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About 5,611 papers for “Parallel coordinates”

Parallel Coordinates

Alfred Inselberg · Encyclopedia of Database Systems · 2018

Cited by 0

Parallel Coordinates

Anobel Odisho · OSF Preprints (OSF Preprints) · 2021

Cited by 0

The desire to augment our 3-dimensional perception and the need to understand multivariate problems spawned several multidimensional visualization methodologies. Understanding the underlying geometry of a multivariate problem provides insight into what is possible and what is not. After a short overview, Parallel Coordinates are introduced and developed rigorously showing, using new didactic software, how multidimensional lines, hyperplanes, flats, curves and smooth hypersurfaces can be visualized unambiguously. The development is interlaced with applications including Visual Data Mining (EDA) on real datasets (i.e. Feature extraction, GIS, Financial, Process Control, and others with hundreds of variables). There follow collision avoidance algorithms for air trafic control and detection of coplanarity and near-coplanarity with numerous applications. A geometric automatic classifier is applied to challenging clustering and classification problems. It provides the classification rule explicity and visually. Nonlinear VISUAL models in terms of hypersurfaces are constructed from data and used interactively for Decision Support discovering Feasibilites, Interelations, Sensitivities, enabling Constraint and Trade-Off Analysis. Our goal is to concentrate the relational information within a dataset into clear patterns eliminating the polygonal lines altogether. In view of recent results this prospect is becoming attainable as illustrated with a difficult problem central to many applications(Computer Vision, Geometric Modeling, Statistics).

Cited by 1Open access

Conditional Parallel Coordinates

Daniel Karl I. Weidele · arXiv (Cornell University) · 2019

Parallel Coordinates [11],[12] are a popular data visualization technique for multivariate data. Dating back to as early as 1880 [8] PC are nearly as old as John Snow's famous cholera outbreak map [18] of 1855, which is frequently regarded as a historic landmark for modern data visualization. Numerous extensions have been proposed to address integrity, scalability and readability. We make a new case to employ PC on conditional data, where additional dimensions are only unfolded if certain criteria are met in an observation. Compared to standard PC which operate on a flat set of dimensions the ontology of our input to Conditional Parallel Coordinates is of hierarchical nature. We therefore briefly review related work around hierarchical PC using aggregation or nesting techniques. Our contribution is a visualization to seamlessly adapt PC for conditional data under preservation of intuitive interaction patterns to select or highlight polylines. We conclude with intuitions on how to operate CPC on two data sets: an AutoML hyperparameter search log, and session results from a conversational agent.

Cited by 0Open access

Continuous Parallel Coordinates

Joachim Heinrich, Daniel Weiskopf · IEEE Transactions on Visualization and Computer Graphics · 2009

Typical scientific data is represented on a grid with appropriate interpolation or approximation schemes,defined on a continuous domain. The visualization of such data in parallel coordinates may reveal patterns latently contained in the data and thus can improve the understanding of multidimensional relations. In this paper, we adopt the concept of continuous scatterplots for the visualization of spatially continuous input data to derive a density model for parallel coordinates. Based on the point-line duality between scatterplots and parallel coordinates, we propose a mathematical model that maps density from a continuous scatterplot to parallel coordinates and present different algorithms for both numerical and analytical computation of the resulting density field. In addition, we show how the 2-D model can be used to successively construct continuous parallel coordinates with an arbitrary number of dimensions. Since continuous parallel coordinates interpolate data values within grid cells, a scalable and dense visualization is achieved, which will be demonstrated for typical multi-variate scientific data.

Cited by 110

Force-Directed Parallel Coordinates

Rick Walker, Phil Legg, Serban R. Pop et al. · 2013

Parallel coordinates are a well-known and valuable technique for the analysis and visualization of high dimensional data sets. However, while Inselberg emphasizes that the strength of parallel coordinates as a methodology is rooted in exploration and interactivity, the set of interaction techniques is currently limited. Axes can be re-ordered and brushing (simple, angular or multi-dimensional) can be performed. In this paper, we propose a force-directed algorithm and related interaction techniques to support the exploration of parallel coordinate plots through a physical metaphor. Our parallel-coordinates visualization offers novel user interaction beyond the standard techniques by allowing the user to rotate the axis according to forcedirected polylines. The new interaction provides the user with a more immersive experience for data exploration that results in greater intuition of the data, especially in cases where many polylines overlap. We demonstrate our approach, then present the results of a qualitative evaluation of the system.

Cited by 7

Interactive parallel coordinates plot

Kaim, Andrea · Figshare · 2020

(Please download HTML file for proper display) Parallel coordinates plot of the results of a four-objective optimization problem. The first four axes show fitness values for the objectives max biodiversity (measured in terms of a bird habitat indicator), max water quantity (lowflow in l/s), max water quality (i.e. min nitrate load in kgN/a) and max contribution margin produced by the entire case study area (€/a). Values of water quality are negative because nitrate load has been minimized. Generally, the better the performance of a solution in the respective objective is, the higher its intersection with the objective's axis is located in the plot. The last four axes show the percental share of the scenarios status quo (SQ), business as usual (BAU), land sharing (LSH) and land sparing (LSP) in the landscape. Each line that connects the axes represents one of the Pareto-optimal solutions. Status quo is marked as a yellow line. Trade-offs and synergies between the objectives and their impact on scenario distributions can be analyzed by selecting value ranges on the different axes. This plot is based on results from A. Kaim, M. Strauch & M. Volk (2020): Using stakeholder preferences to identify optimal land use configurations. Frontiers in Water. DOI: 10.3389/frwa.2020.579087.

Cited by 0Open access

Angle-uniform parallel coordinates

Kaiyi Zhang, Liang Zhou, Lu Chen et al. · Computational Visual Media · 2023

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.

Cited by 2Open access

Interacting with parallel coordinates

Harri Siirtola, Kari‐Jouko Räihä · Interacting with Computers · 2006

Parallel coordinate visualizations have a reputation of being difficult to understand, expert-only representations. We argue that this reputation may be partially unfounded, because many of the parallel coordinate browser implementations lack essential features. This paper presents a survey of current interaction techniques for parallel coordinate browsers and compares them to the visualization design guidelines in the literature. In addition, we report our experiences with parallel coordinate browser prototypes, and describe an experiment where we studied the immediate usability of parallel coordinate visualizations. In the experiment, 16 database professionals performed a set of tasks both with the SQL query language and a parallel coordinate browser. The results show that although the subjects had doubts about the general usefulness of the parallel coordinate technique, they could perform the tasks more efficiently with a parallel coordinate browser than with their familiar query language interface.

Cited by 89

Lecture Notes PARALLEL COORDINATES

Alfred Inselberg C, Senior Fellow, San Diego · 2011

3 Scan0001.tif Figure 1.1: Cholera epidemic in London 1854. Dr. Snow placed dots at the addresses of the deceased and saw the concentration of deaths around the Broad street water pump. From

Cited by 0

Interactive parallel coordinates plot

Kaim, Andrea · Figshare · 2020

Cited by 0Open access

Parallel Coordinates Plot (PCP)

Encyclopedia of Database Systems · 2009

Cited by 0

Parallel Coordinates System (PCS)

Ling Liu, M. TAMER ÖZSU · Encyclopedia of Database Systems · 2009

Cited by 0

Features in Continuous Parallel Coordinates

Donald J. Lehmann, Holger Theisel · IEEE Transactions on Visualization and Computer Graphics · 2011

Continuous Parallel Coordinates (CPC) are a contemporary visualization technique in order to combine several scalar fields, given over a common domain. They facilitate a continuous view for parallel coordinates by considering a smooth scalar field instead of a finite number of straight lines. We show that there are feature curves in CPC which appear to be the dominant structures of a CPC. We present methods to extract and classify them and demonstrate their usefulness to enhance the visualization of CPCs. In particular, we show that these feature curves are related to discontinuities in Continuous Scatterplots (CSP). We show this by exploiting a curve-curve duality between parallel and Cartesian coordinates, which is a generalization of the well-known point-line duality. Furthermore, we illustrate the theoretical considerations. Concluding, we discuss relations and aspects of the CPC's/CSP's features concerning the data analysis.

Cited by 13

Scattering Points in Parallel Coordinates

Xiaoru Yuan, Peihong Guo, He Xiao et al. · IEEE Transactions on Visualization and Computer Graphics · 2009

In this paper, we present a novel parallel coordinates design integrated with points (Scattering Points in Parallel Coordinates, SPPC), by taking advantage of both parallel coordinates and scatterplots. Different from most multiple views visualization frameworks involving parallel coordinates where each visualization type occupies an individual window, we convert two selected neighboring coordinate axes into a scatterplot directly. Multidimensional scaling is adopted to allow converting multiple axes into a single subplot. The transition between two visual types is designed in a seamless way. In our work, a series of interaction tools has been developed. Uniform brushing functionality is implemented to allow the user to perform data selection on both points and parallel coordinate polylines without explicitly switching tools. A GPU accelerated Dimensional Incremental Multidimensional Scaling (DIMDS) has been developed to significantly improve the system performance. Our case study shows that our scheme is more efficient than traditional multi-view methods in performing visual analysis tasks.

Cited by 138

Spectral-Based Contractible Parallel Coordinates

2014

Abstract—Parallel coordinates is well-known as a popular tool for visualizing the underlying relationships among vari-ables in high-dimensional datasets. However, this representa-tion still suffers from visual clutter arising from intersections among polyline plots especially when the number of data samples and their associated dimension become high. This paper presents a method of alleviating such visual clutter by contracting multiple axes through the analysis of correlation between every pair of variables. In this method, we first construct a graph by connecting axis nodes with an edge weighted by data correlation between the corresponding pair of dimensions, and then reorder the multiple axes by projecting the nodes onto the primary axis obtained through the spectral graph analysis. This allows us to compose a dendrogram tree by recursively merging a pair of the closest axes one by one. Our visualization platform helps the visual interpretation of such axis contraction by plotting the principal component of each data sample along the composite axis. Smooth animation of the associated axis contraction and expansion has also been implemented to enhance the visual readability of behavior inherent in the given high-dimensional datasets. Keywords-parallel coordinates; axis contraction; spectral graph theory; dendrograms I.

Cited by 0

Visual Clustering in Parallel Coordinates

Hong Zhou, Xiaoru Yuan, Huamin Qu et al. · Computer Graphics Forum · 2008

Abstract Parallel coordinates have been widely applied to visualize high‐dimensional and multivariate data, discerning patterns within the data through visual clustering. However, the effectiveness of this technique on large data is reduced by edge clutter. In this paper, we present a novel framework to reduce edge clutter, consequently improving the effectiveness of visual clustering. We exploit curved edges and optimize the arrangement of these curved edges by minimizing their curvature and maximizing the parallelism of adjacent edges. The overall visual clustering is improved by adjusting the shape of the edges while keeping their relative order. The experiments on several representative datasets demonstrate the effectiveness of our approach.

Cited by 169

Parallel Coordinates with Data Labels

Hong Zhou, Panpan Xu, Zhong Ming et al. · 2014

Parallel coordinates have been widely used to analyze high-dimensional data. Numerous methods have been designed to provide overview patterns in parallel coordinate plots. However, detailed information is also important in data analysis. When several lines overlap or are close to one another, distinguishing detailed information of polyline crossings is difficult. In this paper, we present a novel approach to address the problem of polyline crossing ambiguity by using data labels. We place different labels along various polylines to give cues for differentiation of lines. We bend the lines and optimize the arrangement of curved lines to provide space for clear visible labels. An energy system that models attractive and repulsive forces of lines is used to guide the search for optimized line arrangement. The experiments on several real datasets demonstrate the effectiveness of our approach.

Cited by 6