An Interdisciplinary Journal

2002, Vol.5, No.2, pp.108-128

Frames in Hilbert Spaces: A Tool for Artificial Intelligence. pp.108-128
A.D. Linkevich

A mathematical framework is presented for development of systems of AI intended to be endowed with ability to understand the meaning of information. The crux of the approach is representation of information by vectors of some Hilbert space treated as a semantic space and construction of frames whose vectors are associated with semantic units corresponding to particular relevant meanings. Two definitions and main properties of frames in a vector space are outlined. It is shown that frames can be used to solve such tasks of information processing as least squares approximation of experimental data, forecasting time series and probability density estimation. Frames are also applied to tackle some problems of AI pertaining to semantic retrieval and classification of (hyper) texts, medical diagnostics, control of operation of the Internet and manufacturing enterprises, etc.
Key words: artificial intelligence, information processing, frame, vector space, Hilbert space, functional analysis, data processing, approximation, forecasting, probability estimation, meaning of information, semantic retrieval, text classification, Internet search, medical diagnostics, neural field, learning, mathematical modelling, distributed complex system, Internet traffic, manufacturing enterprise, intelligent agent.

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