high-performance asset cluster analysis implemented with parallel genetic algorithms on the nvidia...
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MotivationBackground
ApproachResults
References
High-performance asset cluster analysisimplemented with Parallel Genetic Algorithms on
the NVIDIA CUDA platform
by Dariusz Cieslakiewicz1, Diane Wilcox1, Tim Gebbie2
1Department of Computational and Applied MathematicsUniversity of Witwatersrand
2Investec Bank
CHPC Conference, Durban, December 2012
The financial assistance of the National Research Foundation (NRF) towards this research is hereby acknowledged.Opinions expressed and conclusions arrived at, are those of the author and are not necessarily attributed to the NRF.
by Dariusz Cieslakiewicz, Diane Wilcox, Tim Gebbie High-performance asset cluster analysis implemented with Parallel Genetic Algorithms on the NVIDIA CUDA platform
MotivationBackground
ApproachResults
References
Outline
1 MotivationNon-parametric cluster analysis
2 BackgroundGenetic AlgorithmsGenetic operatorsParallel Genetic AlgorithmsComputing Platform
3 ApproachTechnical architecture
4 ResultsResults
5 References
by Dariusz Cieslakiewicz, Diane Wilcox, Tim Gebbie High-performance asset cluster analysis implemented with Parallel Genetic Algorithms on the NVIDIA CUDA platform
MotivationBackground
ApproachResults
References
Non-parametric cluster analysis
Outline
1 MotivationNon-parametric cluster analysis
2 BackgroundGenetic AlgorithmsGenetic operatorsParallel Genetic AlgorithmsComputing Platform
3 ApproachTechnical architecture
4 ResultsResults
5 References
by Dariusz Cieslakiewicz, Diane Wilcox, Tim Gebbie High-performance asset cluster analysis implemented with Parallel Genetic Algorithms on the NVIDIA CUDA platform
MotivationBackground
ApproachResults
References
Non-parametric cluster analysis
Cluster analysis
by Dariusz Cieslakiewicz, Diane Wilcox, Tim Gebbie High-performance asset cluster analysis implemented with Parallel Genetic Algorithms on the NVIDIA CUDA platform
MotivationBackground
ApproachResults
References
Non-parametric cluster analysis
Cluster analysis I
Cluster analysis groups objects and describes theirassociations.Configuration of clusters is represented by a setS = {C1, . . . ,Ci ,Ci+1, . . . ,Cn} where Ci is the cluster thatobject i belongs to and adheres to the following conditions:
Ci 6= ∅ for i = 1, . . . ,K ,Ci ∩ Cj = ∅ for i = 1, . . . ,K , j = 1, . . . ,K and i 6= j
and⋃K
i=1 Ci = S[Giada and Marsili, 2002] addressed the problem of dataclustering by introducing an unsupervised, parameter freeapproach based on the maximum likelihood principle (ML)principle.
by Dariusz Cieslakiewicz, Diane Wilcox, Tim Gebbie High-performance asset cluster analysis implemented with Parallel Genetic Algorithms on the NVIDIA CUDA platform
MotivationBackground
ApproachResults
References
Non-parametric cluster analysis
Log-likelihood function I
Log-likelihood function
[Giada and Marsili, 2002] computed the probability density P({~xi}|G,S) and used this to derive themaximum likelihood of a feature Lc thus resulting in a structure S as P(G∗,S|~xi ) ∝ eDL(S), wherethe resulting likelihood function is denoted by
Lc(S) =12
∑s:ns>1
[logns
cs+ (ns − 1) log
n2s − ns
n2s − cs
] (1)
The likelihood only depends on the Pearson’s coefficient of data:
ci,j =~xi~xj√∥∥∥~xi2∥∥∥ ∥∥∥~xj
2∥∥∥ (2)
by Dariusz Cieslakiewicz, Diane Wilcox, Tim Gebbie High-performance asset cluster analysis implemented with Parallel Genetic Algorithms on the NVIDIA CUDA platform
MotivationBackground
ApproachResults
References
Genetic AlgorithmsGenetic operatorsParallel Genetic AlgorithmsComputing Platform
Outline
1 MotivationNon-parametric cluster analysis
2 BackgroundGenetic AlgorithmsGenetic operatorsParallel Genetic AlgorithmsComputing Platform
3 ApproachTechnical architecture
4 ResultsResults
5 References
by Dariusz Cieslakiewicz, Diane Wilcox, Tim Gebbie High-performance asset cluster analysis implemented with Parallel Genetic Algorithms on the NVIDIA CUDA platform
MotivationBackground
ApproachResults
References
Genetic AlgorithmsGenetic operatorsParallel Genetic AlgorithmsComputing Platform
What are Genetic Algorithms? I
In 1975, Holland, in his book titled Adaptation in naturaland artificial systems, described how to apply theprinciples of natural evolution to optimization problems andbuilt the first Genetic Algorithms.
Genetic algorithms are computationally intensive globalsearch heuristics.
Search space contains all feasiable solutions among whichthe desired solution resides.
by Dariusz Cieslakiewicz, Diane Wilcox, Tim Gebbie High-performance asset cluster analysis implemented with Parallel Genetic Algorithms on the NVIDIA CUDA platform
MotivationBackground
ApproachResults
References
Genetic AlgorithmsGenetic operatorsParallel Genetic AlgorithmsComputing Platform
Outline
1 MotivationNon-parametric cluster analysis
2 BackgroundGenetic AlgorithmsGenetic operatorsParallel Genetic AlgorithmsComputing Platform
3 ApproachTechnical architecture
4 ResultsResults
5 References
by Dariusz Cieslakiewicz, Diane Wilcox, Tim Gebbie High-performance asset cluster analysis implemented with Parallel Genetic Algorithms on the NVIDIA CUDA platform
MotivationBackground
ApproachResults
References
Genetic AlgorithmsGenetic operatorsParallel Genetic AlgorithmsComputing Platform
Genetic operators I
SelectionCrossoverMutationElitismReplacement
by Dariusz Cieslakiewicz, Diane Wilcox, Tim Gebbie High-performance asset cluster analysis implemented with Parallel Genetic Algorithms on the NVIDIA CUDA platform
MotivationBackground
ApproachResults
References
Genetic AlgorithmsGenetic operatorsParallel Genetic AlgorithmsComputing Platform
Genetic operators
by Dariusz Cieslakiewicz, Diane Wilcox, Tim Gebbie High-performance asset cluster analysis implemented with Parallel Genetic Algorithms on the NVIDIA CUDA platform
MotivationBackground
ApproachResults
References
Genetic AlgorithmsGenetic operatorsParallel Genetic AlgorithmsComputing Platform
Cluster determination with GA
Representation: Integer-based individualCh =
{Ci1 ,Cj2 , . . . ,ClK
}for i , j , l = {1, . . . ,K } where Ci is
the cluster that the object at the ordinal position belongs to.Objective function:
Lc(S) =12
∑s:ns>1
[logns
cs+ (ns − 1) log
n2s − ns
n2s − cs
] (3)
by Dariusz Cieslakiewicz, Diane Wilcox, Tim Gebbie High-performance asset cluster analysis implemented with Parallel Genetic Algorithms on the NVIDIA CUDA platform
MotivationBackground
ApproachResults
References
Genetic AlgorithmsGenetic operatorsParallel Genetic AlgorithmsComputing Platform
Outline
1 MotivationNon-parametric cluster analysis
2 BackgroundGenetic AlgorithmsGenetic operatorsParallel Genetic AlgorithmsComputing Platform
3 ApproachTechnical architecture
4 ResultsResults
5 References
by Dariusz Cieslakiewicz, Diane Wilcox, Tim Gebbie High-performance asset cluster analysis implemented with Parallel Genetic Algorithms on the NVIDIA CUDA platform
MotivationBackground
ApproachResults
References
Genetic AlgorithmsGenetic operatorsParallel Genetic AlgorithmsComputing Platform
Parallelisation Schemes
GAs lend themselves to parallelisation.Parallelisation Schemes: Master-slave and Multiple-deme
Master-slave models
Multiple-deme PGAs
by Dariusz Cieslakiewicz, Diane Wilcox, Tim Gebbie High-performance asset cluster analysis implemented with Parallel Genetic Algorithms on the NVIDIA CUDA platform
MotivationBackground
ApproachResults
References
Genetic AlgorithmsGenetic operatorsParallel Genetic AlgorithmsComputing Platform
Migration Topologies
MigrationDeme SizeMigration Topologies: Stepping Stone, One-Way Ring,Ring, Ring+1+2 and Ring+1+2+3
Migration rate
by Dariusz Cieslakiewicz, Diane Wilcox, Tim Gebbie High-performance asset cluster analysis implemented with Parallel Genetic Algorithms on the NVIDIA CUDA platform
MotivationBackground
ApproachResults
References
Genetic AlgorithmsGenetic operatorsParallel Genetic AlgorithmsComputing Platform
Outline
1 MotivationNon-parametric cluster analysis
2 BackgroundGenetic AlgorithmsGenetic operatorsParallel Genetic AlgorithmsComputing Platform
3 ApproachTechnical architecture
4 ResultsResults
5 References
by Dariusz Cieslakiewicz, Diane Wilcox, Tim Gebbie High-performance asset cluster analysis implemented with Parallel Genetic Algorithms on the NVIDIA CUDA platform
MotivationBackground
ApproachResults
References
Genetic AlgorithmsGenetic operatorsParallel Genetic AlgorithmsComputing Platform
NVIDIA CUDA platform
1 Compute Unified Device Architecture(CUDA) is NVIDIA’splatform for massively parallel high-performancecomputing on the NVIDIA GPUs.
2 Utilising Nsight Eclipse Edition 5 with CUDA 5 on LinuxMint 13 using two cards: GTX 560 Ti and GTX 660 Ti
by Dariusz Cieslakiewicz, Diane Wilcox, Tim Gebbie High-performance asset cluster analysis implemented with Parallel Genetic Algorithms on the NVIDIA CUDA platform
MotivationBackground
ApproachResults
References
Technical architecture
Outline
1 MotivationNon-parametric cluster analysis
2 BackgroundGenetic AlgorithmsGenetic operatorsParallel Genetic AlgorithmsComputing Platform
3 ApproachTechnical architecture
4 ResultsResults
5 References
by Dariusz Cieslakiewicz, Diane Wilcox, Tim Gebbie High-performance asset cluster analysis implemented with Parallel Genetic Algorithms on the NVIDIA CUDA platform
MotivationBackground
ApproachResults
References
Technical architecture
Physical View: Master-slave GA on the the NVIDIACUDA platform
by Dariusz Cieslakiewicz, Diane Wilcox, Tim Gebbie High-performance asset cluster analysis implemented with Parallel Genetic Algorithms on the NVIDIA CUDA platform
MotivationBackground
ApproachResults
References
Technical architecture
Physical View: Multiple-deme GA on the the NVIDIACUDA platform [Pospichal et al., 2010]
by Dariusz Cieslakiewicz, Diane Wilcox, Tim Gebbie High-performance asset cluster analysis implemented with Parallel Genetic Algorithms on the NVIDIA CUDA platform
MotivationBackground
ApproachResults
References
Technical architecture
Physical View: Migration of individuals betweenislands/demes [Pospichal et al., 2010]
by Dariusz Cieslakiewicz, Diane Wilcox, Tim Gebbie High-performance asset cluster analysis implemented with Parallel Genetic Algorithms on the NVIDIA CUDA platform
MotivationBackground
ApproachResults
References
Technical architecture
Genetic Operators
Crossover Operator
Single-Point, Two-Point and Custom Crossover implemented and executed at Pc of 0.6 and0.8-0.9.
Custom Crossover utilises a Single-Point Crossover approach with a knowledge directedoperator applying the following measure
f = arg max‖∏→1‖
[12∑
s:ns>1[log nscs
+ (ns − 1) log n2s−ns
n2s−cs
]
]
Mutation Operator
Mutation implemented with Pm at 1genomelength .
Replacement with randomly generated value.
by Dariusz Cieslakiewicz, Diane Wilcox, Tim Gebbie High-performance asset cluster analysis implemented with Parallel Genetic Algorithms on the NVIDIA CUDA platform
MotivationBackground
ApproachResults
References
Technical architecture
Migration Topologies
MigrationDeme Size : VariableMigration Topologies: Stepping Stone, One-Way Ring andRingMigration rate:
Variable Default: 2
by Dariusz Cieslakiewicz, Diane Wilcox, Tim Gebbie High-performance asset cluster analysis implemented with Parallel Genetic Algorithms on the NVIDIA CUDA platform
MotivationBackground
ApproachResults
References
Technical architecture
Implementation: Multiple-deme PGA I
1 Generic Framework for PGAs comprising 50 code artefactsto research different aspects of PGAs on GPUs.
2 Includes templatised C++ artefacts: Processing Context,Chromsome, Individual, SubPopulation, Population,Archipalego, etc.
by Dariusz Cieslakiewicz, Diane Wilcox, Tim Gebbie High-performance asset cluster analysis implemented with Parallel Genetic Algorithms on the NVIDIA CUDA platform
MotivationBackground
ApproachResults
References
Technical architecture
Implementation: Multiple-deme PGA II
by Dariusz Cieslakiewicz, Diane Wilcox, Tim Gebbie High-performance asset cluster analysis implemented with Parallel Genetic Algorithms on the NVIDIA CUDA platform
MotivationBackground
ApproachResults
References
Results
Outline
1 MotivationNon-parametric cluster analysis
2 BackgroundGenetic AlgorithmsGenetic operatorsParallel Genetic AlgorithmsComputing Platform
3 ApproachTechnical architecture
4 ResultsResults
5 References
by Dariusz Cieslakiewicz, Diane Wilcox, Tim Gebbie High-performance asset cluster analysis implemented with Parallel Genetic Algorithms on the NVIDIA CUDA platform
MotivationBackground
ApproachResults
References
Results
Master-Slave model
by Dariusz Cieslakiewicz, Diane Wilcox, Tim Gebbie High-performance asset cluster analysis implemented with Parallel Genetic Algorithms on the NVIDIA CUDA platform
MotivationBackground
ApproachResults
References
Results
Conclusion
Successfully implemented PGAs on the GPU.Speedups of more than 20x are attainable.Marsilli-Giada Log-likelihood function is a viable approachfor isolating residual clusters.
by Dariusz Cieslakiewicz, Diane Wilcox, Tim Gebbie High-performance asset cluster analysis implemented with Parallel Genetic Algorithms on the NVIDIA CUDA platform
MotivationBackground
ApproachResults
References
References I
Chen, D., Chen, W., and Zheng, W. (2012).Cuda-zero: a framework for porting shared memory gpuapplications to multi-gpus.SCIENCE CHINA Information Sciences, 55(3):663–676.
Coley, D. (1999).An Introduction to Genetic Algorithms for Scientists andEngineers.World Scientific.
Giada, L. and Marsili, M. (2001).Data clustering and noise undressing of correlationmatrices.Phys. Rev. E, 63:061101.
by Dariusz Cieslakiewicz, Diane Wilcox, Tim Gebbie High-performance asset cluster analysis implemented with Parallel Genetic Algorithms on the NVIDIA CUDA platform
MotivationBackground
ApproachResults
References
References II
Giada, L. and Marsili, M. (2002).Algorithms of maximum likelihood data clustering withapplications.Physica A: Statistical Mechanics and its Applications,315(3â4):650 – 664.
Hoberock, J. and Bell, N. (2010).Thrust: A parallel template library.Version 1.3.0.
by Dariusz Cieslakiewicz, Diane Wilcox, Tim Gebbie High-performance asset cluster analysis implemented with Parallel Genetic Algorithms on the NVIDIA CUDA platform
MotivationBackground
ApproachResults
References
References III
Langdon, W. B. (2011).Debugging cuda.In Proceedings of the 13th annual conference companionon Genetic and evolutionary computation, GECCO ’11,pages 415–422, New York, NY, USA. ACM.
Noh, J. (2000).Phys. Rev. E, 61.
NVIDIA (2012a).CUDA Toolkit 4.1 CURAND Guide.NVIDIA Corporation.
by Dariusz Cieslakiewicz, Diane Wilcox, Tim Gebbie High-performance asset cluster analysis implemented with Parallel Genetic Algorithms on the NVIDIA CUDA platform
MotivationBackground
ApproachResults
References
References IV
NVIDIA (2012b).NVIDIA CUDA C Programming Guide.NVIDIA Corporation.
Pospichal, P., Jaros, J., and Schwarz, J. (2010).Parallel genetic algorithm on the cuda architecture.In Proceedings of the 2010 international conference onApplications of Evolutionary Computation - Volume Part I,EvoApplicatons’10, pages 442–451, Berlin, Heidelberg.Springer-Verlag.
by Dariusz Cieslakiewicz, Diane Wilcox, Tim Gebbie High-performance asset cluster analysis implemented with Parallel Genetic Algorithms on the NVIDIA CUDA platform
MotivationBackground
ApproachResults
References
References V
Robilliard, D., Marion-Poty, V., and Fonlupt, C. (2009).Genetic programming on graphics processing units.Genetic Programming and Evolvable Machines,10(4):447–471.
Sivanandam, S. and Deepa, S. (2010).Introduction to Genetic Algorithms.Springer.
Xiao, S. and chun Feng, W.Inter-block gpu communication via fast barriersynchronization.
by Dariusz Cieslakiewicz, Diane Wilcox, Tim Gebbie High-performance asset cluster analysis implemented with Parallel Genetic Algorithms on the NVIDIA CUDA platform
MotivationBackground
ApproachResults
References
References VI
Zhang, S. and He, Z. (2009).Implementation of parallel genetic algorithm based oncuda.In Proceedings of the 4th International Symposium onAdvances in Computation and Intelligence, ISICA ’09,pages 24–30, Berlin, Heidelberg. Springer-Verlag.
by Dariusz Cieslakiewicz, Diane Wilcox, Tim Gebbie High-performance asset cluster analysis implemented with Parallel Genetic Algorithms on the NVIDIA CUDA platform
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