Multidimensional Scaling Algorithm Research Articles

Multidimensional scaling for big data

AbstractWe present a set of algorithms implementing multidimensional scaling (MDS) for large data sets. MDS is a family of dimensionality reduction techniques using a $$n \times n$$ n × n distance matrix as input, where n is the number of individuals, and producing a low dimensional configuration: a $$n\times r$$ n × r matrix with $$r<<n$$ r < < n . When n is large, MDS is unaffordable with classical MDS algorithms because their extremely large memory and time requirements. We compare six non-standard algorithms intended to overcome these difficulties. They are based on the central idea of partitioning the data set into small pieces, where classical MDS methods can work. Two of these algorithms are original proposals. In order to check the performance of the algorithms as well as to compare them, we have done a simulation study. Additionally, we have used the algorithms to obtain an MDS configuration for EMNIST: a real large data set with more than 800000 points. We conclude that all the algorithms are appropriate to use for obtaining an MDS configuration, but we recommend to use one of our proposals, since it is a fast algorithm with satisfactory statistical properties when working with big data. An package implementing the algorithms has been created.

Leto: Crowdsourced Radio Map Construction With Learned Topology and a Few Landmarks

Existing crowdsourced indoor positioning systems (CIPSs) usually require prior knowledge about the site and a tedious calibration process. Moreover, they may require a large number of landmarks while ignoring the topology information that may be contained in the crowdsourced data. In this paper, we present Leto, a system that uses <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">le</b> arned <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">to</b> pology information from combined user traces to construct a radio map. Leto relies on crowdsourced WiFi and accelerometer signals only without requiring any prior knowledge about the site. Our key idea is that learned topology information can reduce the required number of landmarks, while available landmarks can transform the topology into a map. We propose a novel framework that efficiently learns the map topology by a hybrid multidimensional scaling (HMDS) algorithm and accurately rectifies the map using only a few anchors by an adaptive force-directed (AFD) algorithm. We also provide a theoretical convergence analysis of the HMDS algorithm. Experimental results on real-world datasets show that Leto can capture useful topology information and achieve significant improvements in radio map construction compared to existing systems.

Correlation-informed ordered dictionary learning for imaging in complex media

We propose a method for imaging in scattering media when large and diverse datasets are available. It has two steps. Using a dictionary learning algorithm the first step estimates the true Green's function vectors as columns in an unordered sensing matrix. The array data comes from many sparse sets of sources whose location and strength are not known to us. In the second step, the columns of the estimated sensing matrix are ordered for imaging using the multidimensional scaling algorithm with connectivity information derived from cross-correlations of its columns, as in time reversal. For these two steps to work together, we need data from large arrays of receivers so the columns of the sensing matrix are incoherent for the first step, as well as from sub-arrays so that they are coherent enough to obtain connectivity needed in the second step. Through simulation experiments, we show that the proposed method is able to provide images in complex media whose resolution is that of a homogeneous medium.

Comparison of leaching behaviour of heavy metals from sediments sampled in sewer systems - environmental and public health aspect.

The article analyzes the content of heavy metals and standard physical as well as chemical pollution indicators in different types of sediments from stormwater, combined sewer and sanitary sewer systems. Nickel, lead, chromium, copper, zinc and cadmium, as well as standard physical and chemical pollution indicators, were determined in sewage sediments. Aqueous extracts of sediments samples, taken from storm water sewer inlet sediments traps, storm sewers, sanitary sewers and combined sewers, were prepared in accordance with PN-EN 12457-2:2006. After mineralization, the concentrations of the metals: nickel, lead, chromium, copper, zinc and cadmium in the extracts were determined using the inductively coupled plasma emission spectroscopy technique. The results were analyzed with a non-metric multidimensional scaling algorithm. The heavy metal content was variable depending on the sediments collection site. The heavy metals nickel, lead, chromium, copper, zinc and cadmium were found in the sediments from stormwater inlets, storm sewer and sanitary sewer channels, with variability in the concentration of individual metals. The sediments from the flushing of sanitary sewers and combined sewers did not contain cadmium. The content of heavy metals in sediments varied depending on the sampling location and type of sewer system, indicating the need for detailed monitoring to identify the sources of emissions. Sediments from stormwater sewers have higher concentrations of heavy metals, with those from sewer inlets showing zinc concentrations exceeding regulatory limits, highlighting the variability and potential environmental impact of different sewer systems.

Mangrove Ecosystem Management for Sustainable Renewable Energy Production: A Multi-Dimensional Analysis

Mangrove ecosystems have become a critical habitat for sustaining renewable energy production, and their management is essential to maintain their ecological, economic, and social functions. This study aimed to analyze the multidimensional aspects of mangrove ecosystem management for sustainable renewable energy production in the Tebing Tinggi, Kepulauan Meranti, Riau. This study formulates sustainable management schemes for the mangrove ecosystem in the Tebing Tinggi, Kepulauan Meranti, Riau by analyzing the ecological, economic, social, legal-institutional, and technological aspects of the ecosystem. To conduct this analysis, researchers used the Multidimensional Scaling (MDS) approach, which relies on an algorithm called the MDS algorithm. The findings from the study reveal that the use of mangroves can increase people's income, but the level of community education is still low, and there is a lack of community participation in mangrove ecosystem management activities. Based on the Rap-Mangrove analysis, the multidimensional index of mangrove ecosystem management is considered sufficiently sustainable. The findings emphasized the significance of community participation and education in managing mangrove ecosystems. The study concludes that sustainable management schemes for mangrove ecosystems are necessary to ensure their continued contribution to renewable energy production.

O.5.1-3 Co-creation of an active transportation promotion intervention: a concept mapping study

Abstract Purpose Active transportation (AT) is an efficient way to increase daily physical activity and reduce pollution from the transportation sector. Mhealth has contributed to behavior change in fields like physical activity and has been explored to encourage AT. Most interventions, however, did not incorporate evidence-based behavior change techniques and were not co-created with potential users. We aim to understand how AT can be promoted via mhealth intervention by using a bottom-up participatory approach. Methods Concept mapping was done online via GroupWisdom platform, with the public of Alpes-Maritimes County, France. Participants were asked to brainstorm, sort, and rate ideas about mobile app features to encourage AT. Multidimensional scaling algorithm and hierarchical cluster analysis were used to create visual cluster maps to illustrate the participants’ conceptual thinking of the topic. We compared the data by participants’ age, education, and typical transportation mode to understand how different groups perceived each idea and clusters. Results Participants generated 44 unique ideas that they believe would encourage AT behaviors. Six themes emerged, from highest to lowest cluster rating: Infrastructure (n = 9 ideas) and Itinerary (n = 9 ideas), which were consistently rated across groups; Contact with government (n = 4 ideas); Data (n = 12 ideas), with the most number of ideas generated; App usability (n = 6 ideas); and Legislation and code of conduct (n = 4 ideas), with the least number of ideas. Conclusions Our findings showed various ways AT can be promoted. Even though the participants were asked about mobile apps features, they quickly pointed out ideas unrelated to mobile apps. The built environment and infrastructure are clearly the most important factors to promote AT, for our participants. However, they have also identified other soft measures like information, participation in decision making, and social aspects that can contribute to behavior change and support sustainable and healthy modes of transportation. Therefore, a systemic and multifaceted approach is recommended to promote AT. Support/Funding Source This work was supported by the French government, managed by the Agence Nationale de la Recherche under the project Investissements d'Avenir UCAJEDI with the reference n° ANR-15-IDEX-01.

Characterization of A/H7 influenza virus global antigenic diversity and key determinants in the hemagglutinin globular head mediating A/H7N9 antigenic evolution.

A/H7 avian influenza viruses cause outbreaks in poultry globally, resulting in outbreaks with significant socio-economical impact and zoonotic risks. Occasionally, poultry vaccination programs have been implemented to reduce the burden of these viruses, which might result in an increased immune pressure accelerating antigenic evolution. In fact, evidence for antigenic diversification of A/H7 influenza viruses exists, posing challenges to pandemic preparedness and the design of vaccination strategies efficacious against drifted variants. Here, we performed a comprehensive analysis of the global antigenic diversity of A/H7 influenza viruses and identified the main substitutions in the hemagglutinin responsible for antigenic evolution in A/H7N9 viruses isolated between 2013 and 2019. The A/H7 antigenic map and knowledge of the molecular determinants of their antigenic evolution add value to A/H7 influenza virus surveillance programs, the design of vaccines and vaccination strategies, and pandemic preparedness.

A cluster positioning architecture and relative positioning algorithm based on pigeon flock bionics

Unmanned clusters can realize collaborative work, flexible configuration, and efficient operation, which has become an important development trend of unmanned platforms. Cluster positioning is important for ensuring the normal operation of unmanned clusters. The existing solutions have some problems such as requiring external system assistance, high system complexity, poor architecture scalability, and accumulation of positioning errors over time. Without the aid of the information outside the cluster, we plan to construct the relative position relationship with north alignment to adopt formation control and achieve robust cluster relative positioning. Based on the idea of bionics, this paper proposes a cluster robust hierarchical positioning architecture by analyzing the autonomous behavior of pigeon flocks. We divide the clusters into follower clusters, core clusters, and leader nodes, which can realize flexible networking and cluster expansion. Aiming at the core cluster that is the most critical to relative positioning in the architecture, we propose a cluster relative positioning algorithm based on spatiotemporal correlation information. With the design idea of low cost and large-scale application, the algorithm uses intra-cluster ranging and the inertial navigation motion vector to construct the positioning equation and solves it through the Multidimensional Scaling (MDS) and Multiple Objective Particle Swarm Optimization (MOPSO) algorithms. The cluster formation is abstracted as a mixed direction-distance graph and the graph rigidity theory is used to analyze localizability conditions of the algorithm. We designed the cluster positioning simulation software and conducted localizability tests and positioning accuracy tests in different scenarios. Compared with the relative positioning algorithm based on Extended Kalman Filter (EKF), the algorithm proposed in this paper has more relaxed positioning conditions and can adapt to a variety of scenarios. It also has higher relative positioning accuracy, and the error does not accumulate over time.

Ground fault location research based on multidimensional scaling and density clustering algorithm

When a single line-to-ground fault occurs in a current distribution network containing distributed power sources, fault location is primarily performed by current-based directional protection. This implies using the switching information at the nodes; however, this does not sufficiently maximize the fault information. To address these issues, a single-phase grounding fault location methodology is planned for distribution networks supported by a combination of three-dimensional scaling (MDS) and density-based spatial clustering of applications with noise (DBSCAN). First, the network description matrix is made to support the network topology. Second, the zero-sequence and negative-sequence currents collected at the terminals square measure pre-processed to obtain two-dimensional fault data feature vectors. Third, the fault feature vectors square measure is subjected to DBSCAN bunch analysis to obtain the fault zones of the distribution network, thus compensating for the disadvantage that DBSCAN cannot efficiently replicate high-dimensional knowledge. The simulation results reveal that the planned methodology is not tormented by fault location, fault resistance, fault angle, or line sort; therefore, the fault location results in a correct square measure and might effectively utilize the fault data.

Bibliometric Literature Review of Adaptive Learning Systems

In this review paper, we computationally analyze a vast volume of published articles in the field of Adaptive Learning, as obtained by the Scopus Database. Particularly, we use a query with search terms targeting the area of Adaptive Learning Systems by utilizing a combination of specific keywords. Accordingly, we apply a multidimensional scaling algorithm to construct bibliometric maps for keywords, authors, and references. Subsequently, we present the computational results for the studied dataset, reveal significant patterns appearing in the field of adaptive learning and the inter-item associations, and interpret the findings based on the current state-of-the-art literature in the area. Furthermore, we demonstrate the time-series of the evolution of the research terms, their trends over time, as well as their prevalent statistical associations.

Multimodal Diagnosis for Pulmonary Embolism from EHR Data and CT Images.

Pulmonary Embolism (PE) is a severe medical condition that can pose a significant risk to life. Traditional deep learning methods for PE diagnosis are based on Computed Tomography (CT) images and do not consider the patient's clinical context. To make full use of patient's clinical information, this article presents a multimodal fusion model ingesting Electronic Health Record (EHR) data and CT images for PE diagnosis. The proposed model is based on multilayer perception and convolutional neural networks. To remove the invalid information in the EHR data, the multidimensional scaling algorithm is performed for feature dimension reduction. The EHR data and CT images of 600 patients are used for experiments. The experiment results show that the proposed models outperform existing methods and the multimodal fusion model shows better performance than the single-input model.

SQuadMDS: A lean Stochastic Quartet MDS improving global structure preservation in neighbor embedding like t-SNE and UMAP

Multidimensional scaling is a process that aims to embed high dimensional data into a lower-dimensional space; this process is often used for the purpose of data visualisation. Common multidimensional scaling algorithms tend to have high computational complexities, making them inapplicable on large data sets. This work introduces a stochastic, force directed approach to multidimensional scaling with a time and space complexity of O(N), with N data points. The method can be combined with force directed layouts of the family of neighbour embedding such as t-SNE, to produce embeddings that preserve both the global and the local structures of the data.Experiments assess the quality of the embeddings produced by the standalone version and its hybrid extension both quantitatively and qualitatively, showing competitive results outperforming state-of-the-art approaches. Codes are available athttps://github.com/PierreLambert3/SQuaD-MDS-and-FItSNE-hybrid.

Infinite multidimensional scaling for metric measure spaces

For a given metric measure space (X, d,μ) we consider finite samples of points, calculate the matrix of distances between them and then reconstruct the points in some finite-dimensional space using the multidimensional scaling (MDS) algorithm with this distance matrix as an input. We show that this procedure gives a natural limit as the number of points in the samples grows to infinity and the density of points approaches the measure μ. This limit can be viewed as “infinite MDS” embedding of the original space, now not anymore into a finite-dimensional space but rather into an infinitedimensional Hilbert space. We further show that this embedding is stable with respect to the natural convergence of metric measure spaces. However, contrary to what is usually believed in applications, we show that in many cases it does not preserve distances, nor is even bi-Lipschitz, but may provide snowflake (Assouad-type) embeddings of the original space to a Hilbert space (this is, for instance, the case of a sphere and a flat torus equipped with their geodesic distances).

A novel auxiliary hole localization algorithm based on multidimensional scaling for wireless sensor networks in complex terrain with holes

As the most critical part of wireless sensor networks, nodes localization plays a decisive role in determining the validity and value of the data collected by the sensors. A novel auxiliary hole localization algorithm based on multidimensional scaling has been proposed in the present study to overcome the poor nodes localization for wireless sensor networks in complex terrain with holes. In the algorithm research, the types of the holes in wireless sensor networks are originally classified and defined, and the localization strategy for the hole boundary nodes is designed. On this basis, an improved distance optimization method is employed to derive the formula of the distance between nodes blocked by holes. Finally, on the strength of the improved distance value, the nodes localization task is completed through the multidimensional scaling-MAP algorithm. As shown by the simulation results, the proposed algorithm is suitable for locating the nodes of wireless sensor networks in complex terrain with different types of holes. In addition, under the condition of each type of hole localization, the localization effect is better than the same type of extended Kalman filter multidimensional scaling algorithm.

Learning hidden chemistry with deep neural networks

We demonstrate a machine learning approach designed to extract hidden chemistry/physics to facilitate new materials discovery. In particular, we propose a novel method for learning latent knowledge from material structure data in which machine learning models are developed to present the possibility that an atom can be paired with a chemical environment in an observed materials. For this purpose, we trained deep neural networks acquiring information from the atom of interest and its environment to estimate the possibility. The models were then used to establish recommendation systems, which can suggest a list of atoms for an environment within a structure. The center atom of that environment was then replaced with the various recommended atoms to generate new structures. Based on these recommendations, we also propose a method of dissimilarity measurement between the atoms and, through hierarchical cluster analysis and visualization using the multidimensional scaling algorithm, illustrate that this dissimilarity can reflect the chemistry of the elements. Finally, our models were applied to the discovery of new structures in the well-known magnetic material Nd2Fe14B. Our models propose 108 new structures, 71 of which are confirmed to converge to local-minimum-energy structures with formation energy less than +0.1 eV by first-principles calculations.

Multidimensional scaling and visualization of patterns in distribution of nontrivial zeros of the zeta-function

In this paper, we analyze the nontrivial zeros of the Riemann zeta-function using the multidimensional scaling (MDS) algorithm and computational visualization features. The nontrivial zeros of the Riemann zeta-function as well as the vectors with several neighboring zeros are interpreted as the basic elements (points or objects) of a data set. Then we employ a variety of different metrics, such as the Jeffreys and Lorentzian ones, to calculate the distances between the objects. The set of the calculated distances is then processed by the MDS algorithm that produces the loci, organized according to the objects features. Then they are analyzed from the perspective of the emerging patterns. Surprisingly, in the case of the Lorentzian metric, this procedure leads to the very clear periodical structures both in the case of the objects in form of the single nontrivial zeros of the Riemann zeta-function and in the case of the vectors with a given number of neighboring zeros. The other tested metrics do not produce such periodical structures, but rather chaotic ones. In this paper, we restrict ourselves to numerical experiments and the visualization of the produced results. An analytical explanation of the obtained periodical structures is an open problem worth for investigation by the experts in the analytical number theory.

Utilizing machine learning dimensionality reduction for risk stratification of chest pain patients in the emergency department

BackgroundChest pain is among the most common presenting complaints in the emergency department (ED). Swift and accurate risk stratification of chest pain patients in the ED may improve patient outcomes and reduce unnecessary costs. Traditional logistic regression with stepwise variable selection has been used to build risk prediction models for ED chest pain patients. In this study, we aimed to investigate if machine learning dimensionality reduction methods can improve performance in deriving risk stratification models.MethodsA retrospective analysis was conducted on the data of patients > 20 years old who presented to the ED of Singapore General Hospital with chest pain between September 2010 and July 2015. Variables used included demographics, medical history, laboratory findings, heart rate variability (HRV), and heart rate n-variability (HRnV) parameters calculated from five to six-minute electrocardiograms (ECGs). The primary outcome was 30-day major adverse cardiac events (MACE), which included death, acute myocardial infarction, and revascularization within 30 days of ED presentation. We used eight machine learning dimensionality reduction methods and logistic regression to create different prediction models. We further excluded cardiac troponin from candidate variables and derived a separate set of models to evaluate the performance of models without using laboratory tests. Receiver operating characteristic (ROC) and calibration analysis was used to compare model performance.ResultsSeven hundred ninety-five patients were included in the analysis, of which 247 (31%) met the primary outcome of 30-day MACE. Patients with MACE were older and more likely to be male. All eight dimensionality reduction methods achieved comparable performance with the traditional stepwise variable selection; The multidimensional scaling algorithm performed the best with an area under the curve of 0.901. All prediction models generated in this study outperformed several existing clinical scores in ROC analysis.ConclusionsDimensionality reduction models showed marginal value in improving the prediction of 30-day MACE for ED chest pain patients. Moreover, they are black box models, making them difficult to explain and interpret in clinical practice.

Cooperative Localization Using Distance Measurements for Mobile Nodes.

This paper considers the two-dimensional (2D) anchorless localization problem for sensor networks in global positioning system (GPS)-denied environments. We present an efficient method, based on the multidimensional scaling (MDS) algorithm, in order to estimate the positions of the nodes in the network using measurements of the inter-node distances. The proposed method takes advantage of the mobility of the nodes to address the location ambiguity problem, i.e., rotation and flip ambiguity, which arises in the anchorless MDS algorithm. Knowledge of the displacement of the moving node is used to produce an analytical solution for the noise-free case. Subsequently, a least squares estimator is presented for the noisy scenario and the associated closed-form solution derived. The simulations show that the proposed algorithm accurately and efficiently estimates the locations of nodes, outperforming alternative methods.

A Bayesian Approach for Model-Based Clustering of Several Binary Dissimilarity Matrices: The dmbc Package in R

We introduce the new package dmbc that implements a Bayesian algorithm for clustering a set of binary dissimilarity matrices within a model-based framework. Specifically, we consider the case when S matrices are available, each describing the dissimilarities among the same n objects, possibly expressed by S subjects (judges), or measured under different experimental conditions, or with reference to different characteristics of the objects themselves. In particular, we focus on binary dissimilarities, taking values 0 or 1 depending on whether or not two objects are deemed as dissimilar. We are interested in analyzing such data using multidimensional scaling (MDS). Differently from standard MDS algorithms, our goal is to cluster the dissimilarity matrices and, simultaneously, to extract an MDS configuration specific for each cluster. To this end, we develop a fully Bayesian three-way MDS approach, where the elements of each dissimilarity matrix are modeled as a mixture of Bernoulli random vectors. The parameter estimates and the MDS configurations are derived using a hybrid Metropolis-Gibbs Markov Chain Monte Carlo algorithm. We also propose a BIC-like criterion for jointly selecting the optimal number of clusters and latent space dimensions. We illustrate our approach referring both to synthetic data and to a publicly available data set taken from the literature. For the sake of efficiency, the core computations in the package are implemented in C/C++. The package also allows the simulation of multiple chains through the support of the parallel package.

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.