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Mining Evolutionary Model MEM

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

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  1. 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

  2. Mining Evolutionary ModelMEM • Talk Outline • MEM Theory. • Evolutionary computation. • Multidimensional Scaling. • Gene Measurements. • Results and Future work.

  3. Mining Evolutionary ModelMEM Evolutionary Computations Symbolic Learning + MEM / LEM

  4. 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

  5. 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

  6. 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

  7. 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

  8. The Problem • Take 2-point recombination data. Mining Evolutionary Model:MEM/LEM CASE I Simple Case CASE II: Five Gene Location (Posed Problem)

  9. 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

  10. 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 !!

  11. 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.

  12. 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) !!!

  13. Mining Evolutionary Model:MEM/LEM The Global Maximum

  14. Mining Evolutionary Model:MEM/LEM The Global Minimum

  15. Mining Evolutionary Model:MEM/LEM Multiple peaks: Different landscape

  16. Mining Evolutionary Model:MEM/LEM Multiple Optima (Minimum) Different landscape

  17. Mining Evolutionary Model:MEM/LEM Convergence Rata : Comparison

  18. Mining Evolutionary Model:MEM/LEM The Optimal Location of 5-genes

  19. 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

  20. 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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