Download Data mining with Artificial Evolution.

Data Mining with Artificial
Evolution.
Helen Johnson
Anna Kwiatkowska
David Sweeney
Panagiotis Tzionas
Problem leader: Michele Sebag
Team leader: Michael Herdy
Data mining
• A multi-objective optimisation problem
• Aims to extract valid, novel and interesting
rules (laws) from data.
Support
Law generality
Validity
Confidence
Law accuracy
The ‘real’ data problem
“The flows of particles of various sizes in the austral seas”
Details of the data set:
Particles at four size groups measured at two depths: 2000 and 3000 m
A total of 51 measurements over a period of a few hundred days
sm 2000
sm 3000
last 2000
last 3000
med 2000
med 3000
lg 2000
Concentration
1,4
1,2
1
0,8
0,6
0,4
0,2
0
-0,2
0
10
20
30
40
50
60
Example
Data provided by V. Athias and C. Jeandel
Interactions between particles
OBSERVATIONS
Adsorption
Agglomeration
Sinking
Dissolved phase
TRANSFORMATIONS
Suspended
particles
Parameters
AIM
Model
interactions
Sinking
particles
Methodology
Target = LAW
Phenotype: a linear combination of terms
1.2x2 + x3sin(x1) + 3.6x1x2
Genotype: coding of the phenotype
(1.2,0,2,3), (1,2,3,1), (3.6,1,1,2)
where 0 = xi ; 1 = xi * xj ; 2 = xisin xj
•
Mixed integer–real valued representation hybrid ES/GA
•
Selection: The problem to find a set of laws
(Michigan, Pittsburgh, Universal Suffrage)
Assessing the fitness of one law
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•
•
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The law is calculated for each example
The results are sorted
Plateaux are identified
Fitness function is calculated
10
P2
9
8
7
Result
6
P1
5
4
3
2
1
0
1
3
5
7
9
11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51
Example
Testing a simple fitness function
Fitness function = Σlength(Pi)
The known law (A0 * A1 = cst).
Found laws
1)
-0.37A0 * A1 – 0.36A2/A2 + 0.07A0/A0
2)
-0.04A0*A0 – 0.008A1*A2 – 0.77A1*A0
Problem with the fitness function:
Fitness=8
Example
Result vj
Result vj
Fitness=8
Example
The new fitness function
Identifying the maximum length plateau for each example.
F
no of plateau examples
 length P
i
i 1
Fitness=8
Example
Result vj
Result vj
Fitness=64
Example
Correct law: A0*A1=0.156
One of our best results:A0*A1=0.12138
The tautology problem
A tautology:
A0-A0=0
A1/A1=1
• A tautology provides no knowledge.
• The derived laws must be checked for tautologies.
• Apply laws to a random data set.
• If the law fits all the data then it is a tautology.
Lessons from preliminary experiments
1. Population size: no influence on the laws
2. Probability of crossover:
Decrease from 0.6 to 0.4: many tautologies
So decrease “tautology threshold”: elimination of some
tautologies.
3. Probability of mutation:
Decrease from 0.1 to 0.05: improvement in laws
4. Plateau threshold
Decreasing the threshold in steps: improved laws
Plot generated after optimisation
1,46
1,44
Result
1,42
1,4
1,38
1,36
1,34
1,32
1
6
11
16
21
26
31
36
41
46
51
56
Example
61
66
71
76
81
86
91
96
Conclusions
• Powerful technique for finding knowledge in data
• The fitness function is crucial
• Tuning of the algorithm is data dependant
• No single optimum algorithm for a specific dataset
Questions arising
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Pre-processing of data ?
Criteria for defining a plateau ?
Number of constructs and type of constructs ?
How important is law interpretation ?