A transformation-based framework for
nonlinear combination operators
Sergio A. Alvarez
Department of Computer Science
Worcester Polytechnic Institute
Worcester, MA 01609
In many different contexts, including knowledge aggregation in knowledge-based
systems, relevance ranking in information retrieval, and lateralization
measurement in neurobiology, the need arises to combine several quantitative
measures of a given phenomenon into a single measure that uses the
information encoded in each of them.
This may be achieved by constructing an appropriate combination operator.
Various ad-hoc approaches are currently in use for this purpose in
different domains. This paper introduces a rational framework that
systematically provides families of combination operators from a
single canonical form by choosing different geometric frames of
reference in the space of measurement values.
We show that previously used combination operators may be obtained
through our approach in a natural way, that they may be easily modified
and generalized for increased flexibility, and that new combination
operators may be systematically generated.
We provide a characterization of the differentiable combination
operators that are expressible via a frame transformation in terms
of the canonical form and give an algorithm to construct an
appropriate reference frame if one exists.
For related work see:
Research Report No. 97-NA-010
Center for Nonlinear Analysis
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