🍩 Database of Original & Non-Theoretical Uses of Topology

(found 6 matches in 0.002002s)

  1. Advancing Precision Medicine: Algebraic Topology and Differential Geometry in Radiology and Computational Pathology (2024)

    Richard M. Levenson, Yashbir Singh, Bastian Rieck, Ashok Choudhary, Gunnar Carlsson, Deepa Sarkar, Quincy A. Hathaway, Colleen Farrelly, Jennifer Rozenblit, Prateek Prasanna, Bradley Erickson
    Abstract Precision medicine aims to provide personalized care based on individual patient characteristics, rather than guideline-directed therapies for groups of diseases or patient demographics. Images—both radiology- and pathology-derived—are a major source of information on presence, type, and status of disease. Exploring the mathematical relationship of pixels in medical imaging (“radiomics”) and cellular-scale structures in digital pathology slides (“pathomics”) offers powerful tools for extracting both qualitative and, increasingly, quantitative data. These analytical approaches, however, may be significantly enhanced by applying additional methods arising from fields of mathematics such as differential geometry and algebraic topology that remain underexplored in this context. Geometry’s strength lies in its ability to provide precise local measurements, such as curvature, that can be crucial for identifying abnormalities at multiple spatial levels. These measurements can augment the quantitative features extracted in conventional radiomics, leading to more nuanced diagnostics. By contrast, topology serves as a robust shape descriptor, capturing essential features such as connected components and holes. The field of topological data analysis was initially founded to explore the shape of data, with functional network connectivity in the brain being a prominent example. Increasingly, its tools are now being used to explore organizational patterns of physical structures in medical images and digitized pathology slides. By leveraging tools from both differential geometry and algebraic topology, researchers and clinicians may be able to obtain a more comprehensive, multi-layered understanding of medical images and contribute to precision medicine’s armamentarium

  2. Classification of Histopathology Slides With Persistence Homology Convolutions (2025)

    Shrunal Pothagoni, Benjamin Schweinhart
    Abstract Convolutional neural networks (CNNs) are a standard tool for computer vision tasks such as image classification. However, typical model architectures may result in the loss of topological information. In specific domains such as histopathology, topology is an important descriptor that can be used to distinguish between disease-indicating tissue by analyzing the shape characteristics of cells. Current literature suggests that reintroducing topological information using persistent homology can improve medical diagnostics; however, previous methods utilize global topological summaries which do not contain information about the locality of topological features. To address this gap, we present a novel method that generates local persistent homology-based data using a modified version of the convolution operator called Persistent Homology Convolutions. This method captures information about the locality and translation invariance of topological features. We perform a comparative study using various representations of histopathology slides and find that models trained with persistent homology convolutions outperform conventionally trained models and are less sensitive to hyperparameters. These results indicate that persistent homology convolutions extract meaningful geometric information from the histopathology slides.

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  3. A Novel Multi-Task Machine Learning Classifier for Rare Disease Patterning Using Cardiac Strain Imaging Data (2024)

    Nanda K. Siva, Yashbir Singh, Quincy A. Hathaway, Partho P. Sengupta, Naveena Yanamala
    Abstract To provide accurate predictions, current machine learning-based solutions require large, manually labeled training datasets. We implement persistent homology (PH), a topological tool for studying the pattern of data, to analyze echocardiography-based strain data and differentiate between rare diseases like constrictive pericarditis (CP) and restrictive cardiomyopathy (RCM). Patient population (retrospectively registered) included those presenting with heart failure due to CP (n = 51), RCM (n = 47), and patients without heart failure symptoms (n = 53). Longitudinal, radial, and circumferential strains/strain rates for left ventricular segments were processed into topological feature vectors using Machine learning PH workflow. In differentiating CP and RCM, the PH workflow model had a ROC AUC of 0.94 (Sensitivity = 92%, Specificity = 81%), compared with the GLS model AUC of 0.69 (Sensitivity = 65%, Specificity = 66%). In differentiating between all three conditions, the PH workflow model had an AUC of 0.83 (Sensitivity = 68%, Specificity = 84%), compared with the GLS model AUC of 0.68 (Sensitivity = 52% and Specificity = 76%). By employing persistent homology to differentiate the “pattern” of cardiac deformations, our machine-learning approach provides reasonable accuracy when evaluating small datasets and aids in understanding and visualizing patterns of cardiac imaging data in clinically challenging disease states.

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  4. Transfer Learning for Autonomous Chatter Detection in Machining (2022)

    Melih C. Yesilli, Firas A. Khasawneh, Brian P. Mann
    Abstract Large-amplitude chatter vibrations are one of the most important phenomena in machining processes. It is often detrimental in cutting operations causing a poor surface finish and decreased tool life. Therefore, chatter detection using machine learning has been an active research area over the last decade. Three challenges can be identified in applying machine learning for chatter detection at large in industry: an insufficient understanding of the universality of chatter features across different processes, the need for automating feature extraction, and the existence of limited data for each specific workpiece-machine tool combination, e.g., when machining one-off products. These three challenges can be grouped under the umbrella of transfer learning, which is concerned with studying how knowledge gained from one setting can be leveraged to obtain information in new settings. This paper studies automating chatter detection by evaluating transfer learning of prominent as well as novel chatter detection methods. We investigate chatter classification accuracy using a variety of features extracted from turning and milling experiments with different cutting configurations. The studied methods include Fast Fourier Transform (FFT), Power Spectral Density (PSD), the Auto-correlation Function (ACF), and decomposition based tools such as Wavelet Packet Transform (WPT) and Ensemble Empirical Mode Decomposition (EEMD). We also examine more recent approaches based on Topological Data Analysis (TDA) and similarity measures of time series based on Discrete Time Warping (DTW). We evaluate transfer learning potential of each approach by training and testing both within and across the turning and milling data sets. Four supervised classification algorithms are explored: support vector machine (SVM), logistic regression, random forest classification, and gradient boosting. In addition to accuracy, we also comment on the automation potential of feature extraction for each approach which is integral to creating autonomous manufacturing centers. Our results show that carefully chosen time-frequency features can lead to high classification accuracies albeit at the cost of requiring manual pre-processing and the tagging of an expert user. On the other hand, we found that the TDA and DTW approaches can provide accuracies and F1-scores on par with the time-frequency methods without the need for manual preprocessing via completely automatic pipelines. Further, we discovered that the DTW approach outperforms all other methods when trained using the milling data and tested on the turning data. Therefore, TDA and DTW approaches may be preferred over the time-frequency-based approaches for fully automated chatter detection schemes. DTW and TDA also can be more advantageous when pooling data from either limited workpiece-machine tool combinations, or from small data sets of one-off processes.

  5. The Shape of Word Embeddings: Quantifying Non-Isometry With Topological Data Analysis (2024)

    Ondřej Draganov, Steven Skiena
    Abstract Word embeddings represent language vocabularies as clouds of d-dimensional points. We investigate how information is conveyed by the general shape of these clouds, instead of representing the semantic meaning of each token. Specifically, we use the notion of persistent homology from topological data analysis (TDA) to measure the distances between language pairs from the shape of their unlabeled embeddings. These distances quantify the degree of non-isometry of the embeddings. To distinguish whether these differences are random training errors or capture real information about the languages, we use the computed distance matrices to construct language phylogenetic trees over 81 Indo-European languages. Careful evaluation shows that our reconstructed trees exhibit strong and statistically-significant similarities to the reference.

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  6. Optimizing Porosity Detection in Wire Laser Metal Deposition Processes Through Data-Driven AI Classification Techniques (2023)

    Meritxell Gomez-Omella, Jon Flores, Basilio Sierra, Susana Ferreiro, Nicolas Hascoët, Francisco Chinesta
    Abstract Additive manufacturing (AM) is an attractive solution for many companies that produce geometrically complex parts. This process consists of depositing material layer by layer following a sliced CAD geometry. It brings several benefits to manufacturing capabilities, such as design freedom, reduced material waste, and short-run customization. However, one of the current challenges faced by users of the process, mainly in wire laser metal deposition (wLMD), is to avoid defects in the manufactured part, especially the porosity. This defect is caused by extreme conditions and metallurgical transformations of the process. And not only does it directly affect the mechanical performance of the parts, especially the fatigue properties, but it also means an increase in costs due to the inspection tasks to which the manufactured parts must be subjected. This work compares three operational solution approaches, product-centric, based on signal-based feature extraction and Topological Data Analysis together with statistical and Machine Learning (ML) techniques, for the early detection and prediction of porosity failure in a wLMD process. The different forecasting and validation strategies demonstrate the variety of conclusions that can be drawn with different objectives in the analysis of the monitored data in AM problems.