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Mining Evolutionary Model MEM. Rida E. Moustafa And Edward J. Wegman George Mason University Email: {rmoustaf,ewegman}@galaxy.gmu.edu Phone:703-993-1680 Interface 2000 April,4. Mining Evolutionary Model MEM. Talk Outline MEM Theory. Evolutionary computation.

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mining evolutionary model mem
Mining Evolutionary ModelMEM

Rida E. Moustafa

And

Edward J. Wegman

George Mason University

Email:

{rmoustaf,ewegman}@galaxy.gmu.edu

Phone:703-993-1680

Interface 2000

April,4

slide2

Mining Evolutionary ModelMEM

  • Talk Outline
  • MEM Theory.
  • Evolutionary computation.
  • Multidimensional Scaling.
  • Gene Measurements.
  • Results and Future work.
mining evolutionary model mem1
Mining Evolutionary ModelMEM

Evolutionary

Computations

Symbolic

Learning

+

MEM / LEM

mining evolutionary model mem lem
Mining Evolutionary Model:MEM/LEM

Symbolic Learning

Evolutionary Algorithms

Generated

Hypotheses

Standard Genetic

Operators

AQ18

New Generation

of Solution

Stopping Criteria

Model

Allocated computational

resources are exhausted

Satisfactory

Solution

OR

NO

START

END

YES

mining evolutionary model mem lem1
Mining Evolutionary Model:MEM/LEM

Evolution types

Standard Genetic

Algorithms (GA)

Darwinian

New Generation of individuals is guided by lessons from analysis of the previous generation of individuals

Lamarckian

Learning System LS (same type)

- Extract Rules (reasons) why what if ...

- Express these Rules to create new generation

mining evolutionary model mem lem2

GA Structure

Random

Generation

Mining Evolutionary Model:MEM/LEM

Population of

Solution

- Crossover

- Mutation

- Replication

Criteria

Evaluation

Selection

Replication: 11110011 11110011

Mutation : 11110011 10110011

Crossover 11110011 11110101

10111101 10111011

mining evolutionary model mem lem3

Search Methods

Mining Evolutionary Model:MEM/LEM

Guided Random

Enumerative

Calculus-Based

Direct

Simulated

Annealing

(SA)

Evolutionary

Computation

(EC)

Indirect

Evolution

Strategies (ES)

Evolutionary

Programming (EP)

Genetic

Algorithms (GA)

Genetic

Programming (GP)

Class of Search Methods

slide8

The Problem

  • Take 2-point recombination data.

Mining Evolutionary Model:MEM/LEM

CASE I

Simple Case

CASE II: Five Gene Location (Posed Problem)

slide9

Mining Evolutionary Model:MEM/LEM

  • Goal : Indicate the relation between recombination
  • percentage and interval length
  • Idea:
  • Permute {A,B,C} S.T. |A-B|=10; |A-C|=5; |B-C|=15
  • The recombination percentage corresponds to an absolute distance
  • Between the relevant gene loci.
  • Sol: Set A=0 you can find the rest easy by inspection (+/- 10,5)

The Solution is not unique

10

-10

0

5

-5

0

slide10

Mining Evolutionary Model:MEM/LEM

  • No Exact Solution:
  • Assume for example you have :
  • |A-B=50; |A-D|=38; |B-D|=13
  • Translate A=0  B= (+/-50); D= (+/- 38)
  •  |B-D|=13 can not hold !!!
  • The data for Shorter lengths is more reliable [Russell 1986]
  •  We must analyze the data set in more Statistical Fashion !!
slide11

Mining Evolutionary Model:MEM/LEM

  • Error Metric Approaches:
  • Simply strike out the larger percentages and work only with smallest
  • Weight the smaller distances preferentially.
  • Represent the distance-percentage relation for genes: |G_I –G_J |=%IJ
  • Error = S[((G_I –G_J )/ %IJ )2 –1] 2 ; I N.EQ J.
  • Important Notice : The Error Proves Metric Space
  • If a coordinate solution is exact  Error is Zero.
  • E(G_I –G_J )= E(G_J –G_ I )  Symmetric.
  • E(G_I –G_J ) + E(G_J –G_ k ) LEQ E(G_I –G_ k )  Triangle Inequality.
slide12

Mining Evolutionary Model:MEM/LEM

  • Possible Test Cases:
  • Set A=0  4-dimension Optimization Problem
  • Set A .NEQ. 0  5-dimension Optimization Problem.
  • Our result here shown for 5-D case:
  • Landscape: [-50,50]5  (10 6 ) point representations
  • Fitness Function is : Fitness=1/Error(GI,GJ)
  • Min_Error Max_Fitness
  • (which we look for) !!!
slide15

Mining Evolutionary Model:MEM/LEM

Multiple peaks: Different landscape

slide16

Mining Evolutionary Model:MEM/LEM

Multiple Optima (Minimum)

Different landscape

slide17

Mining Evolutionary Model:MEM/LEM

Convergence Rata : Comparison

slide18

Mining Evolutionary Model:MEM/LEM

The Optimal Location of 5-genes

slide19

Mining Evolutionary Model:MEM/LEM

Algorithm Generations Error The Optimal Gene locations

EP 5000 5.48812 12.2196 15.9109 3.2243 1.7178 4.1080

EV 4910 5.51054 13.5779 12.7448 -1.3963 -0.7175 5.4734

ES 5000 5.48137 11.4165 14.9727 -4.0696 0.9398 3.0567

MEM 5010 0.387745 -35.0000 9.0000 -50.0000 -2.0000 -43.000

Results and Comparisons

slide20

Mining Evolutionary Model:MEM/LEM

  • Summary and Future Work:
  • Landscape has its own effect and should be chosen to include all possible solutions.
  • Knowing what you’re looking for (Max/Min) and what the package will offer you, Then design your Fitness function .
  • MEM has more accurate Results than EV itself.
  • The code can handle up to 100-D and can be modified for higher.
  • The code easily Parallelize for reducing time complexity.
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