Topological Data Analysis

Boissonnat, Jean‐Daniel; Chazal, Frédéric; Michel, Bertrand

doi:10.1007/978-3-030-96173-2_9

Cited by 2 publications

(2 citation statements)

References 57 publications

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“…In topological data analysis, the idea of homology is often employed to classify point-cloud data. In this paper, we shall use Vietories-Rips simplicial complexes [11,12,4]. Let Y be a given point-set data equipped with a metric structure so that the distance between any two points in Y is assigned.…”

Section: Persistent Homology and Vector Representationmentioning

confidence: 99%

A novel approach for wafer defect pattern classification based on topological data analysis

Ko¹,

Koo²

2022

Preprint

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In semiconductor manufacturing, wafer map defect pattern provides critical information for facility maintenance and yield management, so the classification of defect patterns is one of the most important tasks in the manufacturing process. In this paper, we propose a novel way to represent the shape of the defect pattern as a finite-dimensional vector, which will be used as an input for a neural network algorithm for classification. The main idea is to extract the topological features of each pattern by using the theory of persistent homology from topological data analysis (TDA). Through some experiments with a simulated dataset, we show that the proposed method is faster and much more efficient in training with higher accuracy, compared with the method using convolutional neural networks (CNN) which is the most common approach for wafer map defect pattern classification. Moreover, our method outperforms the CNN-based method when the number of training data is not enough and is imbalanced.

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Section: Persistent Homology and Vector Representationmentioning

confidence: 99%

A novel approach for wafer defect pattern classification based on topological data analysis

Ko¹,

Koo²

2022

Preprint

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“…Here, we demonstrate a novel image segmentation approach using persistence homology as part of a workflow to identify and segment microglia as a complex cell type. In brief, persistence homology is a tool in topological data analysis, a field in mathematics that seeks to represent discrete elements in a dataset as a geometric space and to understand the relationships between those elements [ 14 , 15 ]. Persistence homology identifies the most salient features of a data set by using filtration , a technique where a threshold varies from a maximum to a minimum value.…”

Section: Introductionmentioning

confidence: 99%

PrestoCell: A persistence-based clustering approach for rapid and robust segmentation of cellular morphology in three-dimensional data

Wu,

Brust-Mascher,

Gareau

et al. 2024

PLoS ONE

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Light microscopy methods have continued to advance allowing for unprecedented analysis of various cell types in tissues including the brain. Although the functional state of some cell types such as microglia can be determined by morphometric analysis, techniques to perform robust, quick, and accurate measurements have not kept pace with the amount of imaging data that can now be generated. Most of these image segmentation tools are further burdened by an inability to assess structures in three-dimensions. Despite the rise of machine learning techniques, the nature of some biological structures prevents the training of several current day implementations. Here we present PrestoCell, a novel use of persistence-based clustering to segment cells in light microscopy images, as a customized Python-based tool that leverages the free multidimensional image viewer Napari. In evaluating and comparing PrestoCell to several existing tools, including 3DMorph, Omipose, and Imaris, we demonstrate that PrestoCell produces image segmentations that rival these solutions. In particular, our use of cell nuclei information resulted in the ability to correctly segment individual cells that were interacting with one another to increase accuracy. These benefits are in addition to the simplified graphically based user refinement of cell masks that does not require expensive commercial software licenses. We further demonstrate that PrestoCell can complete image segmentation in large samples from light sheet microscopy, allowing quantitative analysis of these large datasets. As an open-source program that leverages freely available visualization software, with minimum computer requirements, we believe that PrestoCell can significantly increase the ability of users without data or computer science expertise to perform complex image analysis.

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Topological Data Analysis

Cited by 2 publications

References 57 publications

A novel approach for wafer defect pattern classification based on topological data analysis

A novel approach for wafer defect pattern classification based on topological data analysis

PrestoCell: A persistence-based clustering approach for rapid and robust segmentation of cellular morphology in three-dimensional data

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