Towards a Unifying Probabilistic Implicative Normalized Quality Measure for Association Rules

An Extension of Totohasina’s Normalization Theory of Quality Measures of Association Rules

“…In the context of the implicative statistical analysis (ISA) [1], you can never leave aside the probabilistic notions of the measures of quality which assess the degree of implicative link between two patterns of association rule. In light of very rich number of measures in the literature of the binary database, researchers are working [2][3][4][5][6][7] parallelly to find the more general relationships allowing to classify partially or entirely these various measures of interest. Hence the creation of highly founded concept called "normalization under five constraints quality measures" in the context of data mining appeared in 2003 [2].…”

“…In light of very rich number of measures in the literature of the binary database, researchers are working [2][3][4][5][6][7] parallelly to find the more general relationships allowing to classify partially or entirely these various measures of interest. Hence the creation of highly founded concept called "normalization under five constraints quality measures" in the context of data mining appeared in 2003 [2]. This definition of normalized measures is acquired.…”

“…This definition of normalized measures is acquired. It thus turns out that all normalizable measures by affine homeomorphism become comparable [2,8]. Although this author has already well-treated this subject, the problem of normalization of probabilistic quality measures remains not fully resolved.…”

“…[6,[13][14][15]). Let X and Y be itemset of a context of binary data mining = ( , , R), the uniform discrete probability on probabilizable space ( , P( )) [2], all sets of transactions, the set of attributes called items or patterns, R the binary relation from to , a probabilistic quality measure, and → an association rule, with ∩ = 0. ∀ ∈ , = { ∈ / ∀ ∈ ; R } denoted the extention of the itemset :…”

“…= { ∈ / ∀ ∈ ; R }; i.e., the set of all transactions contains the pattern [6]. Note that this measure was discovered independently by three authors from three continents: by S. Guillaume in France in her thesis [15], by A. Totohasina in [2] in Madagascar at his research on normalization, at that time he appointed ION "Implication Oriented Normalised", and by X. Wu, C. Zhang, and S. Zhang in [5] in USA under the name of CPIR "Conditional Probability Incrementation Ratio". Its rich and interesting mathematical properties are studied in [6,15].…”