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Интеллектуальная Система Тематического Исследования НАукометрических данных |
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The manifold hypothesis - an assumption that data samples obtained from real life are not situated arbitrarily in the high-dimensional space but rather live on a lower-dimensional manifold - is a powerful tool to facilitate the study of the data. In particular, it allows one to use methods of diferential geometry in the analysis. In the present talk we shall describe the main concepts of this approach and present several examples of the advantages the manifold hypothesis presents.