Quasiorthogonal dimension

Autoři: RNDr. Věra Kůrková, DSc.
Rok vydání: 2020
Typ publikace: Kapitola v monografii
Periodikum: Beyond Traditional Probabilistic Data Processing Techniques: Interval, Fuzzy, etc. Methods and Their Applications
Projekty: FoNeCo: Analytické základy neurovýpočtů
Bibliografická citace: KAINEN, P.C., KŮRKOVÁ, Věra. Quasiorthogonal dimension. In: KOSHELEVA, O., SHARY, S., XIANG, G., ZAPATRIN, R., eds. Beyond Traditional Probabilistic Data Processing Techniques: Interval, Fuzzy, etc. Methods and Their Applications. Cham: Springer, 2020, S. 615-629. Studies in Computational Intelligence, 835. ISBN 978-3-030-31040-0
Dostupné z: doi:10.1007/978-3-030-31041-7_35
DOI: 10.1007/978-3-030-31041-7_35
ID: 482536

Abstrakt

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.