Visualizing the Stability of 2D Point Sets from Dimensionality Reduction Techniques

Reinbold, Christian; Kumpf, Alexander; Westermann, Rüdiger

doi:10.1111/cgf.13806

Cited by 5 publications

(4 citation statements)

References 49 publications

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“…Investigating the viability of using different dissimilarity measures as well as their effect on the projection will be an important part of improving the flexibility of UAMDS. Investigating ways to make other dimensionality reduction methods, like t-SNE or UMAP, uncertaintyaware and examining their stability [29] under uncertainty is also on our roadmap. Finally, we plan to perform a user study based evaluation [14] of the uncertainty visualization via MDS.…”

Section: Discussionmentioning

confidence: 99%

Uncertainty-Aware Multidimensional Scaling

Hägele

Krake

Weiskopf

2022

IEEE Trans. Visual. Comput. Graphics

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We present an extension of multidimensional scaling (MDS) to uncertain data, facilitating uncertainty visualization of multidimensional data. Our approach uses local projection operators that map high-dimensional random vectors to low-dimensional space to formulate a generalized stress. In this way, our generic model supports arbitrary distributions and various stress types. We use our uncertainty-aware multidimensional scaling (UAMDS) concept to derive a formulation for the case of normally distributed random vectors and a squared stress. The resulting minimization problem is numerically solved via gradient descent. We complement UAMDS by additional visualization techniques that address the sensitivity and trustworthiness of dimensionality reduction under uncertainty.With several examples, we demonstrate the usefulness of our approach and the importance of uncertainty-aware techniques.

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Section: Discussionmentioning

confidence: 99%

Uncertainty-Aware Multidimensional Scaling

Hägele

Krake

Weiskopf

2022

IEEE Trans. Visual. Comput. Graphics

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“…Another related approach investigates stability of topic models within an ensemble via matrix factorization [10]. In terms of visualization of topic modeling ensembles, our work is most closely related to work on stability of dimensionality reduction methods [30] and the analysis of behavior of actors using an LDA ensemble [15]. Our goal is very different though.…”

Section: Related Workmentioning

confidence: 99%

Uncertainty-aware Topic Modeling Visualization

Muller¹,

Sieg²,

Linsen³

2021

Preprint

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Topic modeling is a state-of-the-art technique for analyzing text corpora. It uses a statistical model, most commonly Latent Dirichlet Allocation (LDA), to discover abstract topics that occur in the document collection. However, the LDA-based topic modeling procedure is based on a randomly selected initial configuration as well as a number of parameter values than need to be chosen. This induces uncertainties on the topic modeling results, and visualization methods should convey these uncertainties during the analysis process. We propose a visual uncertainty-aware topic modeling analysis. We capture the uncertainty by computing topic modeling ensembles and propose measures for estimating topic modeling uncertainty from the ensemble. Then, we propose to enhance state-of-the-art topic modeling visualization methods to convey the uncertainty in the topic modeling process. We visualize the entire ensemble of topic modeling results at different levels for topic and document analysis. We apply our visualization methods to a text corpus to document the impact of uncertainty on the analysis.

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“…That is, we don’t just want to know whether a cell is well-embedded one time, but whether it is consistently well-embedded. While there is a large body of work on ensemble visualization [72, 73], only recently [74] has there been an attempt to apply this theory to assess the variability of DR embeddings. Our approach differs in that it proposes a statistical framework in which to consider quality metric variability.…”

Section: Introductionmentioning

confidence: 99%

EMBEDR: Distinguishing Signal from Noise in Single-Cell Omics Data

Johnson

Kath

Mani

2020

Preprint

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Single-cell RNA sequencing (scRNA-seq) experiments often measure thousands of genes, making them high-dimensional data sets. As a result, dimensionality reduction (DR) algorithms such as t-SNE and UMAP are necessary for data visualization. However, the use of DR methods in other tasks, such as for cell-type detection or developmental trajectory reconstruction, is stymied by unquantified non-linear and stochastic deformations in the mapping from the high- to low-dimensional space. In this work, we present a statistical framework for the quantification of embedding quality so that DR algorithms can be used with confidence in unsupervised applications. Specifically, this framework generates a local assessment of embedding quality by statistically integrating information across embeddings. Furthermore, the approach separates biological signal from noise via the construction of an empirical null hypothesis. Using this approach on scRNA-seq data reveals biologically relevant structure and suggests a novel “spectral” decomposition of data. We apply the framework to several data sets and DR methods, illustrating its robustness and flexibility as well as its widespread utility in several quantitative applications.

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Visualizing the Stability of 2D Point Sets from Dimensionality Reduction Techniques

Cited by 5 publications

References 49 publications

Uncertainty-Aware Multidimensional Scaling

Uncertainty-Aware Multidimensional Scaling

Uncertainty-aware Topic Modeling Visualization

EMBEDR: Distinguishing Signal from Noise in Single-Cell Omics Data

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