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Scatterplot layout for high-dimensional data visualization
Abstract
Multi-dimensional data visualization is an important research topic that has been receiving increasing attention. Several techniques that apply scatterplot matrices have been proposed to represent multi-dimensional data as a collection of two-dimensional data visualization spaces. Typically, when using the scatterplot-based approach it is easier to understand relations between particular pairs of dimensions, but it often requires too large display spaces to display all possible scatterplots. This paper presents a technique to display meaningful sets of scatterplots generated from high-dimensional datasets. Our technique first evaluates all possible scatterplots generated from high-dimensional datasets, and selects meaningful sets. It then calculates the similarity between arbitrary pairs of the selected scatterplots, and places relevant scatterplots closer together in the display space while they never overlap each other. This design policy makes users easier to visually compare relevant sets of scatterplots. This paper presents algorithms to place the scatterplots by the combination of ideal position calculation and rectangle packing algorithms, and two examples demonstrating the effectiveness of the presented technique.
Graphical Abstract
... In addition, it can be difficult for humans to visually compare arbitrary pairs of SPs that are distantly placed in the display space. Several studies aimed at selecting meaningful sets of SPs and effectively arrange them onto the display spaces [6] [30] [36] [38] [42]; however, these studies often had difficulty to visually compare large number of SPs. ...
... Suematsu et al. [33] also converted high-dimensional datasets into low-dimensional subsets and visualized these subsets using multiple PCPs arranged on display spaces based upon their similarity and correlation. Using similar ideas, Zheng et al. [42] selected SPs based upon the meaningfulness of the dimensions being displayed and adjusted their layout based upon their similarity. Claessen et al. [5] presented a technique to visualize high-dimensional datasets by selecting sets of low-dimensional subspaces and representing them as a combination of PCPs and SPs. ...
Parallel coordinate plots (PCPs) are among the most useful techniques for the visualization and exploration of high-dimensional data spaces. They are especially useful for the representation of correlations among the dimensions, which identify relationships and interdependencies between variables. However, within these high-dimensional spaces, PCPs face difficulties in displaying the correlation between combinations of dimensions and generally require additional display space as the number of dimensions increases. In this paper, we present a new technique for high-dimensional data visualization in which a set of low-dimensional PCPs are interactively constructed by sampling user-selected subsets of the high-dimensional data space. In our technique, we first construct a graph visualization of sets of well-correlated dimensions. Users observe this graph and are able to interactively select the dimensions by sampling from its cliques, thereby dynamically specifying the most relevant lower dimensional data to be used for the construction of focused PCPs. Our interactive sampling overcomes the shortcomings of the PCPs by enabling the visualization of the most meaningful dimensions (i.e., the most relevant information) from high-dimensional spaces. We demonstrate the effectiveness of our technique through two case studies, where we show that the proposed interactive low-dimensional space constructions were pivotal for visualizing the high-dimensional data and discovering new patterns.
... In addition, it can be difficult for humans to visually compare arbitrary pairs of SPs that are distantly placed in the display space. Several studies aimed at selecting meaningful sets of SPs and effectively arrange them onto the display spaces [6] [30] [36] [38] [42]; however, these studies often had difficulty to visually compare large number of SPs. ...
... Suematsu et al. [33] also converted high-dimensional datasets into low-dimensional subsets and visualized these subsets using multiple PCPs arranged on display spaces based upon their similarity and correlation. Using similar ideas, Zheng et al. [42] selected SPs based upon the meaningfulness of the dimensions being displayed and adjusted their layout based upon their similarity. Claessen et al. [5] presented a technique to visualize high-dimensional datasets by selecting sets of low-dimensional subspaces and representing them as a combination of PCPs and SPs. ...
Parallel coordinate plots (PCPs) are among the most useful techniques for the visualization and exploration of high-dimensional data spaces. They are especially useful for the representation of correlations among the dimensions, which identify relationships and interdependencies between variables. However, within these high-dimensional spaces, PCPs face difficulties in displaying the correlation between combinations of dimensions and generally require additional display space as the number of dimensions increases. In this paper, we present a new technique for high-dimensional data visualization in which a set of low-dimensional PCPs are interactively constructed by sampling user-selected subsets of the high-dimensional data space. In our technique, we first construct a graph visualization of sets of well-correlated dimensions. Users observe this graph and are able to interactively select the dimensions by sampling from its cliques, thereby dynamically specifying the most relevant lower dimensional data to be used for the construction of focused PCPs. Our interactive sampling overcomes the shortcomings of the PCPs by enabling the visualization of the most meaningful dimensions (i.e., the most relevant information) from high-dimensional spaces. We demonstrate the effectiveness of our technique through two case studies, where we show that the proposed interactive low-dimensional space constructions were pivotal for visualizing the high-dimensional data and discovering new patterns.
... Claessen et al. [2] visualized high-dimensional datasets by representing a set of low-dimensional subspaces as a combination of PCPs and scatterplots. Suematsu et al. [15] and Zheng et al. [22] also converted high-dimensional datasets into low-dimensional subsets and visualized these subsets using multiple PCPs or scatterplots respectively. These techniques did not provide rich interaction mechanisms to freely select the numbers of dimensions. ...
Scatterplot selection is an effective approach to represent essential portions of multidimensional data in a limited display space. Various metrics for evaluation of scatterplots such as scagnostics have been presented and applied to scatterplot selection. This paper presents a new scatterplot selection technique that applies multiple metrics. The technique firstly calculates scores of scatterplots with multiple metrics and then constructs a graph by connecting similar scatterplots. The technique applies a graph coloring problem so that different colors are assigned to similar scatterplots. We can extract a set of various scatterplots by selecting them that the specific same color is assigned. This paper introduces visualization examples with a retail dataset containing multidimensional climate and sales values.
... Tables are familiar and popular for investigating and getting acquainted with planning data, and scatterplot is one of the most frequently used multidimensional data visualization techniques (e.g. Zheng et al., 2015). Besides tables and scatterplots, bar charts (histograms) are widely used visualization techniques. ...
Common to multi-objective forest planning situations is that they all require comparisons, searches and evaluation among decision alternatives. Through these actions, the decision maker can learn from the information presented and thus make well-justified decisions. Interactive data visualization is an evolving approach that supports learning and decision making in multidimensional decision problems and planning processes. Data visualization contributes the formation of mental image data and this process is further boosted by allowing interaction with the data. In this study, we introduce a multi-objective forest planning decision problem framework and the corresponding characteristics of data. We utilize the framework with example planning data to illustrate and evaluate the potential of 14 interactive data visualization techniques to support multi-objective forest planning decisions. Furthermore, broader utilization possibilities of these techniques to incorporate the provisioning of ecosystem services into forest management and planning are discussed.
Scatterplot is a popular technique for visualizing high-dimensional datasets by using linear and nonlinear dimension reduction methods. These methods map the original high-dimensional dataset onto scatterplot points directly by dimension reduction, and hence require a high computation cost. Despite many improvements in scatterplot visual effects, however, when the data volume is large, the data mapped onto scatterplot data points will overlap, resulting a low quality of visualization. In this paper, we propose a novel software tool that ensembles five integrated components for fast multiview visualization of high-dimensional datasets: sampling, dimension reduction, clustering, multiview collaborative analysis, and dimension re-arrangement. In our tool, while the sampling component reduces the sizes of the datasets applying the random sampling technique to gain a high visualization efficiency, dimension reduction reduces the dimensions of the datasets applying principal-component analysis to improve the visualization quality. Next, clustering discovers hidden information in the reduced dataset applying fuzzy c-mean clustering to display hidden patterns of the original datasets. Finally, multiview collaborative analysis enables users to analyse multidimensional datasets from different aspects at the same time by combining scatterplot and scatterplot matrices. To optimize the visualization effects, in the scatterplot matrices, we re-arrange their dimensions and adjust the positions of scatterplots so that similar scatterplot points are adjacent in positions. As the result, in comparison with the existing visualization tools that apply some of these techniques, our tool not only improves the efficiency of dimension reduction but also enhances the quality of visualization and enables more comprehensive analysis. We test our tool on different real datasets to demonstrate its effectiveness. The experimental results validate that our method is effective in both efficiency and quality of visualization.
Multidimensional data visualization is one of the most active research topics in information visualization since various information in our daily life forms multidimensional datasets. Scatterplot selection is an effective approach to represent essential portions of multidimensional data in a limited display space. Various metrics for evaluating scatterplots, such as scagnostics, have been applied to scatterplot selection. One of the open problems of this research topic is that various scatterplots cannot be selected if we simply apply one of the metrics. In other words, we may want to apply multiple metrics simultaneously in a balanced manner when we want to select a variety of scatterplots. This paper presents a new scatterplot selection technique that solves this problem. First, the technique calculates the scores of scatterplots with multiple metrics and then constructs a graph by connecting pairs of scatterplots that have similar scores. Next, it uses a graph coloring algorithm to assign different colors to scatterplots that have similar scores. We can extract a set of various scatterplots by selecting them that the specific same color is assigned. This paper introduces two case studies: the former study is with a retail transaction dataset while the latter study is with a design optimization dataset.
This book is devoted to the emerging field of integrated visual knowledge discovery that combines advances in artificial intelligence/machine learning and visualization/visual analytic. A long-standing challenge of artificial intelligence (AI) and machine learning (ML) is explaining models to humans, especially for live-critical applications like health care. A model explanation is fundamentally human activity, not only an algorithmic one. As current deep learning studies demonstrate, it makes the paradigm based on the visual methods critically important to address this challenge. In general, visual approaches are critical for discovering explainable high-dimensional patterns in all types in high-dimensional data offering "n-D glasses," where preserving high-dimensional data properties and relations in visualizations is a major challenge. The current progress opens a fantastic opportunity in this domain.
This book is a collection of 25 extended works of over 70 scholars presented at AI and visual analytics related symposia at the recent International Information Visualization Conferences with the goal of moving this integration to the next level. The sections of this book cover integrated systems, supervised learning, unsupervised learning, optimization, and evaluation of visualizations.
The intended audience for this collection includes those developing and using emerging AI/machine learning and visualization methods. Scientists, practitioners, and students can find multiple examples of the current integration of AI/machine learning and visualization for visual knowledge discovery. The book provides a vision of future directions in this domain. New researchers will find here an inspiration to join the profession and to be involved for further development. Instructors in AI/ML and visualization classes can use it as a supplementary source in their undergraduate and graduate classes.
Strategic foresight, corporate foresight, and technology management enable firms to detect discontinuous changes early and develop future courses for a more sophisticated market positioning. The enhancements in machine learning and artificial intelligence allow more automatic detection of early trends to create future courses and make strategic decisions. Visual Analytics combines methods of automated data analysis through machine learning methods and interactive visualizations. It enables a far better way to gather insights from a vast amount of data to make a strategic decision. While Visual Analytics got various models and approaches to enable strategic decision-making, the analysis of trends is still a matter of research. The forecasting approaches and involvement of humans in the visual trend analysis process require further investigation that will lead to sophisticated analytical methods. We introduce in this paper a novel model of Visual Analytics for decision-making, particularly for technology management, through early trends from scientific publications. We combine Corporate Foresight and Visual Analytics and propose a machine learning-based Technology Roadmapping based on our previous work. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.
There have been a variety of techniques on multi-dimension data visualization techniques. Scatterplot matrix and parallel coordinate plots are typical and famous ones, but they have a problem that they may need a very large screen space when a dataset has a large number of dimensions. We suppose there are two types of solutions for this problem: one of them is to effectively select interesting sets of dimensions, and the other is to develop drawing techniques that realize comprehensive representations in the limited screen space. Based on this direction, we propose a method for selecting important scatterplots from all scatterplots generated from input datasets and for drawing the scatterplots as “outliers” and “regions enclosing non-outlier plots.” The technique is useful for users to determine whether to delete outliers from the datasets and form mathematical models of non-outlier plots. This chapter extends the authors’ conference paper by additionally introducing an example with a design optimization dataset and the user evaluation of this technique.
Visualization of multidimensional data has always been a research hotspot. Dimensional analysis is an efficient way to solve multidimensional problems. The current dimensional analysis methods mostly consider that all dimension correlations are at the same granularity, but actually the correlation between dimensions may be multi-scale. Multi-scale dimensions can also reflect the multi-scale data association mode, which is of certain value for analyzing the hidden information of multidimensional data. In this paper, we propose a method of dimension subdivision to resolve the multi-scale correlations between dimensions. To explore the multi-scale complex relationship between dimensions, we subdivide the original dimensions into finer sub-dimensions and build a graph-based data structure of the correlations to partition strongly relevant and irrelevant dimensions. We also proposed D-div, a visual dimension analysis system to support our method. In D-div, we provide visualization and interaction techniques to explore subdivided dimensions. Via case studies with two datasets, we demonstrate the effectiveness of our method of dimension subdivision.
In a variety of research and application areas, graphs are an important structure for data modeling and analysis. While graph properties can have a crucial influence on the performance of graph algorithms, and thus on the outcome of experiments, often only basic analysis of the graphs under investigation in an experimental evaluation is performed and a few characteristics are reported in publications. We present Graph Landscape, a concept for the visual analysis of graph set properties. The Graph Landscape aims to support researchers to explore graphs and graph sets regarding their properties, to allow to select good experimental test sets, analyze newly generated sets, compare sets and assess the validity (or range) of experimental results and corresponding conclusions.
Graphical Abstract
Graphical Abstract text
In a variety of research and application areas graphs are an important structure for data modeling and analysis. While graph properties can have a crucial influence on the performance of graph algorithms, and thus on the outcome of experiments, often only basic analysis of the graphs under investigation in an experimental evaluation is performed, and a few characteristics are reported in publications.
We present Graph Landscape, a concept for the visual analysis of graph set properties. The Graph Landscape aims to support researchers to explore graphs and graph sets regarding their properties, in order to allow to select good experimental test sets, analyze newly generated sets, compare sets and assess the validity (or range) of experimental results and corresponding conclusions.
In this paper we provide a brief background to data visualization and point to key references. We differentiate between high- dimensional data visualization and high-dimensional data visualizations and review the various high-dimensional visualization techniques. Our goal is to define metrics that identify how visualizations deal with n dimensions when displayed on the screen. We define intrinsic dimensionality metrics that assess these techniques and closely analyze selected high-dimensional visualizations' display of data.
Many graphs used in real-world applications consist of nodes be- longing to more than one category. We call such graph "multiple- category graphs". Socialnetworks aretypical examples ofmultiple- category graphs: nodes are persons, links are friendships, and cate- gories are communities thatthe persons belong to. Itis often helpful to visualize both connectivity and categories of the graphs simulta- neously. In this paper, we present a new visualization technique for multiple-category graphs. The technique firstly constructs hierar- chical clusters of the nodes based on both connectivity and cate- gories. It then places the nodes by a new hybrid space-filling and force-directed layout algorithm to clearly display both connectivity and category information. We show layout results using our hybrid method and compare it with other methods, and present a case study using an active biological network dataset.
Much of the attention in visualization research has focussed on data rooted in physical phenomena, which is generally limited to three or four dimensions. However, many sources of data do not share this dimensional restriction. A critical problem in the analysis of such data is providing researchers with tools to gain insights into characteristics of the data, such as anomalies and patterns. Several visualization methods have been developed to address this problem, and each has its strengths and weaknesses. This paper describes a system named XmdvTool which integrates several of the most common methods for projecting multivariate data onto a two-dimensional screen. This integration allows users to explore their data in a variety of formats with ease. A view enhancement mechanism called an N-dimensional brush is also described. The brush allows users to gain insights into spatial relationships over N dimensions by highlighting data which falls within a user-specified subspace.
Scatterplots remain one of the most popular and widely-used visual representations for multidimensional data due to their simplicity, familiarity and visual clarity, even if they lack some of the flexibility and visual expressiveness of newer multidimensional visualization techniques. This paper presents new interactive methods to explore multidimensional data using scatterplots. This exploration is performed using a matrix of scatterplots that gives an overview of the possible configurations, thumbnails of the scatterplots, and support for interactive navigation in the multidimensional space. Transitions between scatterplots are performed as animated rotations in 3D space, somewhat akin to rolling dice. Users can iteratively build queries using bounding volumes in the dataset, sculpting the query from different viewpoints to become more and more refined. Furthermore, the dimensions in the navigation space can be reordered, manually or automatically, to highlight salient correlations and differences among them. An example scenario presents the interaction techniques supporting smooth and effortless visual exploration of multidimensional datasets.
VizRank is a tool that finds interesting two-dimensional projections of class-labeled data. When applied to multi-dimensional
functional genomics datasets, VizRank can systematically find relevant biological patterns.
Availability: http://www.ailab.si/supp/bi-vizrank
Supplementary information: http://www.ailab.si/supp/bi-vizrank
Contact: blaz.zupan{at}fri.uni-lj.si
We introduce Tukey and Tukey scagnostics and develop graph-theoretic methods for implementing their procedure on large datasets.
By means of parallel coordinates a mapping R
N
→ R
2, which is not a projection is obtained. Relations among N variables, for any positive integer N, are “represented” by their planar images. These planar diagrams have geometrical properties corresponding to certain properties of the relation they represent. Starting from a point ← → line duality when N = 2, the representation of lines in R
N
is given and illustrated by an application to Air Traffic Control (i.e. for R
4). It is followed by the representation of hyperplanes, polytopes and more general convex and some nonconvex (i.e. “pretsels” in R
N
) hypersurfaces. An algorithm for constructing and exhibiting any interior point to such a hypersurface is shown. Such a display shows some local (i.e. near the point) properties of the hypersurface and information on the point’s proximity to the boundary. Graphics from the computer implementation of the representations and algorithms are included.
Graphs with nonuniform nodes arise naturally in many real-world applications. Although graph drawing has been a very active research in the computer science community during the past decade, most of the graph drawing algorithms developed thus far have been designed for graphs whose nodes are represented as single points. As a result, it is of importance to develop drawing methods for graphs whose nodes are of different sizes and shapes, in order to meet the need of real-world applications. To this end, a potential field approach, coupled with an idea commonly found in force-directed methods, is proposed in this paper for drawing graphs with nonuniform nodes in 2-D and 3-D. In our framework, nonuniform nodes are uniformly charged, while edges are modelled by springs. Using certain techniques developed in the field of potential-based path planning, we are able to find analytically tractable procedures for computing the repulsive force and torque of a node in the potential field induced by the remaining nodes. The crucial feature of our approach is that the rotation of every nonuniform node and the multiple edges between two nonuniform nodes are taken into account. In comparison with the existing algorithms found in the literature, our experimental results suggest this new approach to be promising, as drawings of good quality for a variety of moderate-sized graphs in 2-D and 3-D can be produced reasonably efficiently. That is, our approach is suitable for moderate-sized interactive graphs or larger-sized static graphs. Furthermore, to illustrate the usefulness of our new drawing method for graphs with zero-sized nodes, we give an application to the visualization of hierarchical clustered graphs, for which our method offers a very efficient solution.
In this paper, we study the sensitivity of centrality metrics as a key metric of social networks to support visual reasoning. As centrality represents the prestige or importance of a node in a network, its sensitivity represents the importance of the relationship between this and all other nodes in the network. We have derived an analytical solution that extracts the sensitivity as the derivative of centrality with respect to degree for two centrality metrics based on feedback and random walks. We show that these sensitivities are good indicators of the distribution of centrality in the network, and how changes are expected to be propagated if we introduce changes to the network. These metrics also help us simplify a complex network in a way that retains the main structural properties and that results in trustworthy, readable diagrams. Sensitivity is also a key concept for uncertainty analysis of social networks, and we show how our approach may help analysts gain insight on the robustness of key network metrics. Through a number of examples, we illustrate the need for measuring sensitivity, and the impact it has on the visualization of and interaction with social and other scale-free networks.
Many visualization techniques involve mapping high-dimensional data spaces to lower-dimensional views. Unfortunately, mapping a high-dimensional data space into a scatterplot involves a loss of information; or, even worse, it can give a misleading picture of valuable structure in higher dimensions. In this paper, we propose class consistency as a measure of the quality of the mapping. Class consistency enforces the constraint that classes of nD data are shown clearly in 2D scatterplots. We propose two quantitative measures of class consistency, one based on the distance to the classs center of gravity, and another based on the entropies of the spatial distributions of classes. We performed an experiment where users choose good views, and show that class consistency has good precision and recall. We also evaluate both consistency measures over a range of data sets and show that these measures are efficient and robust.
The authors address the problem of visualizing a scalar dependent variable which is a function of many independent variables. In particular, cases where the number of independent variables is three or greater are discussed. A new hierarchical method of plotting that allows one to interactively view millions of data points with up to 10 independent variables is presented. The technique is confined to the case where each independent variable is sampled in a regular grid or lattice-like fashion, i.e., in equal increments. The proposed technique can be described in either an active or a passive manner. In the active view the points of the N -dimensional independent variables lattice are mapped to a single horizontal axis in a hierarchical manner, while in the passive view an observer samples the points of the N -dimensional lattice in a prescribed fashion and notes the values of the dependent variable. In the passive view a plot of the dependent variable versus a single parametric variable, which is simply the sampling number, forms the multidimensional graph
A technique for visualizing intrusion-detection system log files using hierarchical data based on IP addresses represents the number of incidents for thousands of computers in one display space. Our technique applies a hierarchical data visualization technique that represents leaf nodes as black square icons and branch nodes as rectangular borders enclosing the icons. This representation style visualizes thousands of hierarchical data leaf nodes equally in one display space. We applied the technique to bioactive chemical visualization and job distribution in parallel-computing environments.
Discusses how the VisDB system supports the query specification process by representing the result visually. The main idea behind the system stems from the view of relational database tables as sets of multidimensional data where the number of attributes corresponds to the number of dimensions. In such a view, it is often unclear. In this system, each display pixel represents one database item. Pixels are arranged and colored to indicate the item's relevance to a user query and to give a visual impression of the resulting data set
1 Introduction One common problem in graphical user interface design has been n-Vision is a testbed for exploring n-dimensional worlds the need to manipulate and view 3D environments using containing functions of an arbitrary number of variables. inherently 2D interaction devices and displays. Although Although our interaction devices and display hardware are graphics researchers have long been developing true 3D inherently 3D, we demonstrate how they can be used to support interaction and display devices [SUTH65; VICK70; KILP76], it is interaction with these higher-dimensional objects. We introduce a only over the past decade that high-performance 3D graphics new interaction metaphor developed for the system, which we call workstations have been coupled with commercially available 3D "worlds within worlds": nested heterogeneous coordinate devices such as polarized liquid crystal shutters for stereo viewing systems that allow the user to view and manipulate functions. [TEKT87; STER89]...
The vertices of most graphs that appear in real applications are nonuniform. They can be circles, ellipses, rectangles, or other geometric elements of varying shapes and sizes. Unfortunately, current force directed methods for laying out graphs are suitable mostly for graphs whose vertices are zero-sized and dimensionless points. It turns out that naively extending these methods to handle nonuniform vertices results in serious deficiencies in terms of output quality and performance. In this paper we try to remedy this situation by identifying the special characteristics and problematics of such graphs and offering several algorithms for tackling them. The algorithms can be viewed as carefully constructed extensions of force-directed methods, and their output quality and performance are similar.
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