Search results for “topoi”

Where simplicial homology shows up in real life — topological data analysis. The union of balls around a point cloud, persistence modules and their decomposition into a sum of interval modules over a field (the structure theorem and the algorithm), the barcode; the Vietoris–Rips and Čech complexes; the stability theorem for barcodes, the Hausdorff, Gromov–Hausdorff and Wasserstein distances; open covers and their nerves, Leray covers and the nerve theorem, the category of covers, paracompactness, Lebesgue covering dimension, Čech homology and cohomology.

Singular homology — standard simplices and the inclusions of facets, singular simplices and chains, the differential; zeroth homology and path components, the homology of a point, reduced homology; chain maps and maps of homology, functoriality, the chain map induced by a continuous map; chain homotopies and the prism; the homotopy invariance theorem with a full proof via the prism operator; subcomplexes, quotient complexes and the homology of a pair.

Тематическое моделирование. Лекция курса «Машинное обучение» К. В. Воронцова. Задача тематического моделирования коллекции текстовых документов. Метод максимума правдоподобия.

Поиск ассоциативных правил. Лекция курса «Машинное обучение» К. В. Воронцова. Понятие ассоциативного правила и его связь с понятием логической закономерности.