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Extracting correlated sets using the chi-squared
measure within n-ary relations: an implementation
A.
1
Casali ,
C.
2
Ernst ,
F.
3
Gasnier ,
J.
2
Stephan
1: Université de la Méditerranée / LIF ― 2: École des Mines de St Étienne / CMP-GC ― 3: STMicroElectronics Rousset
Motivations
Results
8th European AEC/APC Conference - Dresden 2007
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.
Item1
Retrieved Patterns
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.
Report
INTERPRETATION
Item2
…
…
…
…
3453
3489
-
-
6.29
964
1990
3489
-
15.96
1106
1990
3489
-
23.55
1767
1990
3489
-
15.75
1962
1990
3489
-
28.55
1990
2115
3489
-
46.57
…
…
…
…
…
Attribute1
Attribute2
…
Target Attribute
…
…
…
…
_9592_TRAN-
0.41
[2060.6, 2076.8]
0.39
[328.5, 373.5]
0.37
[328.5, 373.5]
[127.1, 136.5]
Generation
[52.3, 75.5]
[328.5, 373.5]
_4690_ALIY-
[0.3, 11.8]
0.37
[328.5, 373.5]
0.62
[0.3, 11.8]
[79.6, 81.1]
…
0.82
PCTH0.62
[0.3, 11.8]
0.82
PCTH0.62
[0.3, 11.8]
_4748_EPTE0.62
0.82
PCTH-
_4692_IMPT-
_4692_IMPT[328.5, 373.5]
0.62
_4692_IMPT0.38
0.82
PCTH-
_4692_IMPT-
_4572_EOXR-
Knowledge
[0.3, 11.8]
_4692_IMPT-
_3700_ALIX[17.5, 23.0]
PCTH-
-
_2565_EPPO-
SELECTION
Chi2
…
[-47.8, -32.7]
Files with a vast number of numerical
attributes (and often incomplete data)
Item4
- Item decoding
- Presentation (processing) of correlations
Methodology: a KDD approach
Raw (Excel) Data Measurement Files
Item3
0.82
PCTH0.34
…
[0.3, 11.8]
…
0.82
…
A complete data transformation, mining and interpretation
Model for correlation detection within data measurements
Selected
File
Conclusions
PREPROCESSING
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
Preprocessed
File
TRANSFORMATION
- Normalization
- Interval discretization / Item encoding
- Elimination of attributes with no item having the support
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.
Transformed
Future Work
File
Current developments are focused on:
- The optimization of the procedure,
- And the implementation of other search methods.
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 C2 := APrioriGen(I);
// (2-pattern) candidates generation
2 i := 2
3 while Ci <> 0 do
4 Li := 0
5 for each X  Ci 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 Li := Li  X
9
endif
10 end for
11 Ci+1 := APrioriGen(Ci – Li)
12 i := i + 1
13 end while
14 return i Li
// limited to the patterns including one item of ta
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.
→
Acknowledgments
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.