Topological Data Analysis of Biological Aggregation Models

Topaz, Chad M.; Ziegelmeier, Lori; Halverson, Tom

doi:10.1371/journal.pone.0126383

Cited by 160 publications

(157 citation statements)

References 46 publications

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“…In the case of collective behavior, this translates to measuring topological summaries (e.g., connected components and loops) of the resulting patterns from the cellular level to the global level. In [28], TDA was applied to study the velocity and positions of agents in simulations of a flocking model. By tracking global persistent homology features over time, Topaz et al [28] were able to identify agent clusters and detect the presence of global dynamics that would be challenging to notice visually.…”

Section: Introductionmentioning

confidence: 99%

Topological data analysis of zebrafish patterns

McGuirl

Volkening

Sandstede

2020

Proc. Natl. Acad. Sci. U.S.A.

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Self-organized pattern behavior is ubiquitous throughout nature, from fish schooling to collective cell dynamics during organism development. Qualitatively these patterns display impressive consistency, yet variability inevitably exists within pattern-forming systems on both microscopic and macroscopic scales. Quantifying variability and measuring pattern features can inform the underlying agent interactions and allow for predictive analyses. Nevertheless, current methods for analyzing patterns that arise from collective behavior only capture macroscopic features, or rely on either manual inspection or smoothing algorithms that lose the underlying agent-based nature of the data. Here we introduce methods based on topological data analysis and interpretable machine learning for quantifying both agentlevel features and global pattern attributes on a large scale. Because the zebrafish is a model organism for skin pattern formation, we focus specifically on analyzing its skin patterns as a means of illustrating our approach. Using a recent agent-based model, we simulate thousands of wild-type and mutant zebrafish patterns and apply our methodology to better understand pattern variability in zebrafish. Our methodology is able to quantify the differential impact of stochasticity in cell interactions on wild-type and mutant patterns, and we use our methods to predict stripe and spot statistics as a function of varying cellular communication. Our work provides a new approach to automatically quantifying biological patterns and analyzing agent-based dynamics so that we can now answer critical questions in pattern formation at a much larger scale.Keywords topological data analysis | agent-based model | self-organization | pattern quantification | zebrafish arXiv:1910.08433v1 [q-bio.QM]

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Section: Introductionmentioning

confidence: 99%

Topological data analysis of zebrafish patterns

McGuirl

Volkening

Sandstede

2020

Proc. Natl. Acad. Sci. U.S.A.

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“…We find similarities between the MCLEAN approach and topological data analysis (TDA). Analyzing the multidimensional spaces from a topological structure perspective, interpreting the persistent homology by calculating the number of connected components (b 0 from betti numbers) and using the persistence concept to define the optimal threshold of network representation prove that although the aims are distinct they share a same philosophy of analysis (Topaz, Ziegelmeier & Halverson, 2015). The MCLEAN method consists of four parts as illustrated in Fig.…”

Section: Methodsmentioning

confidence: 99%

“…These are subsequently combined in the tree representation called barcode-tree, which is inspired by both a clustering dendrogram and barcode representation (Topaz, Ziegelmeier & Halverson, 2015) as used in topological data analysis.…”

Section: Barcode-treementioning

confidence: 99%

MCLEAN: Multilevel Clustering Exploration As Network

Alcaide

Aerts

2018

PeerJ Computer Science

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Finding useful patterns in datasets has attracted considerable interest in the field of visual analytics. One of the most common tasks is the identification and representation of clusters. However, this is non-trivial in heterogeneous datasets since the data needs to be analyzed from different perspectives. Indeed, highly variable patterns may mask underlying trends in the dataset. Dendrograms are graphical representations resulting from agglomerative hierarchical clustering and provide a framework for viewing the clustering at different levels of detail. However, dendrograms become cluttered when the dataset gets large, and the single cut of the dendrogram to demarcate different clusters can be insufficient in heterogeneous datasets. In this work, we propose a visual analytics methodology called MCLEAN that offers a general approach for guiding the user through the exploration and detection of clusters. Powered by a graphbased transformation of the relational data, it supports a scalable environment for representation of heterogeneous datasets by changing the spatialization. We thereby combine multilevel representations of the clustered dataset with community finding algorithms. Our approach entails displaying the results of the heuristics to users, providing a setting from which to start the exploration and data analysis. To evaluate our proposed approach, we conduct a qualitative user study, where participants are asked to explore a heterogeneous dataset, comparing the results obtained by MCLEAN with the dendrogram. These qualitative results reveal that MCLEAN is an effective way of aiding users in the detection of clusters in heterogeneous datasets. The proposed methodology is implemented in an R package available at https://bitbucket.org/vda-lab/mclean.

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“…Suppose we have a finite set of data points from a sampling of the underlying topological space. We measure data homology by creating connections between nearby data points, varying the scale over which these connections are made (= filtration parameter), and looking for features that persist across scales [26,27]. This can be achieved by building the Vietoris-Rips complex from all pairwise distances between points in the dataset.…”

Section: Persistence Homologymentioning

confidence: 99%

Fingerprints of cancer by persistent homology

Carpio

Bonilla

Mathews

et al. 2019

Preprint

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We have carried out a topological data analysis of gene expressions for different databases based on the Fermat distance between the z scores of different tissue samples. There is a critical value of the filtration parameter at which all clusters collapse in a single one. This critical value for healthy samples is gapless and smaller than that for cancerous ones. After collapse in a single cluster, topological holes persist for larger filtration parameter values in cancerous samples. Barcodes, persistence diagrams and Betti numbers as functions of the filtration parameter are different for different types of cancer and constitute fingerprints thereof.

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Topological Data Analysis of Biological Aggregation Models

Cited by 160 publications

References 46 publications

Topological data analysis of zebrafish patterns

Topological data analysis of zebrafish patterns

MCLEAN: Multilevel Clustering Exploration As Network

Fingerprints of cancer by persistent homology

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