Classical Multidimensional Scaling Algorithm Research Articles

Health Monitoring of Large-Scale Civil Structures: An Approach Based on Data Partitioning and Classical Multidimensional Scaling.

A major challenge in structural health monitoring (SHM) is the efficient handling of big data, namely of high-dimensional datasets, when damage detection under environmental variability is being assessed. To address this issue, a novel data-driven approach to early damage detection is proposed here. The approach is based on an efficient partitioning of the dataset, gathering the sensor recordings, and on classical multidimensional scaling (CMDS). The partitioning procedure aims at moving towards a low-dimensional feature space; the CMDS algorithm is instead exploited to set the coordinates in the mentioned low-dimensional space, and define damage indices through norms of the said coordinates. The proposed approach is shown to efficiently and robustly address the challenges linked to high-dimensional datasets and environmental variability. Results related to two large-scale test cases are reported: the ASCE structure, and the Z24 bridge. A high sensitivity to damage and a limited (if any) number of false alarms and false detections are reported, testifying the efficacy of the proposed data-driven approach.

Straightforward Working Principles Behind Modern Data Visualization Approaches

From state-of-the-art visualization algorithms, we distill six working principles which are, by hypothesis, sufficient to produce visual projections qualitatively similar to those obtained with these state-of-the-art algorithms. These working principles are presented through the geometrical reasoning of the classical Multidimensional Scaling algorithm, and their effectiveness is illustrated through a novel straightforward algorithm for data visualization. We show, using several datasets originated from various applications, that our algorithm can produce visual projections qualitatively similar to those obtained with these state-of-the-art algorithms. Besides, under the same motivation (of simplification), the problem of visualizing large datasets is tackled through a companion algorithm which is able to embed new input patterns.

Embedding graphs in Lorentzian spacetime.

Geometric approaches to network analysis combine simply defined models with great descriptive power. In this work we provide a method for embedding directed acyclic graphs (DAG) into Minkowski spacetime using Multidimensional scaling (MDS). First we generalise the classical MDS algorithm, defined only for metrics with a Riemannian signature, to manifolds of any metric signature. We then use this general method to develop an algorithm which exploits the causal structure of a DAG to assign space and time coordinates in a Minkowski spacetime to each vertex. As in the causal set approach to quantum gravity, causal connections in the discrete graph correspond to timelike separation in the continuous spacetime. The method is demonstrated by calculating embeddings for simple models of causal sets and random DAGs, as well as real citation networks. We find that the citation networks we test yield significantly more accurate embeddings that random DAGs of the same size. Finally we suggest a number of applications in citation analysis such as paper recommendation, identifying missing citations and fitting citation models to data using this geometric approach.

Robust localisation algorithm for large scale 3D wireless sensor networks

Nodes positioning has recently been of great interest in wireless networks owing to its crucial role in many applications. In wireless sensor networks (WSNs), the task of localising sensor nodes with unknown position is important for efficient network configuration and operation. This challenge has stimulated research of various localisation algorithms. In this paper we propose robust localisation algorithm for large scale three-dimensional (3D) WSNs based on multidimensional scaling (MDS). Our approach has two main improvements over classical MDS algorithm. Firstly, it uses heuristic approach for distance matrix calculation, and secondly, it applies Levenberg-Marquardt (LM) method for absolute map refinement using received signal strength (RSS) measurements. Furthermore, the performance of the proposed approach is compared to other 3D WSN localisation techniques and it is shown that the proposed approach outperforms other techniques for 3D localisation.

Indoor Robot Localization Based on Multidimensional Scaling

In pertinence to the application of multidimensional scaling (MDS) methods in ranging-based positioning systems, an analysis is firstly conducted by the classical MDS algorithm. Modified MDS algorithm and subspace method are presented in localization application. We also depicted the unified framework and general solutions of MDS methods. However, the least square solutions under this framework are not optimal. Their performance is still related to selection of coordinate reference points. To address this problem, a minimum residual MDS algorithm based on particle swarm optimization (PSO) is proposed to derive a new solution for indoor robot localization under the unified framework. The result of analysis indicates that the performance of minimum residual MDS method is immune to selection of reference points. Furthermore, the localization accuracy for indoor robot has been enhanced by 41% as compared with the classical MDS algorithm.

Research on Improved Multidimensional Scaling Localization Algorithm for Wireless Sensor Network

Wireless sensor networks, which are energy limited, low hardware configuration and proneness to invalidation, puts a high demand on the positioning algorithm. Therefore the improved multidimensional scaling (IMDS) algorithm is proposed. In IMDS, firstly, local positioning areas (LPA) are established by an adaptive search algorithm. So the centralized multidimensional scaling (MDS) algorithm is changed into a distributed one. Then the shortest path distances between nodes on LPA are corrected with the geometric correction method (GCM) and adjusting weight correction method (AWCM). The distances between nodes become more accurate. Finally, with information of the public nodes of LPA and anchor nodes, we get the wireless sensor nodes coordinates through coordinate transformation by the SMACOF algorithm and the classical MDS algorithm.

BR2OM: RSSI-based Refinement and Optimization Mechanism for Wireless Sensor Networks

There are many RSSI-based localization algorithms for wireless sensor networks (WSN). T his paper proposes a RSSI-based refinement of the optimization mechanism (BR 2 O M) based on multi-dimensional scaling (MDS). The basic idea of the algorithm is that establishing sub-areas for localization to ensure the processing of localization can be completed successfully. The sub-area is divided by cluster which is a tree structure. At the same time, the mechanism filters the Received Signal Strength Indicator (RSSI) based on th e link quality indication ( LQI ) to reduce the error number of RSSI. The RSSI is c orrect ed and refin ed by using cosine rule and the limitation of communication range . T he relationship of relative position among blind node s is obtained by adopt ing classical MDS algorithm . The relative position is finally converted into the global coordinate. The experiment result shows that the algorithm has many advantages, such as high accuracy, simple condition , and moderate cost . The algorithm satisf ies the requirement of large-scale network applications and also is valua ble to the positioning refined problems under circumstance of the non-line-of-sight.

Distributed localization algorithm for wireless sensor network based on multidimensional scaling and the shortest path distance correction

Sensor localization is crucial for the configuration and applications of wireless sensor network (WSN). A novel distributed localization algorithm, MDS-DC was proposed for wireless sensor network based on multidimensional scaling (MDS) and the shortest path distance correction. In MDS-DC, several local positioning regions with reasonable distribution were firstly constructed by an adaptive search algorithm, which ensures the mergence between the local relative maps of the adjacent local position regions and can reduce the number of common nodes in the network. Then, based on the relationships between the estimated distances and actual distances of anchors, the distance estimation vectors of sensors around anchors were corrected in each local positioning region. During the computations of the local relative coordinates, an iterative process, which is the combination of classical MDS algorithm and SMACOF algorithm, was applied. Finally, the global relative positions or absolute positions of sensors were obtained through merging the relative maps of all local positioning regions. Simulation results show that MDS-DC has better performances in positioning precision, energy efficiency and robustness to range error, which can meet the requirements of applications for sensor localization in WSN.

A Supplement to Multidimensional Scaling Framework for Mobile Location: A Unified View

Recently, while the classical multidimensional scaling (MDS) algorithm had been claimed to be infeasible, MDS based algorithms, including modified MDS and subspace approach, have been applied to the range measurements based mobile localization. In this correspondence, we first prove that the classical MDS algorithm is feasible for the mobile localization. Then we show that all MDS-based algorithms can be unified under the same framework and they are not optimal according to the Gaussian-Markov theorem. Based on the unified framework, the weighted MDS analysis is applied to obtain the optimum performance. The performances of both the MDS algorithms and their corresponding weighted MDS-based algorithms in the unified framework are demonstrated through simulations.