidt orthogonalization with simultaneous elements refinement

Slučiak

Straková

Rupp

et al. 2016

EURASIP J. Adv. Signal Process.

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We present a novel distributed QR factorization algorithm for orthogonalizing a set of vectors in a decentralized wireless sensor network. The algorithm is based on the classical Gram-Schmidt orthogonalization with all projections and inner products reformulated in a recursive manner. In contrast to existing distributed orthogonalization algorithms, all elements of the resulting matrices Q and R are computed simultaneously and refined iteratively after each transmission. Thus, the algorithm allows a trade-off between run time and accuracy. Moreover, the number of transmitted messages is considerably smaller in comparison to state-of-the-art algorithms. We thoroughly study its numerical properties and performance from various aspects. We also investigate the algorithm’s robustness to link failures and provide a comparison with existing distributed QR factorization algorithms in terms of communication cost and memory requirements.

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Section: Distributed Classical Gram-schmidt With Simultaneous Elementmentioning

confidence: 89%

“…Preliminary parts of this work were previously published at the 46th Asilomar Conf. Sig., Syst., Comp., Pacific Grove, CA, USA, Nov. 2012 [ 32 ].…”

Section: Acknowledgementsmentioning

confidence: 99%

Distributed Gram-Schmidt orthogonalization with simultaneous elements refinement

Slučiak

Straková

Rupp

et al. 2016

EURASIP J. Adv. Signal Process.

Self Cite

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“…The latter arise due to many reasons such as channel congestions, message collisions, moving nodes, or dynamic topology [18]. Link failures can be modeled by the absence of a bidirectional connection between two nodes.…”

Section: Simulation Resultsmentioning

confidence: 99%

Gradient Descent Localization in Wireless Sensor Networks

Alwan¹,

Hussain²

2017

Wireless Sensor Networks - Insights and Innovations

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Meaningful information sharing between the sensors of a wireless sensor network (WSN) necessitates node localization, especially if the information to be shared is the location itself, such as in warehousing and information logistics. Trilateration and multilateration positioning methods can be employed in two-dimensional and threedimensional space respectively. These methods use distance measurements and analytically estimate the target location; they suffer from decreased accuracy and computational complexity especially in the three-dimensional case. Iterative optimization methods, such as gradient descent (GD), offer an attractive alternative and enable moving target tracking as well. This chapter focuses on positioning in three dimensions using time-of-arrival (TOA) distance measurements between the target and a number of anchor nodes. For centralized localization, a GD-based algorithm is presented for localization of moving sensors in a WSN. Our proposed algorithm is based on systematically replacing anchor nodes to avoid local minima positions which result from the moving target deviating from the convex hull of the anchors. We also propose a GD-based distributed algorithm to localize a fixed target by allowing gossip between anchor nodes. Promising results are obtained in the presence of noise and link failures compared to centralized localization. Convergence factor issues are discussed, and future work is outlined.

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“…Federated QR algorithms have been suggested mainly in the field of peer-to-peer networks relying on the PushSum algorithm and gossiping [12], [13], [14]. While these schemes can be implemented in a modern federated learning system, the assumptions governing FL make these algorithms unsuited.…”

Section: Related Workmentioning

confidence: 99%

Privacy of federated QR decomposition using additive secure multiparty computation

Hartebrodt¹,

Röttger²

2022

Preprint

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Federated learning (FL) is a privacy-aware data mining strategy keeping the private data on the owners' machine and thereby confidential. The clients compute local models and send them to an aggregator which computes a global model. In hybrid FL, the local parameters are additionally masked using secure aggregation, such that only the global aggregated statistics become available in clear text, not the client specific updates. Federated QR decomposition has not been studied extensively in the context of cross-silo federated learning. In this article, we investigate the suitability of three QR decomposition algorithms for cross-silo FL and suggest a privacy-aware QR decomposition scheme based on the Gram-Schmidt algorithm which does not blatantly leak raw data. We apply the algorithm to compute linear regression in a federated manner.

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Distributed Gram-Schmidt orthogonalization based on dynamic consensus

Cited by 8 publications

References 16 publications

Distributed Gram-Schmidt orthogonalization with simultaneous elements refinement

Distributed Gram-Schmidt orthogonalization with simultaneous elements refinement

Gradient Descent Localization in Wireless Sensor Networks

Privacy of federated QR decomposition using additive secure multiparty computation

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