Optimized Back propagation Learning in Neural Networks with Bacterial Foraging Optimization to Predict Forex Gold Index (XAUUSD).
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Optimized Back propagation Learning in Neural
Networks with Bacterial Foraging Optimization to
Predict Forex Gold Index (XAUUSD)
I Made Bayu Permana Putra
Department of Information Technology
Udayana University, Bali, Indonesia
Rukmi Sari Hartati
Department of Electrical Engineering
Udayana University, Bali, Indonesia
I Ketut Gede Darma Putra
Department of Information Technology
Udayana University, Bali, Indonesia
Ni Kadek Ayu Wirdiani
Department of Information Technology
Udayana University, Bali, Indonesia
Copyright ©2014 I Made Bayu Permana Putra, Rukmi Sari Hartati, I Ketut Gede Darma Putra,
and Ni Kadek Ayu Wirdiani. This is an open access article distributed under the Creative
Commons Attribution License, which permits unrestricted use, distribution, and reproduction in
any medium, provided the original work is properly cited.
Abstract
This paper aims to build systems that can predict the gold price index with the
back propagation method so that the back propagation method can run faster and
get more accurate results. Back propagation method optimized in weight and bias
1848
I Made Bayu Permana Putra et al.
with bacterial foraging optimization. Proven by adding bacterial foraging
optimization method, it involve the back propagation method can run 50% faster
and accuracy increased 2% average. System performance testing was conducted
1000 times using many different data. Sample data and test data normalization is
immersely affect the system performance.
Keywords : back propagation, bacterial foraging optimization, forex.
1 Introduction
International monetary market needs important data to its trade from forex rate.
The index value is influenced by many factors such as economics and politics, and
also traders and investors psychological condition. All of that factors make the
gold index are very difficult to predict. People that involved in the field of
international monetary exchanges have been searching for an explanation to
improve the prediction ability. It is this ability to correctly predict gold index rate
changes that allows for the maximization of profits. Trading at the right time with
the relatively correct strategies can bring large profit, but a trade based on wrong
movement can risk big losses. Using the right analytical tool and good methods
can reduce the effect of mistakes and also can increase profitability [2][8].
Artificial neural networks has been extensively used in these days in various
aspects of science and engineering because of its ability to model both linear and
non-linear systems without the need to make assumptions as are implicit in most
traditional statistical approaches. ANN has been a aggressive model over the
simple linear regression model [1][5][9][10].Neural network algorithms can
predict foreign currency exchange rate. Because of back propagation algorithm is
used with AFERFM, which gives the 11.3 percentages more accurate than the
HFERFM[6].
BFO algorithm is a novel evolutionary computation algorithm, it is proposed
based on the foraging behavior of the Escherichia coli (E. coli) bacteria live in
human intestine. Natural selection tends to eliminate animals with poor foraging
strategies such as locating, handling and ingesting food and favor the propagation
of genes of those to achieve successful foraging [7]. The foraging behavior of
E.Coli bacteria is adopted for the evolutionary computation algorithm, and it is
named as Bacterial Foraging Optimization (BFO). BFO is an optimization
technique based on the population search and efficient for global search
method[3][4].
Optimized back propagation learning in neural networks
1849
2 Determination of the Architecture
Architecture determination is conducted to assign inputs number on neural,
hidden layer, output layer, sample data and test data date of use. The number of
input will affect to how many number of history data that will be used in back
propagation process. For example if the hidden layers input which entered is 5
and the date is 2011-01-01 to 2011-01-20, then the sample data that will be
formed after being normalized is as follow:
Table 1 Sample data
1 days ago 2 days ago
0.0820704 0.0936164
0.0885004 0.0820704
0.0910233 0.0885004
0.103515
0.0910233
0.111172
0.103515
3 days ago
0.102236
0.0936164
0.0820704
0.0885004
0.0910233
4 days ago
0.138942
0.102236
0.0936164
0.0820704
0.0885004
5 days ago
0.17167
0.138942
0.102236
0.0936164
0.0820704
today
0.088500
0.091023
0.103515
0.111172
0.109315
date
2011-01-10
2011-01-11
2011-01-12
2011-01-13
2011-01-14
3 Determination of the Bacteria Dimension
Bacterial foraging optimization will be optimized weight and bias before using
back propagation method, where weights and bias optimized result eventually will
be used in back propagation process. To determine cost value on bacterial
foraging optimization, it can be calculated with augment feed forward process.
Where dimensions of bacteria is weights and bias as on back propagation, then
data which included is average value per colom on sample data.
How many dimension of the bacteri is determined in accordance to neural
architectural, calculated as [3][4]:
Dimension = (Input × Hidden)+(Hidden × Output)+Hidden+ Output
Dimension = (3 × 2) + (2 × 1) + 2 + 1 = 11
Dimension of Bacteri
b1
b2
x1
b4
Backpropagation
b11
b7
b3
b10
b6
b8
b9
b5
y1
z
x2
y2
x3
Fig 1 Architectural BPBFO
I Made Bayu Permana Putra et al.
1850
The bacteria foraging optimization algorithm is:
1. Chemotaxis : Bacteria has a habit to move to approach a food source. This
process is the way how bacteria determine its movement between dip and fall
because of flagella. Bacteria will automatically move to an error optimum
(nutrient source). It contains two steps as follows: [3][4]:
Tumbling: Is the process how bacteria falls to the best nourishment
position, to get minimum errors of ANN[3][4].
√
Where
(3.1)
: Random vectors on [-1,1]
: The unit walk in the random direction C : Run length unit
√
: It may represent by P (i, j, k, ell)
: It may represent by P (i, j+1, k, ell) that represents
the next location of bacterial
Swimming: A Bacteria will move towards a certain direction that has a
growing number of nourishment (rich nourishment) [3][4].
2. Swarming: While bacteria is in a group, they have a censor from a dangerous
place, and automatically will stay y from it by following nutrient gradient that
generated by a group of bacteria that obtain nourishment [3][4].
(
∑
Where
∑
)
∑
∑
∑
(3.2)
depth attractant to set a magnitude of secretion of attractant by a cell
width attractant to set how the chemical cohesion signal diffuse
height repellant to set repellant
Reproduction : The fitness value from bacteria sequenced in the array
sequences that order the lowest value to the highest value [3][4].
∑
Where Nc is the chemotaxis steps and j is the value of error.
(3.3)
Optimized back propagation learning in neural networks
1851
Elimination and Dispersal: In the real world bacteria has probability and
spreads to a new location. Here begins by generating random vector.
[3][4].
4 Bacterial Foraging Optimization Optimized Back propagation
The optimized back propagation process plot with bacterial foraging optimization
is as follows:
Sample data
Initialization bacteria
Start BFO
BFO optimizes weights
BP Start training
BP weights and bias result
Fig 2 A Framework of the study
Sample data is calculated, the average is used in bacteri initialization process,
then the process is continued on bacterial training to detect the lowest cost value
which eventually that value is the weight value and the optimal bias. After
weights value and the optimal bias are found, it will be continued on back
propagation process to find the weights result and bias that will be used to predict.
5 Result of Experiment
Result of experiment with sample data and data test from 2011-01-01 to
2011-12-31 and 2012-01-01 to 2012-12-31. The architecture was formed by input
layer is 5, hiden layer is 10, output layer is 1. Bacterial foraging optimization
process that uses chemotaxis is 5, swim step is 5, reproduction is 4, dispersal is 4,
dispersal probability is 0.5, and movement size is 0.5. Back propagation learning
rate process is 0.05, momentum is 0.01, max epoch is 2000, means square error
target is 0.000001.
I Made Bayu Permana Putra et al.
1852
Table 2 Comparation BP with BPBFO
Sample
Method
Interaction
data
2011
BP
232460
2011
BPBFO
134225
2012
BP
51744
2012
BPBFO
31458
epoch
mse
788
455
176
107
0.0000008
0.0000007
0.0000006
0.0000005
time
(second)
216
141
43
26
Accuration
Rate
92,43%
94,60%
95,20%
96,26%
Table 2 shows the processing result of back propagation method and the
back propagation method was developed by bacterial foraging optimization and
comparation between the result accuracy from back propagation method and back
propagation method that optimized with bacterial foraging optimization.
(a)
(b)
Fig 3 (a) BP Result, (b) BPBFO Result test data 2011
(a)
(b)
Fig 4 (a) BP Result, (b) BPBFO Result test data 2012
Fig 3 and fig 4 shows the comparison of test data and the predicted results
where the red line is the target of the data test and the blue line is the predicted
outcome.
6 Conclusion
This experiment concludes that predicting gold price can be conducted by
mathematics methods with using data history from the gold price index. The
selection of the sample data architecture and great influence in the prediction
Optimized back propagation learning in neural networks
1853
results by using back propagation. Sample and data test should be tested against
the data history of stable gold index is not in a state of crisis. Proved that after
optimized with bacterial foraging optimization method it get significantly better in
terms of iterating, epoch, and the value of accuracy. Forex gold index prediction
can be developed with another neural network method to give better accuration. In
further developments, this paper is expected to be a reference in the development
of other forex gold index prediction to make better accurate prediction.
References
[1] T. Abe and T. Saito. An approach to prediction of spatio-temporal patterns
based on binary neural networks and cellular automata. IEEE International
Joint Conference on Neural Networks. 2008; 2494-2499.
[2] Abraham, Ajith and Chowdhury, Morshed U. “An Intelligent FOREX
Monitoring System.” In Proceedings of IEEE International Conference on
Info-tech and Infonet, Beijing, China, pp 523-528, 2001.
[3] I. AL-Hadi, S.Z. Hashim and S.M. Shamsuddin, Bacterial Foraging
Optimization Algorithm for neural network learning enhancement.
978-1-4577-2152-6/11/$26.00 ©2011 IEEE.
[4] I. AL-Hadi, Siti Zaiton. Bacterial Foraging Optimization Algorithm For
Neural Network Learning Enhancement. International Journal of Innovative
Computing 01(1) 8-14. 2012.
[5] O. Deperlioglu and Utku Kose. An educational tool for artificial neural
networks. Computers and Electrical Engineering. 2011; 37: 392-402.
[6] R. Divyapria. 2013. Accurate Forecasting Prediction of Foreign Exchange
Rate Using Neural Network Algorithms. (IJCSMC) International Journal of
Computer Science and Mobile Computing. Vol. 2, Issue. 7, July 2013,
pg.344 – 349
[7] D. Hwa Kim, Ajith Abraham, Jae Hoon Cho A hybrid genetic algorithm and
bacterial foraging approach for global optimization, Information Sciences
177 (2007) 3918–3937
[8] V Lavanya and M Parveentaj. “Foreign Currency Exchange Rate (FOREX)
using Neural Network” International Journal of Science and Research (IJSR
2013) ISSN (Online): 2319-7064.
1854
I Made Bayu Permana Putra et al.
[9] S.Lee, S.Cho and P.M. Wong 1998,”Rainfall prediction using Artificial
neural networks”. journal of geographic information and Decision Analysis,
Vol .2,No2,pp.233-242
[10] H Zhao, J Zhang. Pipelined Chebyshev Functional Link Artificial Recurrent
Neural Network for Nonlinear Adaptive Filter. IEEE Trans. Systems, Man,
and Cybernetics, Part B: Cybernetics. 2010; 40:162-172.
Received: February 11, 2014
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doi:10.12988/ams
ISSN 1312-885X (Print)
ISSN 1314-7552 (Online)
APPLIED
MATHEMATICAL SCIENCES
Journal for Theory and Applications
Editorial Board
K. S. Berenhaut (USA)
Nguyen Buong (Vietnam)
G. Caristi (Italy)
N. Cercone (Canada)
Ping-Teng Chang (Taiwan)
W. Y. C. Chen (China)
K. W. Chow (China)
M. Darus (Malaysia)
M. Ferrara (Italy)
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V. Kreinovich (USA)
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I Made Bayu Permana Putra, Rukmi Sari Hartati, I Ketut Gede Darma Putra, Ni Kadek Ayu Wirdiani
Optimized back propagation learning in neural networks with bacterial foraging optimization to predict forex gold index (XAUUSD)
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Applied Mathematical Sciences, Vol. 8, 2014, no. 38, 1847 - 1854
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http://dx.doi.org/10.12988/ams.2014.4292
Optimized Back propagation Learning in Neural
Networks with Bacterial Foraging Optimization to
Predict Forex Gold Index (XAUUSD)
I Made Bayu Permana Putra
Department of Information Technology
Udayana University, Bali, Indonesia
Rukmi Sari Hartati
Department of Electrical Engineering
Udayana University, Bali, Indonesia
I Ketut Gede Darma Putra
Department of Information Technology
Udayana University, Bali, Indonesia
Ni Kadek Ayu Wirdiani
Department of Information Technology
Udayana University, Bali, Indonesia
Copyright ©2014 I Made Bayu Permana Putra, Rukmi Sari Hartati, I Ketut Gede Darma Putra,
and Ni Kadek Ayu Wirdiani. This is an open access article distributed under the Creative
Commons Attribution License, which permits unrestricted use, distribution, and reproduction in
any medium, provided the original work is properly cited.
Abstract
This paper aims to build systems that can predict the gold price index with the
back propagation method so that the back propagation method can run faster and
get more accurate results. Back propagation method optimized in weight and bias
1848
I Made Bayu Permana Putra et al.
with bacterial foraging optimization. Proven by adding bacterial foraging
optimization method, it involve the back propagation method can run 50% faster
and accuracy increased 2% average. System performance testing was conducted
1000 times using many different data. Sample data and test data normalization is
immersely affect the system performance.
Keywords : back propagation, bacterial foraging optimization, forex.
1 Introduction
International monetary market needs important data to its trade from forex rate.
The index value is influenced by many factors such as economics and politics, and
also traders and investors psychological condition. All of that factors make the
gold index are very difficult to predict. People that involved in the field of
international monetary exchanges have been searching for an explanation to
improve the prediction ability. It is this ability to correctly predict gold index rate
changes that allows for the maximization of profits. Trading at the right time with
the relatively correct strategies can bring large profit, but a trade based on wrong
movement can risk big losses. Using the right analytical tool and good methods
can reduce the effect of mistakes and also can increase profitability [2][8].
Artificial neural networks has been extensively used in these days in various
aspects of science and engineering because of its ability to model both linear and
non-linear systems without the need to make assumptions as are implicit in most
traditional statistical approaches. ANN has been a aggressive model over the
simple linear regression model [1][5][9][10].Neural network algorithms can
predict foreign currency exchange rate. Because of back propagation algorithm is
used with AFERFM, which gives the 11.3 percentages more accurate than the
HFERFM[6].
BFO algorithm is a novel evolutionary computation algorithm, it is proposed
based on the foraging behavior of the Escherichia coli (E. coli) bacteria live in
human intestine. Natural selection tends to eliminate animals with poor foraging
strategies such as locating, handling and ingesting food and favor the propagation
of genes of those to achieve successful foraging [7]. The foraging behavior of
E.Coli bacteria is adopted for the evolutionary computation algorithm, and it is
named as Bacterial Foraging Optimization (BFO). BFO is an optimization
technique based on the population search and efficient for global search
method[3][4].
Optimized back propagation learning in neural networks
1849
2 Determination of the Architecture
Architecture determination is conducted to assign inputs number on neural,
hidden layer, output layer, sample data and test data date of use. The number of
input will affect to how many number of history data that will be used in back
propagation process. For example if the hidden layers input which entered is 5
and the date is 2011-01-01 to 2011-01-20, then the sample data that will be
formed after being normalized is as follow:
Table 1 Sample data
1 days ago 2 days ago
0.0820704 0.0936164
0.0885004 0.0820704
0.0910233 0.0885004
0.103515
0.0910233
0.111172
0.103515
3 days ago
0.102236
0.0936164
0.0820704
0.0885004
0.0910233
4 days ago
0.138942
0.102236
0.0936164
0.0820704
0.0885004
5 days ago
0.17167
0.138942
0.102236
0.0936164
0.0820704
today
0.088500
0.091023
0.103515
0.111172
0.109315
date
2011-01-10
2011-01-11
2011-01-12
2011-01-13
2011-01-14
3 Determination of the Bacteria Dimension
Bacterial foraging optimization will be optimized weight and bias before using
back propagation method, where weights and bias optimized result eventually will
be used in back propagation process. To determine cost value on bacterial
foraging optimization, it can be calculated with augment feed forward process.
Where dimensions of bacteria is weights and bias as on back propagation, then
data which included is average value per colom on sample data.
How many dimension of the bacteri is determined in accordance to neural
architectural, calculated as [3][4]:
Dimension = (Input × Hidden)+(Hidden × Output)+Hidden+ Output
Dimension = (3 × 2) + (2 × 1) + 2 + 1 = 11
Dimension of Bacteri
b1
b2
x1
b4
Backpropagation
b11
b7
b3
b10
b6
b8
b9
b5
y1
z
x2
y2
x3
Fig 1 Architectural BPBFO
I Made Bayu Permana Putra et al.
1850
The bacteria foraging optimization algorithm is:
1. Chemotaxis : Bacteria has a habit to move to approach a food source. This
process is the way how bacteria determine its movement between dip and fall
because of flagella. Bacteria will automatically move to an error optimum
(nutrient source). It contains two steps as follows: [3][4]:
Tumbling: Is the process how bacteria falls to the best nourishment
position, to get minimum errors of ANN[3][4].
√
Where
(3.1)
: Random vectors on [-1,1]
: The unit walk in the random direction C : Run length unit
√
: It may represent by P (i, j, k, ell)
: It may represent by P (i, j+1, k, ell) that represents
the next location of bacterial
Swimming: A Bacteria will move towards a certain direction that has a
growing number of nourishment (rich nourishment) [3][4].
2. Swarming: While bacteria is in a group, they have a censor from a dangerous
place, and automatically will stay y from it by following nutrient gradient that
generated by a group of bacteria that obtain nourishment [3][4].
(
∑
Where
∑
)
∑
∑
∑
(3.2)
depth attractant to set a magnitude of secretion of attractant by a cell
width attractant to set how the chemical cohesion signal diffuse
height repellant to set repellant
Reproduction : The fitness value from bacteria sequenced in the array
sequences that order the lowest value to the highest value [3][4].
∑
Where Nc is the chemotaxis steps and j is the value of error.
(3.3)
Optimized back propagation learning in neural networks
1851
Elimination and Dispersal: In the real world bacteria has probability and
spreads to a new location. Here begins by generating random vector.
[3][4].
4 Bacterial Foraging Optimization Optimized Back propagation
The optimized back propagation process plot with bacterial foraging optimization
is as follows:
Sample data
Initialization bacteria
Start BFO
BFO optimizes weights
BP Start training
BP weights and bias result
Fig 2 A Framework of the study
Sample data is calculated, the average is used in bacteri initialization process,
then the process is continued on bacterial training to detect the lowest cost value
which eventually that value is the weight value and the optimal bias. After
weights value and the optimal bias are found, it will be continued on back
propagation process to find the weights result and bias that will be used to predict.
5 Result of Experiment
Result of experiment with sample data and data test from 2011-01-01 to
2011-12-31 and 2012-01-01 to 2012-12-31. The architecture was formed by input
layer is 5, hiden layer is 10, output layer is 1. Bacterial foraging optimization
process that uses chemotaxis is 5, swim step is 5, reproduction is 4, dispersal is 4,
dispersal probability is 0.5, and movement size is 0.5. Back propagation learning
rate process is 0.05, momentum is 0.01, max epoch is 2000, means square error
target is 0.000001.
I Made Bayu Permana Putra et al.
1852
Table 2 Comparation BP with BPBFO
Sample
Method
Interaction
data
2011
BP
232460
2011
BPBFO
134225
2012
BP
51744
2012
BPBFO
31458
epoch
mse
788
455
176
107
0.0000008
0.0000007
0.0000006
0.0000005
time
(second)
216
141
43
26
Accuration
Rate
92,43%
94,60%
95,20%
96,26%
Table 2 shows the processing result of back propagation method and the
back propagation method was developed by bacterial foraging optimization and
comparation between the result accuracy from back propagation method and back
propagation method that optimized with bacterial foraging optimization.
(a)
(b)
Fig 3 (a) BP Result, (b) BPBFO Result test data 2011
(a)
(b)
Fig 4 (a) BP Result, (b) BPBFO Result test data 2012
Fig 3 and fig 4 shows the comparison of test data and the predicted results
where the red line is the target of the data test and the blue line is the predicted
outcome.
6 Conclusion
This experiment concludes that predicting gold price can be conducted by
mathematics methods with using data history from the gold price index. The
selection of the sample data architecture and great influence in the prediction
Optimized back propagation learning in neural networks
1853
results by using back propagation. Sample and data test should be tested against
the data history of stable gold index is not in a state of crisis. Proved that after
optimized with bacterial foraging optimization method it get significantly better in
terms of iterating, epoch, and the value of accuracy. Forex gold index prediction
can be developed with another neural network method to give better accuration. In
further developments, this paper is expected to be a reference in the development
of other forex gold index prediction to make better accurate prediction.
References
[1] T. Abe and T. Saito. An approach to prediction of spatio-temporal patterns
based on binary neural networks and cellular automata. IEEE International
Joint Conference on Neural Networks. 2008; 2494-2499.
[2] Abraham, Ajith and Chowdhury, Morshed U. “An Intelligent FOREX
Monitoring System.” In Proceedings of IEEE International Conference on
Info-tech and Infonet, Beijing, China, pp 523-528, 2001.
[3] I. AL-Hadi, S.Z. Hashim and S.M. Shamsuddin, Bacterial Foraging
Optimization Algorithm for neural network learning enhancement.
978-1-4577-2152-6/11/$26.00 ©2011 IEEE.
[4] I. AL-Hadi, Siti Zaiton. Bacterial Foraging Optimization Algorithm For
Neural Network Learning Enhancement. International Journal of Innovative
Computing 01(1) 8-14. 2012.
[5] O. Deperlioglu and Utku Kose. An educational tool for artificial neural
networks. Computers and Electrical Engineering. 2011; 37: 392-402.
[6] R. Divyapria. 2013. Accurate Forecasting Prediction of Foreign Exchange
Rate Using Neural Network Algorithms. (IJCSMC) International Journal of
Computer Science and Mobile Computing. Vol. 2, Issue. 7, July 2013,
pg.344 – 349
[7] D. Hwa Kim, Ajith Abraham, Jae Hoon Cho A hybrid genetic algorithm and
bacterial foraging approach for global optimization, Information Sciences
177 (2007) 3918–3937
[8] V Lavanya and M Parveentaj. “Foreign Currency Exchange Rate (FOREX)
using Neural Network” International Journal of Science and Research (IJSR
2013) ISSN (Online): 2319-7064.
1854
I Made Bayu Permana Putra et al.
[9] S.Lee, S.Cho and P.M. Wong 1998,”Rainfall prediction using Artificial
neural networks”. journal of geographic information and Decision Analysis,
Vol .2,No2,pp.233-242
[10] H Zhao, J Zhang. Pipelined Chebyshev Functional Link Artificial Recurrent
Neural Network for Nonlinear Adaptive Filter. IEEE Trans. Systems, Man,
and Cybernetics, Part B: Cybernetics. 2010; 40:162-172.
Received: February 11, 2014
8/10/2014
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1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
Data
2011
2012
0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,136 0,270 0,235
Total Documents
0
0
0
0
0
0
0
0
0
0
260
307
351
617
Total Docs. (3years)
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0
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0
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0
0
0
260
567
918
Total References
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0
0
0
0
0
0
0
0
3.242 4.092 4.821 8.581
Total Cites (3years)
0
0
0
0
0
0
0
0
0
0
0
55
251
Self Cites (3years)
0
0
0
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0
0
0
0
0
0
0
11
44
382
88
Citable Docs. (3years)
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0
0
0
0
0
0
0
0
0
0
260
566
917
Cites / Doc. (4years)
0,00
0,00
0,00
0,00
0,00
0,00
0,00
0,00
0,00
0,00
0,00
0,21
0,44
0,42
Cites / Doc. (3years)
0,00
0,00
0,00
0,00
0,00
0,00
0,00
0,00
0,00
0,00
0,00
0,21
0,44
0,42
Cites / Doc. (2years)
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0,00
0,00
0,00
0,00
0,00
0,00
0,00
0,00
0,00
0,00
0,21
0,44
0,46
References / Doc.
0,00 0,00 0,00 0,00 0,00
0,00 0,00
0,00
0,00
12,47 13,33
13,74src="http://www.scim
13,91