Nonmetric MDS for sensor localization

Nhat, Vo Dinh Minh; Vo, Duc Minh; Challa, Subhash; Lee, Sungyoung

doi:10.1109/iswpc.2008.4556237

Cited by 16 publications

(7 citation statements)

References 19 publications

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“…Such situations arise when the observed data contain significantly large errors when compared to the magnitudes of the true data. The embedding problem has recently attracted lots of attention, see [2,19] and references therein for recent development.…”

Section: Discussionmentioning

confidence: 99%

An Inexact Smoothing Newton Method for Euclidean Distance Matrix Optimization Under Ordinal Constraints

Qi¹

2017

JCM

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When the coordinates of a set of points are known, the pairwise Euclidean distances among the points can be easily computed. Conversely, if the Euclidean distance matrix is given, a set of coordinates for those points can be computed through the well known classical Multi-Dimensional Scaling (MDS). In this paper, we consider the case where some of the distances are far from being accurate (containing large noises or even missing). In such a situation, the order of the known distances (i.e., some distances are larger than others) is valuable information that often yields far more accurate construction of the points than just using the magnitude of the known distances. The methods making use of the order information is collectively known as non-metric MDS. A challenging computational issue among all existing nonmetric MDS methods is that there are often a large number of ordinal constraints. In this paper, we cast this problem as a matrix optimization problem with ordinal constraints. We then adapt an existing smoothing Newton method to our matrix problem. Extensive numerical results demonstrate the efficiency of the algorithm, which can potentially handle a very large number of ordinal constraints.Mathematics subject classification: 90C30, 90C26, 90C90.

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Section: Discussionmentioning

confidence: 99%

An Inexact Smoothing Newton Method for Euclidean Distance Matrix Optimization Under Ordinal Constraints

Qi¹

2017

JCM

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“…Techniques for capturing similarity among items using triplets have been applied in many areas like computer vision [36], sensor localization [37], nearest neighbor search [38] and density estimation [39]. In [40], authors learn perceptual kernels using different similarity methods.…”

Section: Design Space Visualizationmentioning

confidence: 99%

Interpreting Idea Maps: Pairwise Comparisons Reveal What Makes Ideas Novel

Ahmed

Ramachandran

Fuge

et al. 2018

Journal of Mechanical Design

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Assessing similarity between design ideas is an inherent part of many design evaluations to measure novelty. In such evaluation tasks, humans excel at making mental connections among diverse knowledge sets to score ideas on their uniqueness. However, their decisions about novelty are often subjective and difficult to explain. In this paper, we demonstrate a way to uncover human judgment of design idea similarity using two-dimensional (2D) idea maps. We derive these maps by asking participants for simple similarity comparisons of the form “Is idea A more similar to idea B or to idea C?” We show that these maps give insight into the relationships between ideas and help understand the design domain. We also propose that novel ideas can be identified by finding outliers on these idea maps. To demonstrate our method, we conduct experimental evaluations on two datasets—colored polygons (known answer) and milk frother sketches (unknown answer). We show that idea maps shed light on factors considered by participants in judging idea similarity and the maps are robust to noisy ratings. We also compare physical maps made by participants on a white-board to their computationally generated idea maps to compare how people think about spatial arrangement of design items. This method provides a new direction of research into deriving ground truth novelty metrics by combining human judgments and computational methods.

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“…It gains better performance since it demands less rigid relationship between dissimilarities and distances. For the last few years ordinal MDS has widely been applied for node localization issues in WSN [24][25][26][27][28]. Miao and others [25] propose a RI-MDS localization algorithm that combines metric and nonmetric MDS and use affine transformation to translate relative coordinates to absolute ones.…”

Section: Ordinal Mds and Itsmentioning

confidence: 99%

“…Miao and others [25] propose a RI-MDS localization algorithm that combines metric and nonmetric MDS and use affine transformation to translate relative coordinates to absolute ones. Nhat and others [24] propose NMDS-TOA localization algorithm that combines TDOA and MDS-map and uses sufficient number of anchor nodes to form the final estimated map. The significance of applying ordinal MDS over metric MDS is as follows.…”

Section: Ordinal Mds and Itsmentioning

confidence: 99%

Wormhole Detection Based on Ordinal MDS Using RTT in Wireless Sensor Network

Mukherjee

Chattopadhyay

et al. 2016

Journal of Computer Networks and Communications

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In wireless communication, wormhole attack is a crucial threat that deteriorates the normal functionality of the network. Invasion of wormholes destroys the network topology completely. However, most of the existing solutions require special hardware or synchronized clock or long processing time to defend against long path wormhole attacks. In this work, we propose a wormhole detection method using range-based topology comparison that exploits the local neighbourhood subgraph. The Round Trip Time (RTT) for each node pair is gathered to generate neighbour information. Then, the network is reconstructed by ordinal Multidimensional Scaling (MDS) followed by a suspicion phase that enlists the suspected wormholes based on the spatial reconstruction. Iterative computation of MDS helps to visualize the topology changes and can localize the potential wormholes. Finally, a verification phase is used to remove falsely accused nodes and identify real adversaries. The novelty of our algorithm is that it can detect both short path and long path wormhole links. Extensive simulations are executed to demonstrate the efficacy of our approach compared to existing ones.

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Nonmetric MDS for sensor localization

Cited by 16 publications

References 19 publications

An Inexact Smoothing Newton Method for Euclidean Distance Matrix Optimization Under Ordinal Constraints

An Inexact Smoothing Newton Method for Euclidean Distance Matrix Optimization Under Ordinal Constraints

Interpreting Idea Maps: Pairwise Comparisons Reveal What Makes Ideas Novel

Wormhole Detection Based on Ordinal MDS Using RTT in Wireless Sensor Network

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