Parallel Coordinates Research Articles

Accelerated 2D visualization using adaptive resolution scaling and temporal reconstruction

Data visualization relies on efficient rendering to allow users to interactively explore and understand their data. However, achieving interactive frame rates is often challenging, especially for high-resolution displays or large datasets. In computer graphics, several methods temporally reconstruct full-resolution images from multiple consecutive lower-resolution frames. Besides providing temporal image stability, they amortize the rendering costs over multiple frames and thus improve the minimum frame rate. We present a method that adopts this idea to accelerate 2D information visualization, without requiring any changes to the rendering itself. By exploiting properties of orthographic projection, our method significantly improves rendering performance while minimizing the loss of image quality during camera manipulation. For static scenes, it quickly converges to the full-resolution image. We discuss the characteristics and different modes of our method concerning rendering performance and image quality and the corresponding trade-offs. To improve ease of use, we provide automatic resolution scaling in our method to adapt to user-defined target frame rate. Finally, we present extensive rendering benchmarks to examine real-world performance for examples of parallel coordinates and scatterplot matrix visualizations, and discuss appropriate application scenarios and contraindications for usage.Graphical

Exact shell solutions for conical springs. III. Belleville springs with variable thickness

PurposeIn the current manuscript, the authors examine the Belleville spring with the variable thickness. The thickness is assumed to be variable along the meridional and parallel coordinates of conical coordinate system. The calculation of the Belleville springs includes the cases of the free gliding edges and the edges on cylindric curbs, which constrain the radial movement. The equations developed here are based on common assumptions and are simple enough to be applied to the industrial calculations.Design/methodology/approachIn the current manuscript, the authors examine the Belleville spring with the variable thickness. The calculation of the Belleville springs investigates the free gliding edges and the edges on cylindric curbs with the constrained radial movement. The equations developed here are based on common assumptions and are simple enough to be applied to the industrial calculations.FindingsThe developed equations demonstrate that the shift of the inversion point to the inside edge does not influence the bending of the cone. On the contrary, the character of the extensional deformation (circumferential strain) of the middle surface alternates significantly. The extension of the middle surface of free gliding spring occurs outside the inversion. The middle surface of the free gliding spring squeezes inside the inversion point. Contrarily, the complete middle surface of the disk spring on the cylindric curb extends. This behavior influences considerably the function of the spring.Research limitations/implicationsA slotted disk spring consists of two segments: a disk segment and a number of lever arm segments. Currently, the calculation of slotted disk spring is based on the SAE formula (SAE, 1996). This formula is limited to a straight slotted disk spring with freely gliding inner and outer edges.Practical implicationsThe equations developed here are based on common assumptions and are simple enough to be applied to the industrial calculations. The developed method is applicable for disk springs with radially constrained edges. The vertical displacements of a disk spring result from an axial load uniformly distributed on inner and outer edges. The method could be directly applied for calculation of slotted disk springs.Originality/valueThe nonlinear governing equations for the of Belleville spring centres were derived. The equations describe the deformation and stresses of thin and moderately thick washers. The variation method is applicable for the disc springs with free gliding and rigidly constrained edges. The developed method is applicable for Belleville spring with radially constrained edges. The vertical displacements of a disc spring result from an axial load uniformly distributed on inner and outer edges.

Mini‐VLAT: A Short and Effective Measure of Visualization Literacy

AbstractThe visualization community regards visualization literacy as a necessary skill. Yet, despite the recent increase in research into visualization literacy by the education and visualization communities, we lack practical and time‐effective instruments for the widespread measurements of people's comprehension and interpretation of visual designs. We present Mini‐VLAT, a brief but practical visualization literacy test. The Mini‐VLAT is a 12‐item short form of the 53‐item Visualization Literacy Assessment Test (VLAT). The Mini‐VLAT is reliable (coefficient omega = 0.72) and strongly correlates with the VLAT. Five visualization experts validated the Mini‐VLAT items, yielding an average content validity ratio (CVR) of 0.6. We further validate Mini‐VLAT by demonstrating a strong positive correlation between study participants' Mini‐VLAT scores and their aptitude for learning an unfamiliar visualization using a Parallel Coordinate Plot test. Overall, the Mini‐VLAT items showed a similar pattern of validity and reliability as the 53‐item VLAT. The results show that Mini‐VLAT is a psychometrically sound and practical short measure of visualization literacy.

XDAT file of the parallel coordinates plot

XDAT file of the parallel coordinates plot

Water Quality Assessment of Nigerian Port Authority Waterway in Port-Harcourt, Rivers State, Nigeria

The aim of this study is to assess the water quality of the Nigerian Port Authority Water way. A cross-sectional study was carried out using a composite sampling method, where three water samples were collected randomly from each station to ensure that the samples were representative of the entire station. Water samples were taken from four different locations along the waterway with new unused bottles, chosen based on the level of port activity in the area. The samples were thereafter analysed for physiochemical parameters, and heavy metal, and compared to the World Health Organization's Permissible Limits. Data analyses covered descriptive statistics, Pearson correlation coefficient analysis, Agglomerative hierarchy clustering, parallel coordinate plot and Water Quality Index computation. The results showed that most parameters were above the standards, indicating a potential risk of bioaccumulation. The water quality index for the station was found to range from 3192.635 to 5061.35 for the four stations, indicating that the waterway is of poor water quality and unsuitable for consumption, and irrigation purposes. The parallel coordinate plot identified Lead and Salinity as the main contaminant in the waterway.

Penguins Go Parallel: A Grammar of Graphics Framework for Generalized Parallel Coordinate Plots

Parallel Coordinate Plots (PCP) are a valuable tool for exploratory data analysis of high-dimensional numerical data. The use of PCPs is limited when working with categorical variables or a mix of categorical and continuous variables. In this article, we propose Generalized Parallel Coordinate Plots (GPCP) to extend the ability of PCPs from just numeric variables to dealing seamlessly with a mix of categorical and numeric variables in a single plot. In this process we find that existing solutions for categorical values only, such as hammock plots or parsets become edge cases in the new framework. By focusing on individual observations rather than a marginal frequency we gain additional flexibility. The resulting approach is implemented in the R package ggpcp. Supplementary materials for this article are available online.

Sampling linear inverse problems with noise

We study the effect of additive noise to the inversion of FIOs associated to a diffeomorphic canonical relation. We use the microlocal defect measures to measure the power spectrum of the noise in the phase space and analyze how that power spectrum is transformed under the inversion. In general, white noise, for example, is mapped to noise depending on the position and on the direction. In particular, we compute the standard deviation, locally, of the noise added to the inversion as a function of the standard deviation of the noise added to the data. As an example, we study the Radon transform in the plane in parallel and fan-beam coordinates, and present numerical examples.

Angle-uniform parallel coordinates

We present angle-uniform parallel coordinates, a data-independent technique that deforms the image plane of parallel coordinates so that the angles of linear relationships between two variables are linearly mapped along the horizontal axis of the parallel coordinates plot. Despite being a common method for visualizing multidimensional data, parallel coordinates are ineffective for revealing positive correlations since the associated parallel coordinates points of such structures may be located at infinity in the image plane and the asymmetric encoding of negative and positive correlations may lead to unreliable estimations. To address this issue, we introduce a transformation that bounds all points horizontally using an angle-uniform mapping and shrinks them vertically in a structure-preserving fashion; polygonal lines become smooth curves and a symmetric representation of data correlations is achieved. We further propose a combined subsampling and density visualization approach to reduce visual clutter caused by overdrawing. Our method enables accurate visual pattern interpretation of data correlations, and its data-independent nature makes it applicable to all multidimensional datasets. The usefulness of our method is demonstrated using examples of synthetic and real-world datasets.

Improved insights into the SABIO-RK database via visualization

SABIO-RK is a database for biochemical reactions and their kinetics. Data in SABIO-RK are inherently multidimensional and complex. The complex relationships between the data are often difficult to follow or even not represented when using standard tabular views. With an increasing number of data points the mismatch between tables and insights becomes more obvious, and getting an overview of the data becomes harder. Such complex data benefit from being presented using specially adapted visual tools. Visualization is a natural and user-friendly way to quickly get an overview of the data and to detect clusters and outliers. Here, we describe the implementation of a variety of visualization concepts into a common interface within the SABIO-RK biochemical reaction kinetics database. For that purpose, we use a heat map, parallel coordinates and scatter plots to allow the interactive visual exploration of general entry-based information of biochemical reactions and specific kinetic parameter values. Database URL https://sabiork.h-its.org/.

Combining Impedance Spectroscopy and Information Visualization Methods to Optimize the Detection of Carbendazim Using Layer-by-Layer Films

Usually, electronic tongues (e-tongue) do not require specific interactions to discriminate aqueous solutions. Among the several factors which determine the electrical properties of sensing units, the interactions between liquids and interfaces have a crucial role. Here, we explore the interaction between dioctadecyldimethylammonium bromide (DODAB) lipid and carbendazim (MBC) pesticide in an e-tongue to discriminate different MBC concentrations in aqueous solutions. The sensing units were fabricated of gold interdigitated electrodes (IDEs) coated with layer-by-layer (LbL) films of DODAB and nickel tetrasulfonated phthalocyanine (NiTsPc), perylene and 1,2-dipalmitoyl-sn-glycero-3-phospho-(1′-rac-glycerol) (DPPG), namely (DODAB/NiTsPc)5 and (Perylene/DPPG)5, respectively. Besides, a bare electrode also constituted the e-tongue to distinguish MBC concentrations from 1.0 × 10−7 up to 1.0 × 10−10 mol L−1, by impedance spectroscopy. In addition, the experiment was optimized using two IDE geometries. The LbL films were manually fabricated obtaining linear growth monitored via UV-Vis absorption spectroscopy. Optical images associated with chemical mapping reveals the presence of small aggregates in the DODAB/NiTsPc LbL film surface. Although the e-tongue was able to discriminate all MBC concentrations by means of the interactive document map (IDMAP), only the sensing unit covered with DODAB/NiTsPc LbL film presented a satisfactory response. According to the equivalent circuit, the main contribution arises from the bulk and film surface due to the interaction between DODAB and MBC, indicating THE sensitivity of the sensing unit. Finally, the adsorption of MBC molecules onto the film surface induced an irreversible process, although there are some frequencies at which the sensing unit response seems to be reversible, as shown by parallel coordinates.

Lean Manufacturing Soft Sensors for Automotive Industries

Lean and flexible manufacturing is a matter of necessity for the automotive industries today. Rising consumer expectations, higher raw material and processing costs, and dynamic market conditions are driving the auto sector to become smarter and agile. This paper presents a machine learning-based soft sensor approach for identification and prediction of lean manufacturing (LM) levels of auto industries based on their performances over multifarious flexibilities such as volume flexibility, routing flexibility, product flexibility, labour flexibility, machine flexibility, and material handling. This study was based on a database of lean manufacturing and associated flexibilities collected from 46 auto component enterprises located in the Pune region of Maharashtra State, India. As many as 29 different machine learning models belonging to seven architectures were explored to develop lean manufacturing soft sensors. These soft sensors were trained to classify the auto firms into high, medium or low levels of lean manufacturing based on their manufacturing flexibilities. The seven machine learning architectures included Decision Trees, Discriminants, Naive Bayes, Support Vector Machine (SVM), K-nearest neighbour (KNN), Ensembles, and Neural Networks (NN). The performances of all models were compared on the basis of their respective training, validation, testing accuracies, and computation timespans. Primary results indicate that the neural network architectures provided the best lean manufacturing predictions, followed by Trees, SVM, Ensembles, KNN, Naive Bayes, and Discriminants. The trilayered neural network architecture attained the highest testing prediction accuracy of 80%. The fine, medium, and coarse trees attained the testing accuracy of 60%, as did the quadratic and cubic SVMs, the wide and narrow neural networks, and the ensemble RUSBoosted trees. Remaining models obtained inferior testing accuracies. The best performing model was further analysed by scatter plots of predicted LM classes versus flexibilities, validation and testing confusion matrices, receiver operating characteristics (ROC) curves, and the parallel coordinate plot for identifying manufacturing flexibility trends for the predicted LM levels. Thus, machine learning models can be used to create effective soft sensors that can predict the level of lean manufacturing of an enterprise based on the levels of its manufacturing flexibilities.

Visual Analysis of Multidimensional Big Data: A Scalable Lightweight Bundling Method for Parallel Coordinates

Varied edge bundling methods have been used to reduce visual clutter in parallel coordinates plots (PCP). However, existing edge-bundled PCP do not scale well for visual analysis of multidimensional big data and often overplot the bundles in the area near the axes. In this study, we propose a scalable lightweight bundling method to support visual analysis of multidimensional big data in PCP. It helps the users discover trends and detect outliers in the data by bundling the edges between each two adjacent axes independently. We integrate human judgments into the two-dimensional data binning by novel interactions to accelerate the clustering process of the data. We use the frequency-based representation to render the clusters as histogram-like bundles to reveal the distribution of the data and eliminate the overplotting of the bundles. Based on our method, we build a lightweight web-based visual analytics system for exploring multidimensional big data in PCP. The scalability analysis of our method shows that its clustering time increases linearly with the size of the data. Its rendering time is independent of the size of the data. It can cluster and visualize 1 million data records with 6 dimensions in about 1 second in web-based visualization without pre-computation of the data or hardware-accelerated rendering. We conduct two case studies and a user study to compare our method with classic PCP and two state-of-the-art edge-bundled PCP. The results show that our method is more efficient and effective for visually analyzing multidimensional big data.

Visually Enhanced Parallel Coordinates Plot With Two-Dimensional Kernel Density Scatter Plots

Visually Enhanced Parallel Coordinates Plot With Two-Dimensional Kernel Density Scatter Plots

Visual Analysis of Multisource Heterogeneous Data Based on Improved DPCA Algorithm

This paper proposes a multiview collaborative visual analysis system of network security based on a DPCA (clustering by fast search and find of density peaks) clustering algorithm called DPCANETVis, with network security analysis requirements for multisource heterogeneous data. Firstly, the system proposes an improved DPCA clustering algorithm based on the hierarchical relationship of mail sending and receiving to achieve the purpose of accurate classification. Secondly, a three-layer visual layout is designed to display relevant information such as data hierarchy, node relationship, behavior model, and other relevant information, by mixing a variety of interactive visual analysis methods such as tree diagram, word cloud, line diagram, subject river, and parallel coordinate. Lastly, based on the exploration of events, all suspicious nodes and their abnormal behaviors can be displayed in the system. Finally, the prototype system is used to analyze the network security log data set provided by the ChinaVis 2018, and the feasibility of the multilevel interactive visual analysis method for network security is verified through many experiments and discussions.

Rigorous spherical bearing with Soldner coordinates and azimuth angles on sphere

Meridian systems, called Soldner coordinates (parallel coordinate) systems, have found wide application in geodesy. In particular, the meridian system constitutes a suitable base for the Gauss-Kruger projection of the ellipsoid and the sphere. Soldner coordinates can be used in Cassini-Soldner projection without any processing. As it is known, the directions of the edges are shown with azimuth angles in the geographic coordinate system and the bearing angles in the Soldner coordinate system. Bearing or azimuth angles are frequently used in geodetic calculations. These angles give the direction of sides in the clockwise direction from a certain initial direction. Both angle values range from 0 to 360 degrees and are usually calculated from the arctan function. But the arctan function returns an angle value between -90 and +90 degrees. Therefore, it is necessary to analyze the quarter for the angle found. For practical computations, the quadrants of the arctangents are determined by the signs of the numerator and denominator in the tangent formulas. Determining the quarter of the angles is done with if…, then…, end..., blocks on the computer. It should be noted that each comparison requires a separate processing time. This study will be given how to calculate both bearing and azimuth angles with direct formulas without any need to examine them. In addition, a solution proposal will be given against the division by zero errors in the bearing and azimuth angles calculations.

Multivariate Fence: Using Parallel Coordinates to Locate and Compare Attributes of Adjacency Matrix Nodes in Immersive Environment

Adjacency matrix visualization is a common method for presenting graph data, and the Focus+Context technique can be used to explore the details of the ROI (region of interest). Embedded views and multi-view approaches are usually applied when locating and comparing attributes among multiple nodes. However, the embedded view has an issue of edge occlusion, while the multi-view would cause repeated perspective switching. In this paper, we propose a Multivariate Fence (MVF) model as a focus view of the adjacency matrix to locate and compare attributes among nodes. An additional spatial parallel coordinate is added to the 2D adjacency matrix in an immersive environment so that the attribute information can be shown in a single view without blocking edge information. We also conduct a user study to evaluate the performance of the MVF. The results show that the MVF has better efficiency and accuracy in locating and comparing the multivariate adjacency matrix in the immersive environment against the existing focus model. Moreover, the MVF model is easier to understand and is preferred by users.

How neuroticism and locus of control affect user performance in high-dimensional data visualization

The impact of individual differences, such as personality traits, on user performance and human behaviors has been studied in several fields of human–computer interaction, with a growing interest in information visualization. Although most visualizations are still designed with a universal approach, great strides have been made toward the development of user-adaptive visualizations catered to the user’s personality. We analyze how personality affects user interaction with high-dimensional visualizations. Specifically, we explore the impact of neuroticism (including its facets) and locus of control in user performance and confidence. Results suggest that neurotic individuals are faster with the scatterplot matrix, while individuals with an internal locus are more confident when using the parallel coordinates plot. In addition, results indicate that the facets of neuroticism have significant – and distinct from neuroticism – impact on user performance and confidence, pointing toward the need to analyze traits, such as neuroticism, at a lower level.

GPU accelerated scalable parallel coordinates plots

Parallel coordinates are a powerful technique to visually analyze multi-parameter data, i.e., sets of datapoints with potentially many associated parameter values per datapoint. When these sets are large, line rendering becomes a severe performance bottleneck, and since many lines fall into the same pixel the numerical precision of the color buffer is quickly reached. We propose a scalable GPU realization of parallel coordinates building upon 2D pairwise attribute bins, to significantly reduce the number of lines to be rendered. Our approach comprises a GPU compute pipeline that combines shader-based scattering with atomic increment operations to efficiently count how often a line is drawn. These counts are then used to draw all pairwise sub-plots in the parallel coordinates plot, by analytically calculating the opacity for each count and rendering a line with end points determined by the 2D coordinates of the bin. In this way, framebuffer precision issues that are paramount in classical approaches can be overcome. We demonstrate the efficiency of the proposed realization for visualizing a weather forecast ensemble comprising 2.7 billion datapoints, each carrying 7 prognostic floating-point variables like temperature, precipitation and pressure, plus spatial and simulation input variables. We compare our pipeline to a rasterization-based approach regarding performance, and demonstrate interactive brushing at 4 s per frame at full HD viewport resolution.

PCP-Ed: Parallel coordinate plots for ensemble data

The Parallel Coordinate Plot (PCP) is a complex visual design commonly used for the analysis of high-dimensional data. Increasing data size and complexity may make it challenging to decipher and uncover trends and outliers in a confined space. A dense PCP image resulting from overlapping edges may cause patterns to be covered. We develop techniques aimed at exploring the relationship between data dimensions to uncover trends in dense PCPs. We introduce correlation glyphs in the PCP view to reveal the strength of the correlation between adjacent axis pairs as well as an interactive glyph lens to uncover links between data dimensions by investigating dense areas of edge intersections. We also present a subtraction operator to identify differences between two similar multivariate data sets and relationship-guided dimensionality reduction by collapsing axis pairs. We finally present a case study of our techniques applied to ensemble data and provide feedback from a domain expert in epidemiology.

A new multi-factor multi-objective strategy based on a factorial presence-absence design to determine polymer additive residues by means of head space-solid phase microextraction-gas chromatography-mass spectrometry

A new multi-factor multi-objective strategy to approach the joint assessment of the effect of six experimental factors in the determination by head space-solid phase microextraction-gas chromatography-mass spectrometry (HS-SPME-GC-MS) of eight different additives commonly used in the plastic packaging manufacturing is proposed in this work. Five HS-SPME experimental factors, both qualitative and quantitative, are explored: the type of fiber, addition of salt, extraction and desorption time, and extraction temperature. The effect of these factors is studied through a factorial presence-absence model, that include interactions, using a D-optimal design. As a result, the number of experiments is reduced from 128, full factorial design, to 14. The effect of carrying out the measurements in different experimental sessions is considered by including a blocking factor. The response for each compound is estimated in the experimental domain and then the best experimental conditions are chosen by using Pareto front. Parallel coordinates are employed to show the conflicting conditions intrinsic to a multi-objective analysis when compounds of different nature are extracted by HS-SPME. Parallel factor analysis 2 (PARAFAC2) decomposition is used because it makes the determination of target compounds in the presence of unknown interferents possible, which enables the unequivocal identification of target compounds according to official regulations. The developed method is applied to determine 2,6-di-tert-butyl-4-methyl-phenol (BHT), benzophenone (BP), bis(2-ethylhexyl) adipate (DEHA), diethyl phthalate (DEP), diisobutyl phthalate (DiBP), dibutyl phthalate (DBP), benzyl butyl phthalate (BBP) and bis(2-ethylhexyl) phthalate (DEHP). The level of these compounds found in nine types of bottled natural still and sparkling mineral waters is very low, so the compounds were not present in quantities that may be injurious to human health.