[Paper Review] Distributed Sensor Selection using a Truncated Newton Method

Danny Bickson, Danny Dolev|arXiv (Cornell University)|Jul 6, 2009

Distributed Sensor Networks and Detection Algorithms12 references3 citations

TL;DR

This paper proposes two distributed algorithms for the NP-hard sensor selection problem—using a truncated Newton method with belief propagation to approximate the Hessian diagonal—enabling scalable, decentralized optimization. The approach achieves near-optimal performance with significantly reduced computation, validated on synthetic data and real Abilene backbone traffic logs.

ABSTRACT

We propose a new distributed algorithm for computing a truncated Newton method, where the main diagonal of the Hessian is computed using belief propagation. As a case study for this approach, we examine the sensor selection problem, a Boolean convex optimization problem. We form two distributed algorithms. The first algorithm is a distributed version of the interior point method by Joshi and Boyd, and the second algorithm is an order of magnitude faster approximation. As an example application we discuss distributed anomaly detection in networks. We demonstrate the applicability of our solution using both synthetic data and real traffic logs collected from the Abilene Internet backbone.

Motivation & Objective

• Address the scalability limitations of centralized interior point methods for large-scale sensor selection problems.
• Develop a distributed algorithm to enable real-time sensor selection without central data aggregation.
• Provide a fast, lightweight approximation to the interior point method that maintains high accuracy.
• Demonstrate applicability in real-world scenarios such as network anomaly detection and data quality optimization.

Proposed method

• Use Gaussian belief propagation (GaBP) to compute an approximation of the main diagonal of the Hessian inverse, avoiding full Hessian inversion.
• Formulate a distributed version of the interior point method by Joshi and Boyd, enabling decentralized computation of sensor selection.
• Introduce a truncated Newton method that uses only partial Hessian information via GaBP, reducing computational cost.
• Implement a convergence enforcement mechanism using iterative message passing in a networked sensor topology.
• Apply a local search heuristic post-approximation to improve solution quality, using sensor swapping to refine selected subsets.
• Use the duality gap as a convergence and performance metric in both synthetic and real-world experiments.

Experimental results

Research questions

• RQ1 Can belief propagation be effectively used to approximate the Hessian diagonal in a distributed Newton method for sensor selection?
• RQ2 How does the performance of the distributed truncated Newton method compare to centralized interior point methods in terms of accuracy and convergence?
• RQ3 To what extent does the proposed approximation algorithm maintain solution quality while reducing computational overhead?
• RQ4 Can the distributed sensor selection framework be effectively applied to real network traffic data for anomaly detection?
• RQ5 How does the approximation quality vary between synthetic Gaussian data and real-world non-Gaussian network traffic?

Key findings

• The distributed truncated Newton method achieved near-optimal performance with a duality gap comparable to the centralized interior point method, but with significantly reduced computation.
• The lightweight approximation algorithm converged in 9–10 iterations per Newton step, while the full Newton method required 20–50 GaBP iterations per Hessian component.
• The full distributed Newton method required up to 25 outer-loop iterations for convergence enforcement, resulting in hundreds of total iterations, compared to tens for the approximation.
• On synthetic data, the approximation algorithm performed well, but on real Abilene network data, its accuracy was lower due to non-Gaussian traffic distributions.
• A local search heuristic applied after the approximation improved solution quality, outperforming the Newton method in some cases.
• The duality gap and upper bounds confirmed that the approximation algorithm remained within a reasonable distance of the optimal solution, with strong correlation to real-world anomaly indicators in the Abilene dataset.