Nonparametric Models for Uncertainty Visualization

Abstract

An uncertain (scalar, vector, tensor) field is usually perceived as a discrete random field with a priori unknown probability distributions. To compute derived probabilities, e.g. for the occurrence of certain features, an appropriate probabilistic model has to be selected. The majority of previous approaches in uncertainty visualization were restricted to Gaussian fields. In this paper we extend these approaches to nonparametric models, which are much more flexible, as they can represent various types of distributions, including multimodal and skewed ones. We present three examples of nonparametric representations: (a) empirical distributions, (b) histograms and (c) kernel density estimates (KDE). While the first is a direct representation of the ensemble data, the latter two use reconstructed probability density functions of continuous random variables. For KDE we propose an approach to compute valid consistent marginal distributions and to efficiently capture correlations using a principal component transformation. Furthermore, we use automatic bandwidth selection, obtaining a model for probabilistic local feature extraction. The methods are demonstrated by computing probabilities of level crossings, critical points and vortex cores in simulated biofluid dynamics and climate data.

Generation and Visual Exploration of Medical Flow Data: Survey, Research Trends and Future Challenges

“…Pöthkow et al . [PH13] extended the approach by Petz et al . [PPH12] from Gaussian fields to more flexible non‐parametric models.…”

KDE based outlier detection on distributed data streams in multimedia network

“…Considered the changing value of data stream, this paper introduces attenuation model, all values fadings according to time t, which can be expressed as f(t), paper [30] proposed a attenuation model f(t) = 2 − λt ,which is suitable for time based data, where λ is the attenuation factor, and λ > 0. As the data model of this paper is sliding window model, so we proposed an attenuation strategy, which can be expressed as (6).…”

Multi-Granular Trend Detection for Time-Series Analysis

“…Without knowledge of the individual entities that comprise the data such representations may be misleading. Other options to display uncertainty include the display of regular distribution plots [31], and uncertainty isolines [30].…”

“…Different glyphs have been proposed to visualize this variability, for example, box plots, violin plots [17], and summary plots [31]. Higher-dimensional data may be visualized using (probabilistic) isolines to display uncertainty [2,29,30,41]. Local surface distortion [15] and animation [4] have also been applied to display uncertainty in higher-dimensional data.…”