🍩 Database of Original & Non-Theoretical Uses of Topology

(found 3 matches in 0.001458s)

  1. Alzheimer Disease Detection From Raman Spectroscopy of the Cerebrospinal Fluid via Topological Machine Learning (2023)

    Francesco Conti, Martina Banchelli, Valentina Bessi, Cristina Cecchi, Fabrizio Chiti, Sara Colantonio, Cristiano D’Andrea, Marella de Angelis, Davide Moroni, Benedetta Nacmias, Maria Antonietta Pascali, Sandro Sorbi, Paolo Matteini
    Abstract The cerebrospinal fluid (CSF) of 19 subjects who received a clinical diagnosis of Alzheimer’s disease (AD) as well as of 5 pathological controls was collected and analyzed by Raman spectroscopy (RS). We investigated whether the raw and preprocessed Raman spectra could be used to distinguish AD from controls. First, we applied standard Machine Learning (ML) methods obtaining unsatisfactory results. Then, we applied ML to a set of topological descriptors extracted from raw spectra, achieving a very good classification accuracy (\textgreater87%). Although our results are preliminary, they indicate that RS and topological analysis may provide an effective combination to confirm or disprove a clinical diagnosis of AD. The next steps include enlarging the dataset of CSF samples to validate the proposed method better and, possibly, to investigate whether topological data analysis could support the characterization of AD subtypes.

  2. A Topological Machine Learning Pipeline for Classification (2022)

    Francesco Conti, Davide Moroni, Maria Antonietta Pascali
    Abstract In this work, we develop a pipeline that associates Persistence Diagrams to digital data via the most appropriate filtration for the type of data considered. Using a grid search approach, this pipeline determines optimal representation methods and parameters. The development of such a topological pipeline for Machine Learning involves two crucial steps that strongly affect its performance: firstly, digital data must be represented as an algebraic object with a proper associated filtration in order to compute its topological summary, the Persistence Diagram. Secondly, the persistence diagram must be transformed with suitable representation methods in order to be introduced in a Machine Learning algorithm. We assess the performance of our pipeline, and in parallel, we compare the different representation methods on popular benchmark datasets. This work is a first step toward both an easy and ready-to-use pipeline for data classification using persistent homology and Machine Learning, and to understand the theoretical reasons why, given a dataset and a task to be performed, a pair (filtration, topological representation) is better than another.

  3. Raman Spectroscopy and Topological Machine Learning for Cancer Grading (2023)

    Francesco Conti, Mario D’Acunto, Claudia Caudai, Sara Colantonio, Raffaele Gaeta, Davide Moroni, Maria Antonietta Pascali
    Abstract In the last decade, Raman Spectroscopy is establishing itself as a highly promising technique for the classification of tumour tissues as it allows to obtain the biochemical maps of the tissues under investigation, making it possible to observe changes among different tissues in terms of biochemical constituents (proteins, lipid structures, DNA, vitamins, and so on). In this paper, we aim to show that techniques emerging from the cross-fertilization of persistent homology and machine learning can support the classification of Raman spectra extracted from cancerous tissues for tumour grading. In more detail, topological features of Raman spectra and machine learning classifiers are trained in combination as an automatic classification pipeline in order to select the best-performing pair. The case study is the grading of chondrosarcoma in four classes: cross and leave-one-patient-out validations have been used to assess the classification accuracy of the method. The binary classification achieves a validation accuracy of 81% and a test accuracy of 90%. Moreover, the test dataset has been collected at a different time and with different equipment. Such results are achieved by a support vector classifier trained with the Betti Curve representation of the topological features extracted from the Raman spectra, and are excellent compared with the existing literature. The added value of such results is that the model for the prediction of the chondrosarcoma grading could easily be implemented in clinical practice, possibly integrated into the acquisition system.