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Topological data analysis is an emerging mathematical concept for characterizing shapes in multi-scale data. In this field, persistence diagrams are widely used as a descriptor of the input data, and can distinguish robust and noisy…

Machine Learning · Statistics 2017-06-13 Genki Kusano , Kenji Fukumizu , Yasuaki Hiraoka

Topological data analysis (TDA) provides insight into data shape. The summaries obtained by these methods are principled global descriptions of multi-dimensional data whilst exhibiting stable properties such as robustness to deformation and…

Machine Learning · Computer Science 2024-03-18 Ali Zia , Abdelwahed Khamis , James Nichols , Zeeshan Hayder , Vivien Rolland , Lars Petersson

Convolutional Neural Network (CNN) struggle to capture the multi-dimensional structural information of complex high-dimensional data, which limits their feature learning capability. This paper proposes a feature fusion method based on…

Computer Vision and Pattern Recognition · Computer Science 2024-07-16 Yang Han , Qin Guangjun , Liu Ziyuan , Hu Yongqing , Liu Guangnan , Dai Qinglong

Topological data analysis (TDA) is an emerging mathematical concept for characterizing shapes in complex data. In TDA, persistence diagrams are widely recognized as a useful descriptor of data, and can distinguish robust and noisy…

Algebraic Topology · Mathematics 2016-04-27 Genki Kusano , Kenji Fukumizu , Yasuaki Hiraoka

Topological Data Analysis (TDA) is a novel statistical technique, particularly powerful for the analysis of large and high dimensional data sets. Much of TDA is based on the tool of persistent homology, represented visually via persistence…

Applications · Statistics 2017-11-07 Sarit Agami , Robert J. Adler

Surface roughness plays an important role in analyzing engineering surfaces. It quantifies the surface topography and can be used to determine whether the resulting surface finish is acceptable or not. Nevertheless, while several existing…

Signal Processing · Electrical Eng. & Systems 2021-10-20 Melih C. Yesilli , Firas A. Khasawneh

Fault diagnosis of rotating machinery is an important engineering problem. In recent years, fault diagnosis methods based on the Convolutional Neural Network (CNN) and Recurrent Neural Network (RNN) have been mature, but Transformer has not…

Computational Engineering, Finance, and Science · Computer Science 2021-08-31 Yuhong Jin , Lei Hou , Yushu Chen

Semiconductor manufacturing generates vast amounts of image data, crucial for defect identification and yield optimization, yet often exceeds manual inspection capabilities. Traditional clustering techniques struggle with high-dimensional,…

Computer Vision and Pattern Recognition · Computer Science 2025-05-08 Janhavi Giri , Attila Lengyel , Don Kent , Edward Kibardin

Data quality is crucial for the successful training, generalization and performance of machine learning models. We propose to measure the quality of a subset concerning the dataset it represents, using topological data analysis techniques.…

Algebraic Topology · Mathematics 2024-10-01 Álvaro Torras-Casas , Eduardo Paluzo-Hidalgo , Rocio Gonzalez-Diaz

Machine learning models for repeated measurements are limited. Using topological data analysis (TDA), we present a classifier for repeated measurements which samples from the data space and builds a network graph based on the data topology.…

Machine Learning · Computer Science 2019-04-08 Henri Riihimäki , Wojciech Chachólski , Jakob Theorell , Jan Hillert , Ryan Ramanujam

The growing availability of sensors within semiconductor manufacturing processes makes it feasible to detect defective wafers with data-driven models. Without directly measuring the quality of semiconductor devices, they capture the…

Machine Learning · Computer Science 2025-01-08 Yifeng Zhang , Bryan Baker , Shi Chen , Chao Zhang , Yu Huang , Qi Zhao , Sthitie Bom

Topological Data Analysis (TDA) is a recent and growing branch of statistics devoted to the study of the shape of the data. In this work we investigate the predictive power of TDA in the context of supervised learning. Since topological…

Machine Learning · Statistics 2017-09-22 Tullia Padellini , Pierpaolo Brutti

Classification of large and dense networks based on topology is very difficult due to the computational challenges of extracting meaningful topological features from real-world networks. In this paper we present a computationally tractable…

Machine Learning · Computer Science 2022-02-04 Tananun Songdechakraiwut , Bryan M. Krause , Matthew I. Banks , Kirill V. Nourski , Barry D. Van Veen

In this paper we develop a novel Topological Data Analysis (TDA) approach for studying graph representations of time series of dynamical systems. Specifically, we show how persistent homology, a tool from TDA, can be used to yield a…

Chaotic Dynamics · Physics 2020-01-28 Audun Myers , Elizabeth Munch , Firas A. Khasawneh

Machine-vision-based defect classification techniques have been widely adopted for automatic quality inspection in manufacturing processes. This article describes a general framework for classifying defects from high volume data batches…

Computer Vision and Pattern Recognition · Computer Science 2023-07-04 Wenbo Sun , Raed Al Kontar , Judy Jin , Tzyy-Shuh Chang

Deep learning-based semiconductor defect inspection has gained traction in recent years, offering a powerful and versatile approach that provides high accuracy, adaptability, and efficiency in detecting and classifying nano-scale defects.…

Computer Vision and Pattern Recognition · Computer Science 2024-07-18 Amit Prasad , Bappaditya Dey , Victor Blanco , Sandip Halder

Continual shrinking of pattern dimensions in the semiconductor domain is making it increasingly difficult to inspect defects due to factors such as the presence of stochastic noise and the dynamic behavior of defect patterns and types.…

Computer Vision and Pattern Recognition · Computer Science 2023-08-16 Vic De Ridder , Bappaditya Dey , Enrique Dehaerne , Sandip Halder , Stefan De Gendt , Bartel Van Waeyenberge

Controlling defects in semiconductor processes is important for maintaining yield, improving production cost, and preventing time-dependent critical component failures. Electron beam-based imaging has been used as a tool to survey wafers in…

Computer Vision and Pattern Recognition · Computer Science 2025-06-05 Chien-Fu , Huang , Katherine Sieg , Leonid Karlinksy , Nash Flores , Rebekah Sheraw , Xin Zhang

Topological Data Analysis (TDA) is the collection of mathematical tools that capture the structure of shapes in data. Despite computational topology and computational geometry, the utilization of TDA in time series and signal processing is…

Information Retrieval · Computer Science 2018-10-23 Shafie Gholizadeh , Wlodek Zadrozny

Topological data analysis (TDA) is a relatively new field that is gaining rapid adoption due to its robustness and ability to effectively describe complex datasets by quantifying geometric information. In imaging contexts, TDA typically…

Computer Vision and Pattern Recognition · Computer Science 2025-07-15 Aaryam Sharma