🍩 Database of Original & Non-Theoretical Uses of Topology

(found 2 matches in 0.000882s)

  1. 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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  2. Persistent Homology for Breast Tumor Classification Using Mammogram Scans (2022)

    Aras Asaad, Dashti Ali, Taban Majeed, Rasber Rashid
    Abstract An Important tool in the field topological data analysis is known as persistent Homology (PH) which is used to encode abstract representation of the homology of data at different resolutions in the form of persistence diagram (PD). In this work we build more than one PD representation of a single image based on a landmark selection method, known as local binary patterns, that encode different types of local textures from images. We employed different PD vectorizations using persistence landscapes, persistence images, persistence binning (Betti Curve) and statistics. We tested the effectiveness of proposed landmark based PH on two publicly available breast abnormality detection datasets using mammogram scans. Sensitivity of landmark based PH obtained is over 90% in both datasets for the detection of abnormal breast scans. Finally, experimental results give new insights on using different types of PD vectorizations which help in utilising PH in conjunction with machine learning classifiers.