4 research outputs found
Network Topology Mapping from Partial Virtual Coordinates and Graph Geodesics
For many important network types (e.g., sensor networks in complex harsh
environments and social networks) physical coordinate systems (e.g.,
Cartesian), and physical distances (e.g., Euclidean), are either difficult to
discern or inapplicable. Accordingly, coordinate systems and characterizations
based on hop-distance measurements, such as Topology Preserving Maps (TPMs) and
Virtual-Coordinate (VC) systems are attractive alternatives to Cartesian
coordinates for many network algorithms. Herein, we present an approach to
recover geometric and topological properties of a network with a small set of
distance measurements. In particular, our approach is a combination of shortest
path (often called geodesic) recovery concepts and low-rank matrix completion,
generalized to the case of hop-distances in graphs. Results for sensor networks
embedded in 2-D and 3-D spaces, as well as a social networks, indicates that
the method can accurately capture the network connectivity with a small set of
measurements. TPM generation can now also be based on various context
appropriate measurements or VC systems, as long as they characterize different
nodes by distances to small sets of random nodes (instead of a set of global
anchors). The proposed method is a significant generalization that allows the
topology to be extracted from a random set of graph shortest paths, making it
applicable in contexts such as social networks where VC generation may not be
possible.Comment: 17 pages, 9 figures. arXiv admin note: substantial text overlap with
arXiv:1712.1006
Matrix Completion Optimization for Localization in Wireless Sensor Networks for Intelligent IoT
Localization in wireless sensor networks (WSNs) is one of the primary functions of the intelligent Internet of Things (IoT) that offers automatically discoverable services, while the localization accuracy is a key issue to evaluate the quality of those services. In this paper, we develop a framework to solve the Euclidean distance matrix completion problem, which is an important technical problem for distance-based localization in WSNs. The sensor network localization problem is described as a low-rank dimensional Euclidean distance completion problem with known nodes. The task is to find the sensor locations through recovery of missing entries of a squared distance matrix when the dimension of the data is small compared to the number of data points. We solve a relaxation optimization problem using a modification of Newton’s method, where the cost function depends on the squared distance matrix. The solution obtained in our scheme achieves a lower complexity and can perform better if we use it as an initial guess for an interactive local search of other higher precision localization scheme. Simulation results show the effectiveness of our approach
Matrix Completion Optimization for Localization in Wireless Sensor Networks for Intelligent IoT
Localization in wireless sensor networks (WSNs) is one of the primary functions of the intelligent Internet of Things (IoT) that offers automatically discoverable services, while the localization accuracy is a key issue to evaluate the quality of those services. In this paper, we develop a framework to solve the Euclidean distance matrix completion problem, which is an important technical problem for distance-based localization in WSNs. The sensor network localization problem is described as a low-rank dimensional Euclidean distance completion problem with known nodes. The task is to find the sensor locations through recovery of missing entries of a squared distance matrix when the dimension of the data is small compared to the number of data points. We solve a relaxation optimization problem using a modification of Newton’s method, where the cost function depends on the squared distance matrix. The solution obtained in our scheme achieves a lower complexity and can perform better if we use it as an initial guess for an interactive local search of other higher precision localization scheme. Simulation results show the effectiveness of our approach