Graph induced complex on point data

Dey, Tamal K.; Fan, Fengtao; Wang, Yusu

doi:10.1145/2462356.2462387

Cited by 33 publications

(39 citation statements)

References 24 publications

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“…The task for extracting the topological signatures from the vertices set, i.e., the data point cloud. There are different ways to build the complex to approximate the topological space, such as Vietoris-Rips complex [32,33], Graph-induced complex [34], and Sparsified Cěch complex [35]. In this work we adopt the Vietoris-Rips complex, which sometimes was called Rips complex for simplicity.…”

Section: The Rips Complex and Graph Filtrationmentioning

confidence: 99%

Gait Rhythm Dynamics for Neuro-Degenerative Disease Classification via Persistence Landscape- Based Topological Representation

Yan

Ivanov

Omisore

et al. 2020

Sensors

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Neuro-degenerative disease is a common progressive nervous system disorder that leads to serious clinical consequences. Gait rhythm dynamics analysis is essential for evaluating clinical states and improving quality of life for neuro-degenerative patients. The magnitude of stride-to-stride fluctuations and corresponding changes over time—gait dynamics—reflects the physiology of gait, in quantifying the pathologic alterations in the locomotor control system of health subjects and patients with neuro-degenerative diseases. Motivated by algebra topology theory, a topological data analysis-inspired nonlinear framework was adopted in the study of the gait dynamics. Meanwhile, the topological representation–persistence landscapes were used as input of classifiers in order to distinguish different neuro-degenerative disease type from healthy. In this work, stride-to-stride time series from healthy control (HC) subjects are compared with the gait dynamics from patients with amyotrophic lateral sclerosis (ALS), Huntington’s disease (HD), and Parkinson’s disease (PD). The obtained results show that the proposed methodology discriminates healthy subjects from subjects with other neuro-degenerative diseases with relatively high accuracy. In summary, our study is the first attempt to provide a topological representation-based method into the disease classification with gait rhythms measured from the stride intervals to visualize gait dynamics and classify neuro-degenerative diseases. The proposed method could be potentially used in earlier interventions and state monitoring.

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Section: The Rips Complex and Graph Filtrationmentioning

confidence: 99%

Gait Rhythm Dynamics for Neuro-Degenerative Disease Classification via Persistence Landscape- Based Topological Representation

Yan

Ivanov

Omisore

et al. 2020

Sensors

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“…However, the Cěch complex needs intensive computation. Several reduction complexes had been proposed, such as Vietoris − Rips complex [60,61], Graph − induced complex [62], and Sparsi f ied Cěch complex [63]. The Vietoris − Rips complex had already proved to be computational efficiently and used in data analysis; therefore we use the Vietoris − Rips complex to approximate the data point cloud topological space, and later for topological analysis.…”

Section: Topological Data Analysismentioning

confidence: 99%

Persistence Landscape based Topological Data Analysis for Personalized Arrhythmia Classification

Yan¹,

Ivanov²,

Cen³

et al. 2019

Preprint

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Data can be illustrated in shapes, and the shapes could provide insight for data modeling and information extraction. Topological data analysis provides an alternative insight in biomedical data analysis and knowledge discovery with the algebra topology tools. In present work, we study the application of topological data analysis for personalized electrocardiographic signal classification toward arrhythmia analysis. Using phase space reconstruction technique, the signal samples are converted into point clouds for topological analysis facility. With topological techniques the persistence landscapes from the point clouds are extracted as features to perform the arrhythmia classification task. We find that the proposed method is robust to the training set size, with only a training set size of 20% percents, the normal heartbeat class are 100% recognized, ventricular beats for 97.13%, supra-ventricular beats for 94.27% and fusion beats for 94.27% within the corresponding experiments. The property of keeping high performance when using smaller training sample proves that the proposed method is especially applicable to personalized analysis. With the present study, we show that the topological data analysis technique could be a useful tool in biomedical signal analysis, and provide powerful ability in personalized analysis.

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“…Graph Induced Complex GIC. T. Dey et al [DFW13] built GIC depending on a scale α and a user‐defined graph that spans a cloud C . If C is an ε‐sample of a good manifold, then GIC has the same homology H 1 as the Vietoris‐Rips complex on C at scales α ≥ 4ε.…”

Section: Comparison With Related Past Skeletonization Workmentioning

confidence: 99%

“…Graph Induced Complex GIC. T. Dey et al [DFW13] built GIC depending on a scale α and a user-defined graph that spans a cloud C. If C is an ε-sample of a good manifold, then GIC has the same homology H 1 as the Vietoris-Rips complex on C at scales α ≥ 4ε. Theorem 15 describes graphs G that can be geometrically and topologically approximated from any ε-sample C without extra input parameters.…”

Section: Comparison With Related Past Skeletonization Workmentioning

confidence: 99%

A one‐dimensional homologically persistent skeleton of an unstructured point cloud in any metric space

Kurlin

2015

Computer Graphics Forum

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Real data are often given as a noisy unstructured point cloud, which is hard to visualize. The important problem is to represent topological structures hidden in a cloud by using skeletons with cycles. All past skeletonization methods require extra parameters such as a scale or a noise bound. We define a homologically persistent skeleton, which depends only on a cloud of points and contains optimal subgraphs representing 1‐dimensional cycles in the cloud across all scales. The full skeleton is a universal structure encoding topological persistence of cycles directly on the cloud. Hence a 1‐dimensional shape of a cloud can be now easily predicted by visualizing our skeleton instead of guessing a scale for the original unstructured cloud. We derive more subgraphs to reconstruct provably close approximations to an unknown graph given only by a noisy sample in any metric space. For a cloud of n points in the plane, the full skeleton and all its important subgraphs can be computed in time O(n log n).

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Graph induced complex on point data

Cited by 33 publications

References 24 publications

Gait Rhythm Dynamics for Neuro-Degenerative Disease Classification via Persistence Landscape- Based Topological Representation

Gait Rhythm Dynamics for Neuro-Degenerative Disease Classification via Persistence Landscape- Based Topological Representation

Persistence Landscape based Topological Data Analysis for Personalized Arrhythmia Classification

A one‐dimensional homologically persistent skeleton of an unstructured point cloud in any metric space

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