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relaxed intersection : ウィキペディア英語版
relaxed intersection
The ''relaxed intersection'' of ''m'' sets corresponds to the classical
intersection between sets except that it is allowed to relax few sets in order to avoid an empty intersection.
This notion can be used to solve Constraints Satisfaction Problems
that are inconsistent by relaxing a small number of constraints.
When a bounded-error approach is considered for parameter estimation,
the relaxed intersection makes it possible to be robust with respect
to some outliers.
==Definition==

The ''q''-relaxed intersection of the ''m'' subsets
X_,\dots ,X_
of R^,
denoted by

X^}X_

is the set of all

x \in R^

which belong to all

X_

's, except
q
at most.
This definition is illustrated by Figure 1.
Define

\lambda (x) =\text \left\.

We have

X^(()) .

Characterizing the q-relaxed intersection is a thus a set inversion problem.



抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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