Granular-Relational Data Mining by Piotr Hońko

By Piotr Hońko

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By Piotr Hońko

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23 ∀ M(rltgen (o)) ⊆ UDT . 1, where 0 ≤ i ≤ nD , 0 ≤ j ≤ nD − i. i+j ∀ M(rltgen (o)) o∈UDT ⊆ i M(rltgen (o)), Based on the above property, we can see that with increasing depth level, the pattern candidate may became more specific. i Let SM (o) = {M(rltgen (o)) : 0 ≤ i ≤ nD , rlt i (o) = ∅}, where o ∈ UDT . 25 The set SM (o) (o ∈ UDT ) is partially ordered by relation ⊆. Thanks to this property, we can find the most (or least) general pattern candidates. 1, the set SM (o) o ∈ UDT is well totally ordered by the relation ⊆.

The component of an approximation space that needs to be adapted to operating on granules is the uncertainty function. It can be constructed based on similarity measures. Typical measure can be used for attribute values. 7 (Similarity of values) Let v, v ∈ Va be values of an attribute. The similarity of values v and v is calculated as sima (v, v ) = (v = v ) |v−v | |maxVa −minVa | if a is nominal, if a is numerical, where (v = v ) returns 1 if v = v and 0 otherwise. The first step is to measure the similarity of objects of the same relation.

The remaining part of this subsection shows properties of the framework that can be useful for relational patterns generation. When generating a pattern, we mainly consider its semantics to determine the pattern’s quality. e. semantics. It is assumed that the higher number of objects satisfying a pattern candidate is, the more general the pattern candidate is. 23 ∀ M(rltgen (o)) ⊆ UDT . 1, where 0 ≤ i ≤ nD , 0 ≤ j ≤ nD − i. i+j ∀ M(rltgen (o)) o∈UDT ⊆ i M(rltgen (o)), Based on the above property, we can see that with increasing depth level, the pattern candidate may became more specific.

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