23,481 research outputs found
Approximations from Anywhere and General Rough Sets
Not all approximations arise from information systems. The problem of fitting
approximations, subjected to some rules (and related data), to information
systems in a rough scheme of things is known as the \emph{inverse problem}. The
inverse problem is more general than the duality (or abstract representation)
problems and was introduced by the present author in her earlier papers. From
the practical perspective, a few (as opposed to one) theoretical frameworks may
be suitable for formulating the problem itself. \emph{Granular operator spaces}
have been recently introduced and investigated by the present author in her
recent work in the context of antichain based and dialectical semantics for
general rough sets. The nature of the inverse problem is examined from
number-theoretic and combinatorial perspectives in a higher order variant of
granular operator spaces and some necessary conditions are proved. The results
and the novel approach would be useful in a number of unsupervised and semi
supervised learning contexts and algorithms.Comment: 20 Pages. Scheduled to appear in IJCRS'2017 LNCS Proceedings,
Springe
Validation of Matching
We introduce a technique to compute probably approximately correct (PAC)
bounds on precision and recall for matching algorithms. The bounds require some
verified matches, but those matches may be used to develop the algorithms. The
bounds can be applied to network reconciliation or entity resolution
algorithms, which identify nodes in different networks or values in a data set
that correspond to the same entity. For network reconciliation, the bounds do
not require knowledge of the network generation process
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