Measures on Boolean polynomials and their applications in data mining. (English) Zbl 1050.68033
Summary: We characterize measures on free Boolean algebras and we examine the relationships that exist between measures and binary tables in relational databases. It is shown that these measures are completely defined by their values on positive conjunctions, and a formula that yields this value is obtained using the method of indicators. An extension of the notion of support that is well suited for tables with missing values is presented. Finally, we obtain Bonferroni-type inequalities that allow for approximative evaluations of these measures for several types of queries. An approximation algorithm and an analysis of the results produced is also included.
MSC:
| 68P15 | Database theory |
| 68T05 | Learning and adaptive systems in artificial intelligence |
| 28A12 | Contents, measures, outer measures, capacities |
Keywords:
free Boolean algebra; measure; Bonferroni-type inequality; inclusion-exclusion; missing values; frequent itemset; relational databases; approximation algorithm; data miningSoftware:
UCI-mlReferences:
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