Beyond Traditional Probabilistic Data Processing Techniques: Interval, Fuzzy, etc. Methods and Their Applications

0482536 - ÚI 2021 RIV CH eng M - Část monografie knihy
Kainen, P.C. - Kůrková, Věra
Quasiorthogonal dimension.
Beyond Traditional Probabilistic Data Processing Techniques: Interval, Fuzzy, etc. Methods and Their Applications. Cham: Springer, 2020 - (Kosheleva, O.; Shary, S.; Xiang, G.; Zapatrin, R.), s. 615-629. Studies in Computational Intelligence, 835. ISBN 978-3-030-31040-0
Grant CEP: GA ČR(CZ) GA19-05704S
Institucionální podpora: RVO:67985807
Klíčová slova: high-dimensional geometry * interval approach to dimension * quasiorthogonal dimension
Obor OECD: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

An interval approach to the concept of dimension is presented. The concept of quasiorthogonal dimension is obtained by relaxing exact orthogonality so that angular distances between unit vectors are constrained to a fixed closed symmetric interval about pi/2. An exponential number of such quasiorthogonal vectors exist as the Euclidean dimension increases. Lower bounds on quasiorthogonal dimension are proven using geometry of high-dimensional spaces and a separate argument is given utilizing graph theory. Related notions are reviewed.
Trvalý link: http://hdl.handle.net/11104/0277964