◤KDD procedures – KL-Collaps◢
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Václav Lín
Václav Lín (theory), Václav Lín (software), Václav Lín (help)
KL-Collaps is a submodule of KL-Miner. Given a K×L contingency table corresponding to some KL-hypothesis discovered by KL-Miner, the user can use KL-Collaps to search for the strongest interactions in the contingency table. Thus the user can gain some additional insight into the results of KL-Miner.
More formally, consider a contingency table with rows r_{1}, …, r_{K} and columns c_{1}, …, c_{L}. Let n_{kl} be the frequency at intersection of r_{k} and c_{l}. Any pair κ_{1} ⊂ {r_{1}, …, r_{K}}, κ_{2} ⊂ {c_{1}, …, c_{L}} determines a four fold contingency table
〈a, b, c, d〉
where a = ∑{n_{kl}: k∈κ_{1}, l∈κ_{2}}, b = ∑{n_{kl}: k∈κ_{1}, l∉κ_{2}}, c = ∑{n_{kl}: k∉κ_{1}, l∈κ_{2}}, d = ∑{n_{kl}: k∉κ_{1}, l∉κ_{2}}. KL-Collaps searches the set of all such pairs of κ_{1} and κ_{2}, and outputs all the pairs for which the Χ^{2}-statistic exceeds a critical value supplied by the user. The search set and the output set of pairs [κ_{1}, κ_{2}] can be restricted by some optional parameters that concern syntactic form and maximal number of the returned pairs. Such a restriction may have a great impact on computational complexity of the search and on intelligibility of the output.
To sum up, the pairs [κ_{1}, κ_{2}] on output of KL-Collaps describe the most important “sources” of dependence underlying the given KL-hypothesis.
LM.KL.Collaps.zip | 400.43 kB | October 29, 2009 |
The original COLLAPS procedure was designed by D. Pokorný in 1970’s [Po 78] (see also [Ha 83]). KL-Collaps is a subset of the original COLLAPS. It was implemented by V. Lín in 2004.
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