Weighted-multidimensional Scaling Research Articles

On Absoluteness and Stationary Condition of WMDS for Range-Based Localization

Weighted multidimensional scaling (WMDS), an algorithm extending multidimensional scaling (MDS), has been utilized in a broad spectrum of localization. However, there are still two unsolved theoretical questions. (i) The estimator provided by MDS depicts a relative placement of targets which requires further Procrustes analysis to recover the actual placement, referred to as the absolute placement. This fact produces a question: Does the estimator of WMDS is still relative? If not, what underlying mechanisms assert the absoluteness? (ii) It has been proved that WMDS attains the Cramér-Rao lower bound (CRLB) when the ranging distribution is Gaussian. Does it hold for a general distribution? If not, what restrictions on distributions are required? Motivated by such theoretical incompleteness, this paper offers an in-depth theoretical analysis on WMDS in the scheme of range-based localization. With regard to question (i), we reveal the mechanisms that assert the estimator of WMDS always represents exactly the actual locations, and prove that the absoluteness is introduced at the moment of variable separation and all the subsequent matrix equation transformations preserve the absoluteness. As for question (ii), the functional behaviors and maximum condition of CRLB are examined under a general ranging distribution. Then, via the comparison to the variance of WMDS estimator, the stationary condition on ranging distributions for WMDS to attain the CRLB is provided. Extensive simulations are performed to validate the theoretical conclusions numerically. And there exists conformity between numerical and theoretical results.

On Optimality of Weighted Multidimensional Scaling for Range-Based Localization

Weighted multidimensional scaling (WMDS) is an attractive technique and is of extensive application for range-based localization. However, the optimality of the WMDS is not proved thoroughly because of the difficult Moore-Penrose pesudo-inverse operation, and it is only verified by simulation examples in the unified WMDS framework. The aim of this paper is to deal with the theoretical incompleteness to the optimality of the WMDS technique. This study presents two fundamental corollaries in the unified framework and then gives an elegant and detailed analytical proof thoroughly. They are established with no requirement about the measurement statistical distribution or no approximations with small measurement errors either. The optimality of the WMDS are verified consequently in the absence and presence of sensors position errors, respectively. Our theoretical results are not established on the specific WMDS, such as the versions of classical MDS, modified MDS or subspace MDS, but based on the unified WMDS framework itself, which are applicable to arbitrary type of the WMDS. The theoretical derivation is corroborated by numerical examples.

A Multitag Cooperative Localization Algorithm Based on Weighted Multidimensional Scaling for Passive UHF RFID

Radio frequency identification (RFID) technology, which is one of the important implementation ways of Internet-of-Things (IoT), has achieved much attention in indoor localization areas. Passive ultrahigh frequency (UHF) RFID tag localization has a great development recently. Most of traditional passive UHF RFID localization algorithms can only achieve the position of one tag at a time while multitag localization is desired in many RFID applications. In this paper, we proposed the weighted multidimensional scaling (WMDS) based on received signal strength (RSS) method and the tag-to-tag communication system to achieve multitag cooperative localization. The targets are marked with passive UHF RFID tags. RSS method is used to determine the distance between readers and target tags through channel models. We can also obtain the estimated distances between target tags by the tag-to-tag communication system. The estimated locations of the tags are determined by the calculation of Euclidean distance matrix through a few iterations. Simulation results show that the WMDS algorithm achieves higher localization accuracy than traditional algorithms and the cooperation between tags improves the localization accuracy.

Multidimensional scaling approach for node localization using received signal strength measurements

Node localization has played an important role in wireless sensor networks. In this paper, cooperative localization using received signal strength (RSS) measurements is addressed. The technique of weighted multidimensional scaling (WMDS) which relies on pairwise distance information between nodes is utilized in our algorithm development. Assuming that the transmit power is available, we first convert the original nonlinear localization problem to a system of linear equations, leading to computational attractiveness. It is also proved that the positioning accuracy of the WMDS solution attains the Cramér–Rao lower bound at sufficiently small noise conditions. Furthermore, the proposed method is extended to the unknown transmit power case by exploiting the ratio of squared distance estimates extracted from the RSS information. The effectiveness of the WMDS approach is demonstrated via comparison with several conventional RSS-based positioning methods.

New variant of ISOMAP for imperfect manifold

Isometric Feature Mapping(ISOMAP) requires that the data belong to a single well-sampled manifold;however,when the data are sampled from an imperfect manifold,ISOMAP tends to overcluster the data.To alleviate this problem,this paper presented a new variant of ISOMAP called Weighted ISOMAP(WISOMAP),which used Weighted Multidimensional Scaling(WMDS) instead of Classical Multidimensional Scaling(CMDS) to map the data into the low-dimensional embedding space.As a new variant of MDS,WMDS gave smaller weight to the distances with more edges,which were generally worse approximated and then less trustworthy than those with fewer edges,and thus could limit the effects of the generally worse-approximated distances with many edges and preserved the more trustworthy distances with few edges in the low-dimensional embedding space more precisely,by which the data relying on an imperfect manifold could be visualized better.The efficiency of WISOMAP is verified by experimental results well.

Localization from Connectivity in Wireless Sensor Networks Based on Distributed Weight-Multidimensional Scaling

A localization algorithm from connectivity based on distributed weighted-multidimensional scaling (cdwMDS) algorithm is proposed in this paper. Each sensor selects a neighbor sensor adaptively, calculates the iteration step size with the average connectivity and updates the estimate location by optimizing the local cost function. Connectivity is used to determine the step size of gradient iterative optimization in this algorithm. After getting the estimated positions, a relative map is built and the absolute coordinates can be obtained. Simulation results show that this method could achieve higher localization accuracy and more stable convergence.

Robust Node Localization Based on Distributed Weighted-multidimensional Scaling in Wireless Sensor Networks

This paper focuses on the robustness of node localization in various topological and sparse network. By taking account of the number of 1-hop neighboring nodes, the node position accuracy and the ranging errors, we introduce concepts of node relative localization error and relative reliability, and then propose a robust node localization algorithm based on distributed weighted-multidimensional scaling. It adaptively chooses those neighboring nodes with high relative reliability to join in the node position refinement according to local node density and their relative localization errors within 2 hops, and adopts a weighting scheme proportional to the relative reliability which emphasizes the lowest relative error within the sensor networks. For received signal strength based range measurements, extensive simulation shows that this algorithm can prevent large localization errors from spreading through the networks. Compared with dwMDS (G), this algorithm can decrease iterative times by one half and gain about 5% smaller localization errors in sparse node density or anisotropic topologies.

A decomposition of electrocortical activity as a function of spatial frequency: A weighted multidimensional scaling analysis

In this study, we examined the usefulness of weighted multidimensional scaling (WMDS) to decompose electrocortical activity of multiple brain sources. This electrocortical activity was evoked by checkerboard stimuli of four different spatial frequencies (0.75, 1.5, 3.0, and 6.0 cpd), presented to 12 participants under passive viewing conditions. Visual evoked potentials (VEPs) were recorded with a high density montage of 60 electrodes. These data were analyzed by using WMDS, resulting in four different dimensions, each of which can be considered equivalent to a potential scalp distribution, i.e. dipole source. The first of these dipole sources, which were determined by brain electrical source analysis (BESA), was predominantly activated by higher spatial frequencies, the second and third were predominantly activated by lower spatial frequencies, while the third and fourth sources were characterized by hemispheric asymmetry. Moreover, the neural activity of these brain sources was characterized by different patterns as a function of spatial frequency and time. The results suggest that visual processing of spatial frequencies comprises relatively separate subsystems with different spatiotemporal response characteristics.

Distributed weighted-multidimensional scaling for node localization in sensor networks

Accurate, distributed localization algorithms are needed for a wide variety of wireless sensor network applications. This article introduces a scalable, distributed weighted-multidimensional scaling (dwMDS) algorithm that adaptively emphasizes the most accurate range measurements and naturally accounts for communication constraints within the sensor network. Each node adaptively chooses a neighborhood of sensors, updates its position estimate by minimizing a local cost function and then passes this update to neighboring sensors. Derived bounds on communication requirements provide insight on the energy efficiency of the proposed distributed method versus a centralized approach. For received signal-strength (RSS) based range measurements, we demonstrate via simulation that location estimates are nearly unbiased with variance close to the Cramér-Rao lower bound. Further, RSS and time-of-arrival (TOA) channel measurements are used to demonstrate performance as good as the centralized maximum-likelihood estimator (MLE) in a real-world sensor network.

Unraveling the Brow: What and How of Choice in Musical Preference

Mapping the association between social position and cultural disposition—“patterns of cultural choice”—is a long-standing practice in sociological research. These maps, often read in terms of “brow level,” concern primarily the question of what people choose, neglecting that of how they choose. I extend the analytic focus to take into account the co-constitutive roles played by classifying operations. Using the weighted multidimensional scaling (WMDS) method, I examine the musical preference data and show that it is not only what type of music the respondents choose but also how they choose that distinguish them. I find that varying combinations of multiple evaluation-distinction criteria are appropriated by different status groups, coalescing into three distinct clusters of sensibility. The findings and the elaboration of the notion of dual basis of taste help to put some of the theoretical as well as empirical issues in the field in perspective.

Local Evaluations of Neighborhood Change

Abstract Questions arise concerning the nature and organization of residents' perceptual responses to neighborhood change. Transactionalism, with its focus on context and change, provides a theoretical basis for an empirical study that attempts to identify and evaluate the human dimensions of change within the context of an inner-city neighborhood of San Diego, California. Using quasi-nonmetric weighted multi-dimensional scaling (WMDS), I analyzed similarity matrices, which are derived from asking a sample of residents to respond to different neighborhood contexts. The WMDS suggests that residents place great importance on neighborhood stability. A modified form of repertory grid analysis provides insight into how individuals respond to specific neighborhood changes. Residential and commercial establishments that had disappeared from the area are, on the whole, preferred. Residents dislike large new developments, finding them cold, mass-produced and impersonal. A non-metric classic multi-dimensional scali...