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An efficient eigenspace updating scheme for high-dimensional systems
Simon Gangl, Domen Mongus, Borut Žalik, 2014, izvirni znanstveni članek

Opis: Systems based on principal component analysis have developed from exploratory data analysis in the past to current data processing applications which encode and decode vectors of data using a changing projection space (eigenspace). Linear systems, which need to be solved to obtain a constantly updated eigenspace, have increased significantly in their dimensions during this evolution. The basic scheme used for updating the eigenspace, however, has remained basically the same: (re)computing the eigenspace whenever the error exceeds a predefined threshold. In this paper we propose a computationally efficient eigenspace updating scheme, which specifically supports high-dimensional systems from any domain. The key principle is a prior selection of the vectors used to update the eigenspace in combination with an optimized eigenspace computation. The presented theoretical analysis proves the superior reconstruction capability of the introduced scheme, and further provides an estimate of the achievable compression ratios.
Ključne besede: eigenspace, projection space, data compression, principal component analysis
Objavljeno v DKUM: 10.07.2015; Ogledov: 1492; Prenosov: 92
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Some functional equations on standard operator algebras
Ajda Fošner, Joso Vukman, 2008, izvirni znanstveni članek

Opis: Naj bo ▫$H$▫ kompleksni Hilbertov prostor, ▫$mathcal{B}(H)$▫ algebra vseh omejenih linearnih operatorjev na ▫$H$▫ ter ▫$mathcal{A}(H)$▫ standardna operatorska algebra, zaprta za adjungiranje. Če je ▫$T: mathcal{A}(H) to mathcal{B}(H)$▫ linearna preslikava, ki zadošča identiteti ▫$T(AA^ast A) = T(A)A^ast A - AT(A^ast)A + AA^ast T(A)$▫ za vsak ▫$A$▫ iz ▫$mathcal{A}(H)$▫, potem je ▫$T(A) = AB + BA$▫ za vsak ▫$A$▫ iz A(H), kjer je ▫$B$▫ operator iz ▫$mathcal{B}(H)$▫.
Ključne besede: matematika, algebra, kolobar, prakolobar, polprakolobar, Banachov prostor, Hilbertov prostor, standardna operatorska algebra, odvajanje, jordansko odvajanje, bicirkularni projektor, mathematics, algebra, ring, ▫$^ast$▫-ring, prime ring, semiprime ring, Banach space, Hilbert space, standard operator algebra, derivation, Jordan derivation, bicircular projection
Objavljeno v DKUM: 10.07.2015; Ogledov: 1406; Prenosov: 98
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