dr m f abbod using intelligent optimisation methods to improve the group method of data handling in...
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Dr M F Abbod
Using Intelligent Optimisation Methods to Improve the Group Method
of Data Handling in Time Series Prediction
Maysam Abbod and Karishma Dashpande
School of Engineering and DesignBrunel University, West London
Dr M F Abbod
Outline
• GMDH
• Genetic Algorithms
• Particle Swarm Optimisation
• Financial Data
• Prediction Results
• Conclusions
Dr M F Abbod
Introduction
• The GMDH is an algorithm to learn inductively, combinatorial multi-layers for modelling complex systems.
• The method was introduced by A. G. Ivakhnenko in 1966 and several scholars has since developed the theory GMDH for various applications.
Dr M F Abbod
GMDH
An important feature of the algorithm GMDH is providing robust polynomial regression models of linear and non-linear systems.
Dr M F Abbod
Principle of Selection
Ivakhnenko uses the principles of selectivity - "to get plants, for example, with certain properties, there is the first cross and then the first harvest. Later picks up the best plants and it is the second crossing and the second harvest and thus to find a plant that is desired. "
Dr M F Abbod
GMDHGMDH-layers
All combinations of inputs are generated and issued the first layer of the network. The outputs of these are classified and then selected for entry into the next layer with all combinations of selected outlets.
Only those elements whose performance was acceptable survive to form the next layer.
This process is continued as long as each layer (n +1) subsequent produce a better result than the layer (n). When the layer (n +1) is not better as the layer (n), the process is stopped.
Dr M F Abbod
SELECTION 1
SELECTION 2
x1 x2 x3 x4 . . . xn
y1 y2 y3 . . . yn
A11
A12
A13
A1n
A21
A22
A23
A2n
Layer 1 Layer 2
.
.
.
.
.
.
GMDH
Dr M F Abbod
• GMDHEach layer consists of Polynomial Equation generated from combinations of pairs of inputs. Each node is the way Ivakhnenko polynomial which is a polynomial of the second order:
The error we are computed by RMSE and MAPE:
The Choice of Plymomial Eq
%1001
1
n
i i
ii
y
zy
nMAPE
n
iii zy
nRMSE
1
21
ijijjjjiiijjii xaxaxaxaxaay 22
Dr M F Abbod
The Coefficients
Determining the values that can produce the best adjustment of the equation
Dr M F Abbod
Genetic Algorithms
It was developed by Goldberg in 1989.
Genetic Algorithms (GAs) are randomised search and optimisation techniques guided by the principles of evolution and natural genetics
Dr M F Abbod
Genetic Algorithms
• Chromosomes are an encoded representations of the solutions, each gene represents a feature
• A fitness value that reflects how good it is
• A crossover mechanism that exchanges portions between strings
• Mutation plays the role of regenerating lost genetic material
Dr M F Abbod
Particle Swarm OptimisationRules of movement – the formulas:
)()()()1( 21 xgxptvtv
)1()()1( tvtxtx
x
y
Dr M F Abbod
The Data• USD2EURO from 29
Sept, 2004 to 5 Oct, 2007.
• GBP2USD from 29 Sept, 2004 to 5 Oct, 2007.
• www.oanda.com 1.7
1.75
1.8
1.85
1.9
1.95
2
2.05
2.1
Jan-
04
Mar
-04
May
-04
Jul-04
Sep-
04
Nov
-04
Jan-
05
Mar
-05
May
-05
Jul-05
Sep-
05
Nov
-05
Jan-
06
Mar
-06
May
-06
Jul-06
Sep-
06
Nov
-06
Jan-
07
Mar
-07
May
-07
Jul-07
Sep-
07
Date
Exc
hang
e R
ate
ll
0.7
0.72
0.74
0.76
0.78
0.8
0.82
0.84
0.86
0.88
Jan-
04
Mar
-04
May
-04
Jul-04
Sep-
04
Nov
-04
Jan-
05
Mar
-05
May
-05
Jul-05
Sep-
05
Nov
-05
Jan-
06
Mar
-06
May
-06
Jul-06
Sep-
06
Nov
-06
Jan-
07
Mar
-07
May
-07
Jul-07
Sep-
07
Date
Exc
hang
e R
ate
ll
Dr M F Abbod
The Data
• 2 data sets (GBP2USD & USD2EUR)
• 120 Data points
• 100 for training
• 20 for testing
Dr M F Abbod
Training Data Performance
USD2EUR GBP2USD Algorithm type
MAPE RMSE MAPE RMSE
GMDH 0.31024 0.0035959 0.29232 0.0076715
PSO-GMDH gbest 0.30258 0.0035831 0.29009 0.0076768
PSO-GMDH lbest 0.30351 0.0035822 0.29024 0.0076835
GA-GMDH 0.30553 0.0036046 0.29429 0.0076953
GA-PSO-GMDH 0.30198 0.0035611 0.29006 0.0076707
Dr M F Abbod
GMDH
GMDH predictions on testing set for (a) USD2EUR, and (b) GBP2USD
Dr M F Abbod
PSO-GMDH (gbest)
PSO-GMDH gbest model predictions on testing set for (a) USD2EUR and (b) GBP2USD
Dr M F Abbod
PSO-GMDH (lbest)
PSO-GMDH lbest model predictions on testing set for(a) USD2EUR and (b) GBP2USD
Dr M F Abbod
GA-GMDH
GA-GMDH predictions on testing set for
(a) USD2EUR, and (b) GBP2USD
Dr M F Abbod
GA-PSO-GMDH
GA-PSO-GMDH predictions on testing set for
(a) USD2EUR and (b) GBP2USD
Dr M F Abbod
Testing Data Performance
USD2EUR GBP2USD Algorithm type
MAPE RMSE MAPE RMSE
GMDH 0.18276 0.0017923 0.17727 0.0049046
PSO-GMDH gbest 0.16956 0.0017084 0.17718 0.0048962
PSO-GMDH lbest 0.16709 0.0016749 0.17705 0.0049657
GA-GMDH 0.17630 0.0017688 0.17809 0.0050035
GA-PSO-GMDH 0.16537 0.0016672 0.17592 0.0048144
Dr M F Abbod
USD2EUR
0.7
0.71
0.72
0.73
0.74
0.75
0.76
20/0
4/2
007
04/0
5/2
007
18/0
5/2
007
01/0
6/2
007
15/0
6/2
007
29/0
6/2
007
13/0
7/2
007
27/0
7/2
007
10/0
8/2
007
24/0
8/2
007
07/0
9/2
007
21/0
9/2
007
Date
Exchange R
ate
US
D2E
UR
a
Actual GMDH GA PSO lbest PSO gbest GA-PSO
Dr M F Abbod
GBP2USD
1.92
1.94
1.96
1.98
2
2.02
2.04
2.06
2.08
20/0
4/2
007
04/0
5/2
007
18/0
5/2
007
01/0
6/2
007
15/0
6/2
007
29/0
6/2
007
13/0
7/2
007
27/0
7/2
007
10/0
8/2
007
24/0
8/2
007
07/0
9/2
007
21/0
9/2
007
Date
Exchange R
ate
GB
P2U
SD
a
Actual GMDH GA PSO lbest PSO gbest GA-PSO
Dr M F Abbod
Performance Improvements
USD2EUR % improvement
GBP2USD % improvement Algorithm type
MAPE RMSE MAPE RMSE
PSO-GMDH gbest 7.22 4.68 0.05 0.17
PSO-GMDH lbest 8.57 6.55 0.12 -1.24
GA-GMDH 3.53 1.31 -0.46 -2.01
GA-PSO-GMDH 9.52 6.98 0.76 1.84
Dr M F Abbod
Computational Requirements
Algorithm type Number of layers Computation Time (sec)
GMDH 2 0.36
PSO-GMDH gbest 4 73.91
PSO-GMDH lbest 2 312.76
GA-GMDH 4 3694.88
GA-PSO-GMDH 4 3039.18
Dr M F Abbod
Conclusions
• Improvements can be achieved
• Model Complexity and Computational burden
• Parallel Processing (Matlab: Parallel Computing Toolbox)
• Other data sets
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