Table Of ContentSPRINGER BRIEFS IN APPLIED SCIENCES AND
TECHNOLOGY COMPUTATIONAL INTELLIGENCE
João Baúto · Rui Neves · Nuno Horta
Parallel Genetic
Algorithms for
Financial Pattern
Discovery Using
GPUs
123
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ã ú
Jo o Ba to Rui Neves Nuno Horta
(cid:129) (cid:129)
Parallel Genetic Algorithms
for Financial Pattern
Discovery Using GPUs
123
João Baúto Nuno Horta
Instituto Superior Técnico Instituto Superior Técnico
Instituto deTelecomunicações Instituto deTelecomunicações
Lisbon Lisbon
Portugal Portugal
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Instituto Superior Técnico
Instituto deTelecomunicações
Lisbon
Portugal
ISSN 2191-530X ISSN 2191-5318 (electronic)
SpringerBriefs inApplied SciencesandTechnology
ISSN 2520-8551 ISSN 2520-856X (electronic)
SpringerBriefs inComputational Intelligence
ISBN978-3-319-73328-9 ISBN978-3-319-73329-6 (eBook)
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To Maria, Manuel and Miguel
João Baúto
To Susana and Tiago
Rui Neves
To Carla, João and Tiago
Nuno Horta
Preface
Thefinancialmarketsmovevastamountsofcapitalaroundtheworld.Thisfactand
the easy access to trading in a manual or automatic way that creates a more
accessiblewaytoparticipateinthemarketsactivityattractedtheinterestofalltype
ofinvestors,fromthe“manonthestreet”toacademicresearchers.Thistypeofnew
investorsandtheautomatictradingsystemsinfluencethemarketbehavior.Inorder
to adapt to this new reality, the domain of computational finance has received an
increasing attention by people from both finance and computational intelligence
domains.
Themaindrivingforceinthefieldofcomputationalfinance,withapplicationto
financial markets, is to define highly profitable and less risky trading strategies. In
order to accomplish this main objective, the defined strategies must process large
amounts of data which include financial markets time series, fundamental analysis
data, technical analysis data. and produce appropriate buy and sell signals for the
selected financial market securities. What may appear, at a first glance, as an easy
problemis,infact,ahugeandhighlycomplexoptimizationproblem,whichcannot
besolvedanalytically.Therefore,thismakesthesoftcomputingandingeneralthe
computational intelligence domains especially appropriate for addressing the
problem.
Theuseofchartpatternsiswidelyspreadamongtradersasanadditionaltoolfor
decision making. The chartists, as these analysts are known, try to identify some
known pattern formations and based on previous appearances try to predict future
markettrends.Thevisualpatternidentificationishardandlargelysubjecttoerrors,
andpatternsinthefinancialtimeseriesarenotascleanastheimagesinthebooks,
sotheneedtocreatesomesolutionthathelpsonthistaskwillalwaysbewelcomed.
Together,withthis,thegeneralavailabilityofGPUboards,today,presentsitselfas
an excellent alternative execution system, to traditional CPU architectures, to cope
with high-speed processing requirements at relatively low cost.
Thisworkexploresthebenefitsofputtingtogetheralow-costhigh-performance
computingsolution,aGPU-basedarchitecture,andastate-of-the-artcomputational
financeapproach,SAX/GAwhichcombinesaSymbolicAggregateapproXimation
(SAX) technique together with an optimization kernel based ongeneticalgorithms
vii
viii Preface
(GA). The SAX representation is used to describe the financial time series, so that
relevantpatterns canbeefficientlyidentified.The evolutionaryoptimizationkernel
is here used to identify the most relevant patterns and generate investment rules.
The SAX technique uses an alphabetic symbolic representation of data defined by
adjustable parameters. In order to capture and preserve the essence of the
explored financial time series, a search for the optimal combination of SAX
parameters is presented. The proposed approach considers a tailored implementa-
tionoftheSAX/GAtechniquetoaGPU-basedarchitectureinordertoimprovethe
computational efficiency of the referenced approach. This approach was tested
using real data from S&P500. The achieved results show that the proposed
approach outperforms CPU alternative with speed gains reaching 200 times faster.
The book is organized in five chapters as follows:
(cid:129) Chapter1presentsabriefdescriptionontheproblematicaddressedbythisbook,
namely the investment optimization based on pattern discovery techniques and
high-performance computing based on GPU architectures. Additionally, the
main goals for the work presented in this book as well as the document’s
structure are, also, highlighted in this chapter.
(cid:129) Chapter 2 discusses fundamental concepts, key to understand the proposed
work, such as pattern recognition or matching, GAs and GPUs.
(cid:129) Chapter3presentsareviewofthestate-of-the-artpatternrecognitiontechniques
with practical application examples.
(cid:129) Chapter 4 addresses the CPU implementation of the SAX/GA algorithm along
with a detailed explanation of the genetic operators involved. A benchmark
analysis discusses the performance of SAX/GA and introduces possible loca-
tions to accelerate the algorithm.
(cid:129) Chapter 5 presents the developed solutions along with previous attempts to
accelerate the SAX/GA algorithm. Each solution started as a prototype that
evolved based on the advantages and disadvantages identified.
(cid:129) Chapter 6 discusses the experimental results obtained for each solution and
comparesthemtotheoriginalimplementation.Solutionsareevaluatedbasedon
two metrics, the speedup and the ROI indicator.
(cid:129) Chapter 7 summarizes the provided book and supplies the respective
conclusions and future work.
Lisbon, Portugal João Baúto
Rui Neves
Nuno Horta
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Goals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Book Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1 Time Series Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.1 Euclidean Distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.2 Dynamic Time Warping. . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1.3 Piecewise Linear Approximation. . . . . . . . . . . . . . . . . . . . 6
2.1.4 Piecewise Aggregate Approximation. . . . . . . . . . . . . . . . . 7
2.1.5 Symbolic Aggregate approXimation . . . . . . . . . . . . . . . . . 8
2.2 Genetic Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2.1 Selection Operator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.2 Crossover Operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.3 Mutation Operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3 Graphics Processing Units. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3.1 NVIDIA’s GPU Architecture Overview. . . . . . . . . . . . . . . 13
2.3.2 NVIDIA’s GPU Architectures. . . . . . . . . . . . . . . . . . . . . . 15
2.3.3 CUDA Architecture. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3 State-of-the-Art in Pattern Recognition Techniques . . . . . . . . . . . . . 21
3.1 Middle Curve Piecewise Linear Approximation . . . . . . . . . . . . . . 21
3.2 Perceptually Important Points . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.3 Turning Points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
ix
x Contents
3.4 Symbolic Aggregate approXimation. . . . . . . . . . . . . . . . . . . . . . . 28
3.5 Shapelets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4 SAX/GA CPU Approach. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.1 SAX/GA CPU Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.1.1 Population Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.1.2 Fitness Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.1.3 Population Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.1.4 Chromosome Crossover . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.1.5 Individual Mutation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.2 SAX/GA Performance Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
5 GPU-Accelerated SAX/GA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
5.1 Parallel SAX Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
5.1.1 Prototype 1: SAX Transformation On-Demand . . . . . . . . . 45
5.1.2 Prototype 2: Speculative FSM . . . . . . . . . . . . . . . . . . . . . 47
5.1.3 Solution A: SAX/GA with Speculative GPU
SAX Transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
5.2 Parallel Dataset Training. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5.2.1 Prototype 3: Parallel SAX/GA Training . . . . . . . . . . . . . . 55
5.2.2 Solution B: Parallel SAX/GA Training with GPU
Fitness Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.3 Fully GPU-Accelerated SAX/GA. . . . . . . . . . . . . . . . . . . . . . . . . 60
5.3.1 Population Generation Kernel. . . . . . . . . . . . . . . . . . . . . . 61
5.3.2 Population Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.3.3 Gene Crossover Kernel . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.3.4 Gene Mutation Kernel . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.3.5 Execution Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
Reference. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
6 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
6.1 SAX/GA Initial Constraints. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
6.2 Study Case A: Execution Time . . . . . . . . . . . . . . . . . . . . . . . . . . 68
6.2.1 Solution A: SAX/GA with Speculative FSM. . . . . . . . . . . 68
6.2.2 Solution B: Parallel Dataset Training . . . . . . . . . . . . . . . . 74
6.2.3 Solution C: Fully GPU-Accelerated SAX/GA . . . . . . . . . . 77
6.3 Study Case B: FSM Prediction Rate . . . . . . . . . . . . . . . . . . . . . . 81
