Matching Evolving Hilbert Spaces and Language for Semantic Access to Digital Libraries

Extended by function (Hilbert) spaces, the 5S model of digital libraries (DL) [1] enables a physical interpretation of vectors and functions to keep track of the evolving semantics and usage context of the digital objects by support vector machines (SVM) for text categorization (TC). For this conceptual transition, three steps are necessary: (1) the application of the formal theory of DL to Lebesgue (function, L2) spaces; (2) considering semantic content as vectors in the physical sense (i.e. position and direction vectors) rather than as in linear algebra, thereby modelling word semantics as an evolving field underlying classifications of digital objects; (3) the replacement of vectors by functions in a new compact support basis function (CSBF) semantic kernel utilizing wavelets for TC by SVMs