Persistent Homology Guided Force-Directed Graph Layouts

Suh, Ashley; Hajij, Mustafa; Wang, Bei; Scheidegger, Carlos; Rosen, Paul

doi:10.1109/tvcg.2019.2934802

Cited by 24 publications

(16 citation statements)

References 75 publications

(102 reference statements)

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“…[SMC07] has seen widespread applications in data science, including cancer research [NLC11, MNL*19], sports analytics [Ala12], gene expression analysis [JCR*19], micro‐epidemiology [KGCFR*20], genomic profiling [CZJ*19], and neuroscience [GSPS19, SSGC*18], to name a few; see [PVP17] for an overview. In visualization, topological approaches such as persistent homology and mapper have recently been applied in graph visualization [HWR18, HWSR18, SHW*20].…”

Section: Related Workmentioning

confidence: 99%

TopoAct: Visually Exploring the Shape of Activations in Deep Learning

Rathore

Chalapathi

Palande

et al. 2021

Computer Graphics Forum

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Deep neural networks such as GoogLeNet, ResNet, and BERT have achieved impressive performance in tasks such as image and text classification. To understand how such performance is achieved, we probe a trained deep neural network by studying neuron activations, i.e.combinations of neuron firings, at various layers of the network in response to a particular input. With a large number of inputs, we aim to obtain a global view of what neurons detect by studying their activations. In particular, we develop visualizations that show the shape of the activation space, the organizational principle behind neuron activations, and the relationships of these activations within a layer. Applying tools from topological data analysis, we present TopoAct, a visual exploration system to study topological summaries of activation vectors. We present exploration scenarios using TopoAct that provide valuable insights into learned representations of neural networks. We expect TopoAct to give a topological perspective that enriches the current toolbox of neural network analysis, and to provide a basis for network architecture diagnosis and data anomaly detection.

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Section: Related Workmentioning

confidence: 99%

TopoAct: Visually Exploring the Shape of Activations in Deep Learning

Rathore

Chalapathi

Palande

et al. 2021

Computer Graphics Forum

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“…For graph simplification, a number of works focused on algorithmic developments [38], [39], [40] and visualization [41], [42], [43], [44], [45]. In particular, Suh et al [46] proposed a topology-based graph simplification tool, which enables contraction of edges whose weight is below a user-specified threshold. There are only a few research works on hypergraph simplification.…”

Section: Related Workmentioning

confidence: 99%

“…Suh et al [46] used the barcode to control the contraction and repulsion of edges in the force-directed layout of a graph. Instead, in this paper, we use the barcode to guide the merging of vertices into super-vertices as part of the simplification pipeline.…”

Section: Topological Simplifications Of Graphsmentioning

confidence: 99%

Topological Simplifications of Hypergraphs

Zhou¹,

Rathore²,

Purvine³

et al. 2021

Preprint

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We study hypergraph visualization via its topological simplification. We explore both vertex simplification and hyperedge simplification of hypergraphs using tools from topological data analysis. In particular, we transform a hypergraph to its graph representations known as the line graph and clique expansion. A topological simplification of such a graph representation induces a simplification of the hypergraph. In simplifying a hypergraph, we allow vertices to be combined if they belong to almost the same set of hyperedges, and hyperedges to be merged if they share almost the same set of vertices. Our proposed approaches are general, mathematically justifiable, and they put vertex simplification and hyperedge simplification in a unifying framework.

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“…TDA has received significant attention in the visualization community, e.g., [73]. We utilize a foundational tool of TDA, persistent homology, which has been studied in graph analysis [34,35,67,71], high-dimensional data analysis [78], and multivariate analysis [68]. We utilize persistent homology to capture the topology of the landmarks of each facial pose into a structure known as a persistence diagram.…”

Section: Overview Of the Pipelinementioning

confidence: 99%

AffectiveTDA: Using Topological Data Analysis to Improve Analysis and Explainability in Affective Computing

Elhamdadi¹,

Canavan²,

Rosen³

2021

Preprint

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Fig. 1. Our affective computing visualization provides numerous options for comparing and contrasting the data. For example, the small multiples view (left) is comparing a male (left) subject to a female (right) subject considering different subsets of facial landmarks (columns), across emotions (rows) of anger , disgust, fear , happiness, sadness, and surprise. Each point represents one facial pose. The embedding graph (top right) compares all facial poses across all emotions, in this case showing the female full face using MDS on non-metric topology. The 3D landmarks (lower right) show a single facial pose per emotion. Settings are selected on the bottom.

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Persistent Homology Guided Force-Directed Graph Layouts

Cited by 24 publications

References 75 publications

TopoAct: Visually Exploring the Shape of Activations in Deep Learning

TopoAct: Visually Exploring the Shape of Activations in Deep Learning

Topological Simplifications of Hypergraphs

AffectiveTDA: Using Topological Data Analysis to Improve Analysis and Explainability in Affective Computing

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