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A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Information Theory, Probability and Statistics".

Deadline for manuscript submissions: closed (30 April 2019) | Viewed by 55331

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Special Issue Editors

Prof. Dr. Mateu Sbert

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Guest Editor

Department of Informàtica i Matemàtica Aplicada, University of Girona, 17071 Girona, Spain
Interests: application of Monte Carlo; integral geometry and information theory techniques to radiosity; global illumination; visualization and image processing

Prof. Dr. Min Chen

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Guest Editor

Pembroke College, University of Oxford, Oxford OX1 1DW, UK
Interests: visualization; computer graphics and human-computer interaction

Prof. Dr. Han-Wei Shen

E-Mail Website1 Website2
Guest Editor

Computer Science and Engineering, The Ohio State University, Columbus, OH 43210, USA
Interests: scientific visualization; computer graphics

Special Issue Information

Dear Colleagues,

Information theory is “the science of quantification, coding and communication of information” (Usher, 1984). Since the pioneering work by Shannon and Wiener in the late 1940s, information theory has played an underpinning role in the field of tele- and data communication. It has also been applied to disciplines such as physics, biology, neurology, and psychology. In computer science, its applications include computer graphics, medical imaging, computer vision, data mining, and machine learning. Visualization is concerned with visually coding and communicating information. Many aspects of a visualization pipeline feature events of a probabilistic nature, bearing a striking resemblance to a communication pipeline. This Special Issue of Entropy focuses on the applications of information theory in visualization.

The holistic nature of information-theoretic reasoning has enabled many applications in visualization, including light source placement, view selection in mesh rendering, view selection in volume rendering, focus of attention in volume rendering, multiresolution volume visualization, feature highlighting in unsteady multi-field visualization, feature highlighting in time-varying volume visualization, transfer function design, multimodal data fusion, evaluating isosurfaces, measuring of observation capacity, measuring information content in multivariate data, and confirming the mathematical feasibility of visual multiplexing. Perhaps one of the most exciting applications is the potential to use information theory to underpin the discipline of visualization, i.e., to explain some or all observed phenomena or events in visualization, to provide effective abstraction and quantitative measurements of visual designs and visualization processes, and to enable processes and algorithms for modelling, predicting, and optimizing the effects of visualization.

This Special Issue of Entropy will be co-edited by Mateu Sbert, Min Chen and Han-Wei Shen, co-authors, together with Miquel Feixas, Ivan Viola and Anton Bardera of the recent CRC book, Information Theory for Visualization. Topics of interest include, but are not limited to:

1. Information-theoretic frameworks for

visualization in general;
a sub-domain of visualization, such as
- volume visualization,
- network visualization,
- visualization-assisted machine learning,
- interaction in visualization, and
- empirical studies in visualization;
perception and cognition in visualization;
uncertainty visualization;
privacy-preserving visualization;
distribution-based data management and visualization.

2. Information-theoretic metrics in visualization, such as for measuring

abstraction;
aesthetics;
complexity of data, visualization, tasks and user spaces (alphabets);
cost-benefit of visualization processes;
distinguishability or similarity of visual objects (e.g., glyphs);
information preservation (or loss) of visual mapping;
salience in visualization;
uncertainty in visualization;
visualization capacities.

3. Information-theoretic algorithms, such as for

filtering and selection (e.g., isosurfacing, seeding);
grouping and clustering (e.g., edge bundling);
layout (e.g. clutter minimization);
view optimization;
feature extraction and tracking;
time-varying data;
multivariate visualization;
in situ visualization;
ensemble visualisation;
transfer function design.

Prof. Dr. Mateu Sbert
Prof. Dr. Min Chen
Prof. Dr. Han-Wei Shen
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

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Keywords

information theory
visualization
data science
visualization theories
metrics
algorithms

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Published Papers (10 papers)

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Research

25 pages, 25441 KiB

Open AccessArticle

Multivariate Pointwise Information-Driven Data Sampling and Visualization

by Soumya Dutta, Ayan Biswas and James Ahrens

Entropy 2019, 21(7), 699; https://doi.org/10.3390/e21070699 - 16 Jul 2019

Cited by 12 | Viewed by 6273

Abstract

With increasing computing capabilities of modern supercomputers, the size of the data generated from the scientific simulations is growing rapidly. As a result, application scientists need effective data summarization techniques that can reduce large-scale multivariate spatiotemporal data sets while preserving the important data properties so that the reduced data can answer domain-specific queries involving multiple variables with sufficient accuracy. While analyzing complex scientific events, domain experts often analyze and visualize two or more variables together to obtain a better understanding of the characteristics of the data features. Therefore, data summarization techniques are required to analyze multi-variable relationships in detail and then perform data reduction such that the important features involving multiple variables are preserved in the reduced data. To achieve this, in this work, we propose a data sub-sampling algorithm for performing statistical data summarization that leverages pointwise information theoretic measures to quantify the statistical association of data points considering multiple variables and generates a sub-sampled data that preserves the statistical association among multi-variables. Using such reduced sampled data, we show that multivariate feature query and analysis can be done effectively. The efficacy of the proposed multivariate association driven sampling algorithm is presented by applying it on several scientific data sets. Full article

(This article belongs to the Special Issue Information Theory Application in Visualization)

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22 pages, 12183 KiB

Open AccessArticle

Visual Analysis of Research Paper Collections Using Normalized Relative Compression

by Pere-Pau Vázquez

Entropy 2019, 21(6), 612; https://doi.org/10.3390/e21060612 - 21 Jun 2019

Cited by 1 | Viewed by 3997

Abstract

The analysis of research paper collections is an interesting topic that can give insights on whether a research area is stalled in the same problems, or there is a great amount of novelty every year. Previous research has addressed similar tasks by the analysis of keywords or reference lists, with different degrees of human intervention. In this paper, we demonstrate how, with the use of Normalized Relative Compression, together with a set of automated data-processing tasks, we can successfully visually compare research articles and document collections. We also achieve very similar results with Normalized Conditional Compression that can be applied with a regular compressor. With our approach, we can group papers of different disciplines, analyze how a conference evolves throughout the different editions, or how the profile of a researcher changes through the time. We provide a set of tests that validate our technique, and show that it behaves better for these tasks than other techniques previously proposed. Full article

(This article belongs to the Special Issue Information Theory Application in Visualization)

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24 pages, 11005 KiB

Open AccessArticle

Gaze Information Channel in Cognitive Comprehension of Poster Reading

by Qiaohong Hao, Mateu Sbert and Lijing Ma

Entropy 2019, 21(5), 444; https://doi.org/10.3390/e21050444 - 28 Apr 2019

Cited by 12 | Viewed by 5011

Abstract

Today, eye trackers are extensively used in studying human cognition. However, it is hard to analyze and interpret eye movement data from the cognitive comprehension perspective of poster reading. To find quantitative links between eye movements and cognitive comprehension, we tracked observers’ eye movement for reading scientific poster publications. We model in this paper eye tracking fixation sequences between content-dependent Areas of Interests (AOIs) as a Markov chain. Furthermore, we use the fact that a Markov chain is a special case of information or communication channel. Then, the gaze transition can be modeled as a discrete information channel, the gaze information channel. Next, some traditional eye tracking metrics, together with the gaze entropy and mutual information of the gaze information channel are calculated to quantify cognitive comprehension for every participant. The analysis of the results demonstrate that the gaze entropy and mutual information from individual gaze information channel are related to participants’ individual differences. This is the first study that eye tracking technology has been used to assess the cognitive comprehension of poster reading. The present work provides insights into human cognitive comprehension by using the novel gaze information channel methodology. Full article

(This article belongs to the Special Issue Information Theory Application in Visualization)

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21 pages, 11465 KiB

Open AccessArticle

Dissecting Deep Learning Networks—Visualizing Mutual Information

by Hui Fang, Victoria Wang and Motonori Yamaguchi

Entropy 2018, 20(11), 823; https://doi.org/10.3390/e20110823 - 26 Oct 2018

Cited by 10 | Viewed by 6306

Abstract

Deep Learning (DL) networks are recent revolutionary developments in artificial intelligence research. Typical networks are stacked by groups of layers that are further composed of many convolutional kernels or neurons. In network design, many hyper-parameters need to be defined heuristically before training in order to achieve high cross-validation accuracies. However, accuracy evaluation from the output layer alone is not sufficient to specify the roles of the hidden units in associated networks. This results in a significant knowledge gap between DL’s wider applications and its limited theoretical understanding. To narrow the knowledge gap, our study explores visualization techniques to illustrate the mutual information (MI) in DL networks. The MI is a theoretical measurement, reflecting the relationship between two sets of random variables even if their relationship is highly non-linear and hidden in high-dimensional data. Our study aims to understand the roles of DL units in classification performance of the networks. Via a series of experiments using several popular DL networks, it shows that the visualization of MI and its change patterns between the input/output with the hidden layers and basic units can facilitate a better understanding of these DL units’ roles. Our investigation on network convergence suggests a more objective manner to potentially evaluate DL networks. Furthermore, the visualization provides a useful tool to gain insights into the network performance, and thus to potentially facilitate the design of better network architectures by identifying redundancy and less-effective network units. Full article

(This article belongs to the Special Issue Information Theory Application in Visualization)

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28 pages, 27741 KiB

Open AccessArticle

An Information-Theoretic Framework for Evaluating Edge Bundling Visualization

by Jieting Wu, Feiyu Zhu, Xin Liu and Hongfeng Yu

Entropy 2018, 20(9), 625; https://doi.org/10.3390/e20090625 - 21 Aug 2018

Cited by 11 | Viewed by 4916

Abstract

Edge bundling is a promising graph visualization approach to simplifying the visual result of a graph drawing. Plenty of edge bundling methods have been developed to generate diverse graph layouts. However, it is difficult to defend an edge bundling method with its resulting layout against other edge bundling methods as a clear theoretic evaluation framework is absent in the literature. In this paper, we propose an information-theoretic framework to evaluate the visual results of edge bundling techniques. We first illustrate the advantage of edge bundling visualizations for large graphs, and pinpoint the ambiguity resulting from drawing results. Second, we define and quantify the amount of information delivered by edge bundling visualization from the underlying network using information theory. Third, we propose a new algorithm to evaluate the resulting layouts of edge bundling using the amount of the mutual information between a raw network dataset and its edge bundling visualization. Comparison examples based on the proposed framework between different edge bundling techniques are presented. Full article

(This article belongs to the Special Issue Information Theory Application in Visualization)

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19 pages, 3621 KiB

Open AccessArticle

Information Guided Exploration of Scalar Values and Isocontours in Ensemble Datasets

by Subhashis Hazarika, Ayan Biswas, Soumya Dutta and Han-Wei Shen

Entropy 2018, 20(7), 540; https://doi.org/10.3390/e20070540 - 20 Jul 2018

Cited by 3 | Viewed by 3914

Abstract

Uncertainty of scalar values in an ensemble dataset is often represented by the collection of their corresponding isocontours. Various techniques such as contour-boxplot, contour variability plot, glyphs and probabilistic marching-cubes have been proposed to analyze and visualize ensemble isocontours. All these techniques assume that a scalar value of interest is already known to the user. Not much work has been done in guiding users to select the scalar values for such uncertainty analysis. Moreover, analyzing and visualizing a large collection of ensemble isocontours for a selected scalar value has its own challenges. Interpreting the visualizations of such large collections of isocontours is also a difficult task. In this work, we propose a new information-theoretic approach towards addressing these issues. Using specific information measures that estimate the predictability and surprise of specific scalar values, we evaluate the overall uncertainty associated with all the scalar values in an ensemble system. This helps the scientist to understand the effects of uncertainty on different data features. To understand in finer details the contribution of individual members towards the uncertainty of the ensemble isocontours of a selected scalar value, we propose a conditional entropy based algorithm to quantify the individual contributions. This can help simplify analysis and visualization for systems with more members by identifying the members contributing the most towards overall uncertainty. We demonstrate the efficacy of our method by applying it on real-world datasets from material sciences, weather forecasting and ocean simulation experiments. Full article

(This article belongs to the Special Issue Information Theory Application in Visualization)

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22 pages, 30998 KiB

Open AccessArticle

A Survey of Viewpoint Selection Methods for Polygonal Models

by Xavier Bonaventura, Miquel Feixas, Mateu Sbert, Lewis Chuang and Christian Wallraven

Entropy 2018, 20(5), 370; https://doi.org/10.3390/e20050370 - 16 May 2018

Cited by 32 | Viewed by 7421

Abstract

Viewpoint selection has been an emerging area in computer graphics for some years, and it is now getting maturity with applications in fields such as scene navigation, scientific visualization, object recognition, mesh simplification, and camera placement. In this survey, we review and compare twenty-two measures to select good views of a polygonal 3D model, classify them using an extension of the categories defined by Secord et al., and evaluate them against the Dutagaci et al. benchmark. Eleven of these measures have not been reviewed in previous surveys. Three out of the five short-listed best viewpoint measures are directly related to information. We also present in which fields the different viewpoint measures have been applied. Finally, we provide a publicly available framework where all the viewpoint selection measures are implemented and can be compared against each other. Full article

(This article belongs to the Special Issue Information Theory Application in Visualization)

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19 pages, 40974 KiB

Open AccessArticle

Viewpoint-Driven Simplification of Plant and Tree Foliage

by Cristina Gasch, Inmaculada Remolar, Miguel Chover and Cristina Rebollo

Entropy 2018, 20(4), 213; https://doi.org/10.3390/e20040213 - 21 Mar 2018

Cited by 2 | Viewed by 5956

Abstract

Plants and trees are an essential part of outdoor scenes. They are represented by such a vast number of polygons that performing real-time visualization is still a problem in spite of the advantages of the hardware. Some methods have appeared to solve this drawback based on point- or image-based rendering. However, geometry representation is required in some interactive applications. This work presents a simplification method that deals with the geometry of the foliage, reducing the number of primitives that represent these objects and making their interactive visualization possible. It is based on an image-based simplification that establishes an order of leaf pruning and reduces the complexity of the canopies of trees and plants. The proposed simplification method is viewpoint-driven and uses the mutual information in order to choose the leaf to prune. Moreover, this simplification method avoids the pruned appearance of the tree that is usually produced when a foliage representation is formed by a reduced number of leaves. The error introduced every time a leaf is pruned is compensated for if the size of the nearest leaf is altered to preserve the leafy appearance of the foliage. Results demonstrate the good quality and time performance of the presented work. Full article

(This article belongs to the Special Issue Information Theory Application in Visualization)

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15 pages, 1641 KiB

Open AccessFeature PaperArticle

IBVis: Interactive Visual Analytics for Information Bottleneck Based Trajectory Clustering

by Yuejun Guo, Qing Xu and Mateu Sbert

Entropy 2018, 20(3), 159; https://doi.org/10.3390/e20030159 - 2 Mar 2018

Cited by 2 | Viewed by 4976

Abstract

Analyzing trajectory data plays an important role in practical applications, and clustering is one of the most widely used techniques for this task. The clustering approach based on information bottleneck (IB) principle has shown its effectiveness for trajectory data, in which a predefined number of the clusters and an explicit distance measure between trajectories are not required. However, presenting directly the final results of IB clustering gives no clear idea of both trajectory data and clustering process. Visual analytics actually provides a powerful methodology to address this issue. In this paper, we present an interactive visual analytics prototype called IBVis to supply an expressive investigation of IB-based trajectory clustering. IBVis provides various views to graphically present the key components of IB and the current clustering results. Rich user interactions drive different views work together, so as to monitor and steer the clustering procedure and to refine the results. In this way, insights on how to make better use of IB for different featured trajectory data can be gained for users, leading to better analyzing and understanding trajectory data. The applicability of IBVis has been evidenced in usage scenarios. In addition, the conducted user study shows IBVis is well designed and helpful for users. Full article

(This article belongs to the Special Issue Information Theory Application in Visualization)

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2474 KiB

Open AccessFeature PaperArticle

Rate-Distortion Theory for Clustering in the Perceptual Space

by Anton Bardera, Roger Bramon, Marc Ruiz and Imma Boada

Entropy 2017, 19(9), 438; https://doi.org/10.3390/e19090438 - 23 Aug 2017

Cited by 4 | Viewed by 5327

Abstract

How to extract relevant information from large data sets has become a main challenge in data visualization. Clustering techniques that classify data into groups according to similarity metrics are a suitable strategy to tackle this problem. Generally, these techniques are applied in the data space as an independent step previous to visualization. In this paper, we propose clustering on the perceptual space by maximizing the mutual information between the original data and the final visualization. With this purpose, we present a new information-theoretic framework based on the rate-distortion theory that allows us to achieve a maximally compressed data with a minimal signal distortion. Using this framework, we propose a methodology to design a visualization process that minimizes the information loss during the clustering process. Three application examples of the proposed methodology in different visualization techniques such as scatterplot, parallel coordinates, and summary trees are presented. Full article

(This article belongs to the Special Issue Information Theory Application in Visualization)

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