Anthropocentric visualization of optimal cover of association rules - PowerPoint PPT Presentation

Outline Anthropocentric visualization of optimal cover of association rules Amira Mouakher Sadok Ben Yahia High Institute of Computer Science, Tunisia Faculty of Sciences of Tunis, Tunisia Concept Lattices and Their Applications, CLA 2010 Mouakher, Ben Yahia Anthropocentric visualization of optimal cover of association rules CLA 2010 1 / 30

Outline Outilne Introduction and motivation 1 Extraction of a minimal cover from a binary relation 2 Virtual reality based visualization of association rules 3 Conclusion and future work 4 Mouakher, Ben Yahia Anthropocentric visualization of optimal cover of association rules CLA 2010 2 / 30

Outline Outilne Introduction and motivation 1 Extraction of a minimal cover from a binary relation 2 Virtual reality based visualization of association rules 3 Conclusion and future work 4 Mouakher, Ben Yahia Anthropocentric visualization of optimal cover of association rules CLA 2010 2 / 30

Outline Outilne Introduction and motivation 1 Extraction of a minimal cover from a binary relation 2 Virtual reality based visualization of association rules 3 Conclusion and future work 4 Mouakher, Ben Yahia Anthropocentric visualization of optimal cover of association rules CLA 2010 2 / 30

Outline Outilne Introduction and motivation 1 Extraction of a minimal cover from a binary relation 2 Virtual reality based visualization of association rules 3 Conclusion and future work 4 Mouakher, Ben Yahia Anthropocentric visualization of optimal cover of association rules CLA 2010 2 / 30

Introduction Extraction of a minimal cover from a binary relation Virtual reality based visualization of association rules Conclusion and future work KDD process Mouakher, Ben Yahia Anthropocentric visualization of optimal cover of association rules CLA 2010 3 / 30

Introduction Extraction of a minimal cover from a binary relation Virtual reality based visualization of association rules Conclusion and future work Extraction of association rules Definition Association rules : Form : premise ⇒ conclusion (support, confidence) Example : "cheese" ⇒ "bread"(50 % , 90 % ). Having The agreement A dataset, that every Discovering all the association transaction is described rules that express correlations by an identifier and a list between two itemsets. of items. Mouakher, Ben Yahia Anthropocentric visualization of optimal cover of association rules CLA 2010 4 / 30

Introduction Extraction of a minimal cover from a binary relation Virtual reality based visualization of association rules Conclusion and future work Statistical Metrics Support : probability that a transaction contains X and Y (frequency of appearance of XY). Confidence : conditional probability that a transaction containing X also contains Y. (support(XY) / support(X)). � = 1 → Exact association rule . Confidence ( R ) < 1 → Approximate association rule . Aim : Extracting all the association rules minSup and minConf (User-given thresholds). How to do that ? Collecting the frequent itemsets (support ≥ minsupp ), 1 Extracting valid association rules (confidence ≥ minconf ). 2 However ! ! ! ! The extraction cost is exponential with the number of items, i.e., 2 |I| . Mouakher, Ben Yahia Anthropocentric visualization of optimal cover of association rules CLA 2010 5 / 30

Introduction Extraction of a minimal cover from a binary relation Virtual reality based visualization of association rules Conclusion and future work Association rules : Statistics Dataset minsup Exact rules T10I4D100K 0.5% 0 Mushroom 30% 7 476 C73D10K 90% 52 035 Dataset minsup minconf Approximate rules T10I4D100K 0.5% 70% 20 419 50% 21 686 Mushroom 30% 70% 37 671 50% 56 703 C73D10K 90% 95% 1 606 726 85% 2 053 936 Mouakher, Ben Yahia Anthropocentric visualization of optimal cover of association rules CLA 2010 6 / 30

Introduction Extraction of a minimal cover from a binary relation Virtual reality based visualization of association rules Conclusion and future work Our approach Mouakher, Ben Yahia Anthropocentric visualization of optimal cover of association rules CLA 2010 7 / 30

Introduction Extraction of a minimal cover from a binary relation Virtual reality based visualization of association rules Conclusion and future work Concept lattice structure Advantages : Compact representation. Without loss of information. Drawbacks : Big redundancy. Complexity of the lattice’s construction. Extraction of a minimal cover NP-hard problem. Several related works. Are mainly based on heuristics. Mouakher, Ben Yahia Anthropocentric visualization of optimal cover of association rules CLA 2010 8 / 30

Introduction Extraction of a minimal cover from a binary relation Virtual reality based visualization of association rules Conclusion and future work Extraction of a minimal cover Belkhiter and al. (1994) : Optimal rectangular decomposition of a binary relation. An application to documentary databases. The gain function of a formal concept C = ( E , I ) : gain ( C ) = ( | E | × | I | ) − ( | E | + | I | ) Mouakher, Ben Yahia Anthropocentric visualization of optimal cover of association rules CLA 2010 9 / 30

Introduction Extraction of a minimal cover from a binary relation Virtual reality based visualization of association rules Conclusion and future work Extraction of a minimal cover Kcherif and al. (2000) : A rectangular decomposition approach based on the Riguet’s difunctional relation. A set of isolated points allowing the determination of the minimal set of formal concepts covering a given binary relation : R d = R ◦ R − 1 ◦ R ∩ R Mouakher, Ben Yahia Anthropocentric visualization of optimal cover of association rules CLA 2010 10 / 30

Introduction Extraction of a minimal cover from a binary relation Virtual reality based visualization of association rules Conclusion and future work Extraction of a minimal cover Belohlavek & Vychodil (2009) : A new method of decomposition of an n × m binary matrix I into a boolean product A ◦ B of an n × k binary matrix A and a k × m binary matrix B , with k as small as possible. Formal concept � E , I � , I can be expressed like I = � i ∈ I { ψ ◦ φ ( i ) } . The election of the column y which maximizes the following value : | I ⊕ y | = ( φ ( I ∪ y ) × ψ ◦ φ ( I ∪ y ) ∩ K Mouakher, Ben Yahia Anthropocentric visualization of optimal cover of association rules CLA 2010 11 / 30

Introduction Extraction of a minimal cover from a binary relation Virtual reality based visualization of association rules Conclusion and future work Criticism of these approaches Static metrics : cardinality of the concept, Cover is extracted regardless of the quality of knowledge . Mouakher, Ben Yahia Anthropocentric visualization of optimal cover of association rules CLA 2010 12 / 30

Introduction Extraction of a minimal cover from a binary relation Virtual reality based visualization of association rules Conclusion and future work Proposed solution Relies on the formal concept lattice representation. A greedy algorithm for discovering a reduced cover of "pertinent" concepts. Pertinence of a concept is based on the strength of the association rules. The user is an actor of the extraction process and validates pertinent concepts. Mouakher, Ben Yahia Anthropocentric visualization of optimal cover of association rules CLA 2010 13 / 30

Introduction Extraction of a minimal cover from a binary relation Virtual reality based visualization of association rules Conclusion and future work Correlation measures Many correlation measures have been proposed in the literature. The discovery of frequent patterns will be of benefit in the reduction of high added value association rule number. Only informative frequent patterns will be derived from the highly correlated patterns. Some of the most used correlation measures. Mouakher, Ben Yahia Anthropocentric visualization of optimal cover of association rules CLA 2010 14 / 30

Introduction Extraction of a minimal cover from a binary relation Virtual reality based visualization of association rules Conclusion and future work Correlation measures The confidence correlation measure The ratio of the number of transactions that include all items in the consequent as well as the antecedent (namely, the support) to the number of transactions that include all items in the antecedent. Conf ( R ) = Supp ( XY ) Supp ( X ) Mouakher, Ben Yahia Anthropocentric visualization of optimal cover of association rules CLA 2010 15 / 30

Introduction Extraction of a minimal cover from a binary relation Virtual reality based visualization of association rules Conclusion and future work Correlation measures The Lift correlation measure The lift Ratio of an association rule is defined as follows : Lift ( R ) = Conf ( R ) Pr ( R ) Pr ( R ) is called the expected confidence . The number of transactions having the consequent items divided by the total number of transactions. Mouakher, Ben Yahia Anthropocentric visualization of optimal cover of association rules CLA 2010 16 / 30