Information fusion framework
From OTBWiki
This page intends to describe a possible design for a Dempster-Shafer fusion framework. This framewok will be useful to implement work of V. Poulain on databases update, and other task involving information fusion. It should be extending to support other fusion techniques like bayesian fusion or fuzzy logic.
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Design for a Dempster-Shafer framework
For a very quick reminder on Dempster-Shafer theory, one can refer to the Wikipedia page.
Universal set
The universal set is the set of all the possible states. This set can be represented by a set of labels (either integer or string type). It can be indexed.
Power-set
The power set is the set of all the sub-part of the universal set, including the empty set. If the universal set contains labels {0,1,2}, then the power set is {{0},{1},{2},{0,1},{0,2},{2,3},{1,2,3}}. Therefore, the size of the power set is 2^n. An efficient way to represent on element of the power set is to use binary words, where the ith byte is set to 1 is the element contains the ith label and 0 instead. For instance, the {2,3} element would be 110 in base-2, or 6 in base-10. Therefore, the power set for the {0, ..., n} universal set can be indexed (and represented) by the set {0,...,2^n}, and the index in base-2 allows to know which element of the universal set are used.
Masses
In Dempster-Shafer theory, a source of information assigns a belief mass to each element of the power set, such that the total mass equals one. Therefore, we could represent a mass function as a std::map<long,float>, where the key represent the base-10 index of the power set elements and the floating point value represents the mass associated with a given element.
In many cases, a source of information will only bring belief to a few element of the power set, so we could save space by not including null masses into our map.
Combining two distinct masses
If two sources of information assign distinct masses to the elements of the same power set, Dempster-Shafer theory provides a rule to combine them into a joint mass function, also defined on the whole power set. To compute this joint mass, we first need to determine all the pairs of elements of the power set whose intersections are empty.
