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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
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Talk Outline MEM Theory. Evolutionary computation. Multidimensional Scaling. Gene Measurements. Results and Future work. Mining Evolutionary Model MEM
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Evolutionary Computations Symbolic Learning MEM / LEM +
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Mining Evolutionary Model:MEM/LEM Symbolic Learning Generated Hypotheses AQ18 Evolutionary Algorithms Standard Genetic Operators New Generation of Solution Stopping Criteria Allocated computational resources are exhausted Satisfactory Solution YES Model NO END OR START
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Mining Evolutionary Model:MEM/LEM Evolution types Darwinian Lamarckian Standard Genetic Algorithms (GA) New Generation of individuals is guided by lessons from analysis of the previous generation of individuals Learning System LS (same type) - Extract Rules (reasons) why what if... - Express these Rules to create new generation
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Mining Evolutionary Model:MEM/LEM Population of Solution Criteria Evaluation Selection - Crossover - Mutation - Replication Random Generation GA Structure Replication: 11110011 11110011 Mutation : 11110011 10110011 Crossover 11110011 11110101 10111101 10111011
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Mining Evolutionary Model:MEM/LEM Enumerative Evolutionary Computation (EC) Simulated Annealing (SA) Calculus-Based Guided Random Genetic Programming (GP) Genetic Algorithms (GA) Evolutionary Programming (EP) Evolution Strategies (ES) Direct Indirect Search Methods Class of Search Methods
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The Problem Take 2-point recombination data. Gene Loci % Recombination A,B10 A,C5 B,C15 Gene Loci % Recombination A,B50 A,C15 A,D38 A,E8 B,C50 B,D13 B,E50 C,D50 C,E7 D,E45 CASE I Simple Case CASE II: Five Gene Location (Posed Problem) Mining Evolutionary Model:MEM/LEM
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Goal 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) -5 0 10-1005 The Solution is not unique Mining Evolutionary Model:MEM/LEM
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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 !!! |B-D|=13 can not hold !!! The data for Shorter lengths is more reliable [Russell 1986]The data for Shorter lengths is more reliable [Russell 1986] We must analyze the data set in more Statistical Fashion !! We must analyze the data set in more Statistical Fashion !! Mining Evolutionary Model:MEM/LEM
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Error Metric Approaches: 1.Simply strike out the larger percentages and work only with smallest 2.Weight the smaller distances preferentially. 3.Represent the distance-percentage relation for genes: |G_ I –G_ J |=% IJ 4.Error = (G_ I –G_ J )/ % IJ ) 2 – 1 ] 2 ; I N.EQ J. Important Notice : The Error Proves Metric Space 1.If a coordinate solution is exact Error is Zero. 2.E(G_ I –G_ J )= E(G_ J –G_ I ) Symmetric. 3.E(G_ I –G_ J ) + E(G_ J –G_ k ) LEQ E(G_ I –G_ k ) Triangle Inequality. Mining Evolutionary Model:MEM/LEM
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Possible Test Cases: 1.Set A=0 4-dimension Optimization Problem 2.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(G I,G J ) Min_Error Max_Fitness (which we look for) !!! Mining Evolutionary Model:MEM/LEM
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The Global Maximum Mining Evolutionary Model:MEM/LEM
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The Global Minimum Mining Evolutionary Model:MEM/LEM
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Multiple peaks: Different landscape Mining Evolutionary Model:MEM/LEM
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Multiple Optima (Minimum) Different landscape Mining Evolutionary Model:MEM/LEM
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Convergence Rata : Comparison Mining Evolutionary Model:MEM/LEM
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The Optimal Location of 5-genes Mining Evolutionary Model:MEM/LEM
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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 13.577912.7448-1.3963-0.7175 5.4734 ES 5000 5.4813711.416514.9727-4.0696 0.9398 3.0567 MEM 5010 0.387745 -35.0000 9.0000 -50.0000 -2.0000 -43.000 Results and Comparisons
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Summary and Future Work: 1.Landscape has its own effect and should be chosen to include all possible solutions. 2.Knowing what you’re looking for (Max/Min) and what the package will offer you, Then design your Fitness function. 3.MEM has more accurate Results than EV itself. 4.The code can handle up to 100-D and can be modified for higher. 5.The code easily Parallelize for reducing time complexity. Mining Evolutionary Model:MEM/LEM
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