1. 8 th European AEC/APC Conference - Dresden 2007 Extracting correlated sets using the chi-squared measure within n-ary relations: an implementation A. Casali 1, C. Ernst 2, F. Gasnier 3, J. Stephan 2 1: Université de la Méditerranée / LIF ― 2: École des Mines de St Étienne / CMP-GC ― 3: STMicroElectronics Rousset The field of APC aims at highlighting correlations between Production parameters. This study focuses on the device analysis of the principal trajectories impacting the yield. The goal is to detect correlations between data measurements structured as n-ary relations and involving (at least) one target attribute. The method uses a data mining levelwise algorithm based on both the chi-squared and the support measures. Motivations Methodology: a KDD approach Results This approach makes it possible for STMicroElectronics Rousset to highlight unknown correlations between various parameters, validated by electrical and/or physical analysis. While the proposed mining method confirmed that levelwise algorithms do not provide results beyond four search levels, it proved its value for n-ary relations with a very large number of numerical attributes. The study aims at supporting the development of effective R2R control loops. Conclusions Future Work This work was initiated while the fourth author was at Ecole des Mines de Saint-Étienne / CMP-GC, and was supported by Research Project “Rousset 2003-2008”, financed by the Communauté du Pays d'Aix, Conseil Général des Bouches du Rhône and Conseil Régional Provence Alpes Côte d'Azur. Acknowledgments Selected File Raw (Excel) Data Measurement Files Preprocessed File Transformed File SELECTION PREPROCESSING TRANSFORMATION DATA MINING IN : ItemSet I, Fraction p%, Threshold mc (chi2), Threshold s (support), Target Attribute ta, Relation r OUT : Set of minimal correlated patterns 1 C 2 := APrioriGen(I);// (2-pattern) candidates generation 2 i := 2 3 while C i <> 0 do 4 L i := 0 5 for each X  C i do 6 Build the contingency table of X 7 if p% of the table’s cells have a support  s then 8 if chi2(X)  mc then L i := L i  X 9 endif 10 end for 11 C i+1 := APrioriGen(C i – L i ) 12 i := i + 1 13 end while 14 return  i L i // limited to the patterns including one item of ta Attribute removal. Criteria: attributes - with too few distinct values - having too many null values - presenting doubles (one is kept) - with a too small standard deviation Files with a vast number of numerical attributes (and often incomplete data) Current developments are focused on: - The optimization of the procedure, - And the implementation of other search methods. We plan to initiate a background procedure integrating different sets of methods, measurements and results. → Automatic generation of the most suitable result for each new analysis. - Normalization - Interval discretization / Item encoding - Elimination of attributes with no item having the support INTERPRETATION - Item decoding - Presentation (processing) of correlations Knowledge Generation Retrieved Patterns Report Item1Item2Item3Item4Chi2 …………… 34533489--6.29 96419903489-15.96 110619903489-23.55 176719903489-15.75 196219903489-28.55 199021153489-46.57 …………… A complete data transformation, mining and interpretation Model for correlation detection within data measurements Attribute1Attribute2…Target Attribute ………… _9592_TRAN-- PCTH- [-47.8, -32.7]0.41- [0.3, 11.8]0.82 _2565_EPPO-_4692_IMPT- PCTH- [2060.6, 2076.8]0.39[328.5, 373.5]0.62 [0.3, 11.8]0.82 _3700_ALIX-_4692_IMPT- PCTH- [17.5, 23.0]0.37[328.5, 373.5]0.62 [0.3, 11.8]0.82 _4572_EOXR-_4692_IMPT- PCTH- [127.1, 136.5]0.38[328.5, 373.5]0.62 [0.3, 11.8]0.82 _4690_ALIY-_4692_IMPT- PCTH- [52.3, 75.5]0.37[328.5, 373.5]0.62 [0.3, 11.8]0.82 _4692_IMPT-_4748_EPTE- PCTH- [328.5, 373.5]0.62[79.6, 81.1]0.34 [0.3, 11.8]0.82 …………