Supervised vs. unsupervised learning for construction

Automation in Construction 22 (2012) 271–276

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Automation in Construction journal homepage: www.elsevier.com/locate/autcon

Supervised vs. unsupervised learning for construction crew productivity prediction Mustafa Oral a,⁎, Emel Laptali Oral b, Ahmet Aydın c a b c

Çukurova Üniversitesi, Mühendislik Mimarlık Fakültesi, Bilgisayar Mühendisliği Bölümü, Balcalı, Adana, Turkey Çukurova Üniversitesi, Mühendislik Mimarlık Fakültesi, İnşaat Mühendisliği Bölümü, Balcalı, Adana, Turkey Çukurova Üniversitesi, Mühendislik Mimarlık Fakültesi, Elektrik Elektronik Mühendisliği Bölümü, Balcalı, Adana, Turkey

a r t i c l e

i n f o

Article history: Accepted 16 September 2011 Available online 24 October 2011 Keywords: Supervised learning Unsupervised learning Self Organizing Maps Construction crew Productivity

a b s t r a c t Complex variability is a significant problem in predicting construction crew productivity. Neural Networks using supervised learning methods like Feed Forward Back Propagation (FFBP) and General Regression Neural Networks (GRNN) have proved to be more advantageous than statistical methods like multiple regression, considering factors like the modelling ease and the prediction accuracy. Neural Networks using unsupervised learning like Self Organizing Maps (SOM) have additionally been introduced as methods that overcome some of the weaknesses of supervised learning methods through their clustering ability. The objective of this article is thus to compare the performances of FFBP, GRNN and SOM in predicting construction crew productivity. Related data has been collected from 117 plastering crews through a systematized time study and comparison of prediction performances of the three methods showed that SOM have a superior performance in predicting plastering crew productivity. © 2011 Elsevier B.V. All rights reserved.

1. Introduction Realistic project scheduling is one of the vital issues for successful completion of construction projects and this can only be achieved if schedules are based on realistic man-hour values. Yet, determination of realistic man-hour values has been a complicated issue due to the complex variability of construction labor productivity [1–9]. Thus, recent researches have focused on artificial neural network applications which provide a flexible environment to deal with such kind of variability. These applications have been based on supervised learning methods, primarily Feed Forward Back Propagation (FFBP) [1–2,10–18], and recently General Regression Neural Network (GRNN) [19–20]. While strengths of these methods over multiple regression models, related with the modeling ease and the prediction accuracy, have been well discussed; the weaknesses of the supervised learning process, i.e. requiring the output vector to be known for training, has also been pointed out [21–22]. In parallel, Self Organizing Maps (SOM), based on unsupervised learning, have been introduced as applications which overcome the weaknesses of both the statistical methods and the neural network applications based on supervised learning [21–25]. However, few researchers like Hwa and Miklas [26], Du et al. [27] and Mochnache et al. [28] used SOM for prediction purposes and these were related with heavy metal removal performance, oil temperature of transformers and thermal aging of transformer oil, respectively. A recent application, alternatively, has ⁎ Corresponding author. Tel.: + 90 322 338 60 84/2663 17; fax: + 90 322 3386702. E-mail addresses: [email protected] (M. Oral), [email protected] (E.L. Oral), [email protected] (A. Aydın). 0926-5805/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.autcon.2011.09.002

focused on prediction of construction crew man-hour values for concrete, reinforcement and formwork crews [29] and prediction results have been compared with the results of previous research based on both multi regression analysis and Feed Forward Back Propagation (FFBP) [2,30]. The objective of the current research, however, has been to use a specific sample data and compare the prediction results of the models developed by using SOM, FFBP and GRNN. 2. Data collection and nature of the data Collecting realistic and consistent productivity related data is one of the key factors in arriving at realistic man-hour estimates by using any of the prediction methods. Various work, labor and site related factors affect construction labor/crew productivity and these have to be observed and analyzed systematically in order to arrive at realistic man-hour values, and “time study” is a methodical process of directly observing and measuring work [31]. Thus, time study has been undertaken with 1181 construction crews in Turkey through the use of standard time study sheets between the years 2006 and 2008 and details related with concrete pouring, reinforcement and formwork crews have been presented in various publications [17,29,32]. For plastering crews, quantity and details of plastering work undertaken by each crew were recorded together with work (location of the site, location of the work on site, the type and the size of the material used and the weather conditions), labor (age, education, experience, working hours, payment method, absenteeism and crew size), and site (site congestion, transport distances, and the availability of the; crew, machinery, materials, equipments and site management) related factors for 31 crews initially. Man-hour values were then

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determined by calculating duration of undertaking 1 m 2 plastering work. Required number of observations for the sample size to be representative within a targeted confidence interval (90%) was then determined by using Eq. 1 [31]. 2 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   ffi32 N∑ni¼1 Χ2i − ∑ni¼1 Χi 2 5 N ¼ 4A ∑ni¼1 Χi ′

ð1Þ

where: N' A N Xi n

required number of observations within the targeted confidence interval. 20 for 90% confidence level number of observations during the pilot study. unit output of the related labor (crew) during the ith observation. number of observations during the pilot study.

Calculations showed that a minimum of 71 crews were required for the sample size to be representative of the population within 90% confidence level. Data was then collected from 117 crews. The number of crews was satisfactory regarding the sample size requirement. Normality of the collected data was then tested by determining the skewness (to be between ±3), and kurtosis (to be between ±10) coefficients for productivity values [33]. Table 1 shows that normality assumptions were satisfied by the data set. Data analysis and selection, additionally focused on the fact that productivity models including fewer significant factors predict better than models based on many factors without considering significance [2]. Collected data/information related with the work and the site factors showed that most of the data/information were unevenly distributed; for example weather conditions were usually ‘very hot’ and ‘not rainy’ due to the prolonged draughts between 2006 and 2008 in Turkey, or there were usually no problems with the availability of resources and so on. So labor related factors of age, education and experience were decided to be used as independent variables in the developed models. This decision was in good agreement with the literature findings which recognize labor related factors to be the most important factors affecting crew productivity [3,34–44]. 3. Prediction methods: supervised learning vs unsupervised learning Supervised and unsupervised learning differ theoretically due to the causal structure of the learning processes. While inputs are at the beginning and outputs are at the end of the causal chain in supervised learning, observations are at the end of the causal chain in unsupervised learning. Unlike supervised learning, output vector is not required to be known with unsupervised learning, i.e. the system does not use pairs consisting of an input and the desired output for training but instead uses the input and the output patterns; and locates remarkable patterns, regularities or clusters among them. Thus, learning task is often easier with unsupervised learning if; the causal relationship between the input and the output observations has a complex variability; there is a deep hierarchy in the model or some of the input data are missing [45].

3.1. Feed-Forward Back Propagation (FFBP) A Feed Forward Back Propagation neural network (FFBP) is the generalization of the Widrow–Hoff learning rule to multiple-layer networks and nonlinear differentiable transfer functions [46]. A FFBP usually consists of three layers; input, hidden and output. Input layer contains as many neurons as the number of parameters affecting the problem. One hidden layer is usually sufficient for nearly all problems. Even though multiple hidden layers rarely improve a data model, they may be required for modeling data with discontinuities. Number of neurons in a hidden layer should be selected arbitrarily. A neuron has Tan-sigmoid (TSig) activation function in a hidden layer and linear activation function in the output layer. Thus, the hidden layer squeezes the output to a narrow range, from which the output layer with linear function can predict all values [46–48]. Fig. 1 illustrates the architecture of a FFBP Neural Network with two hidden layers. FFBP network is initialized with random weights and biases, and is then trained with a set of input vectors that sufficiently represents the input space. For the current problem, the input vectors have three components; experience of the crew on the particular site, crew size, and age of the crew members. The target vector, on the other hand, has only one component; the crew productivity. Training is achieved by using two steps. In the first step, a randomly selected input vector from the training data set is fed into the input layer. The output from the activated neurons is then propagated forward from hidden layer(s) to the output layer. The back propagation step, on the other hand, starts with calculating the error in the gradient descent and propagates it backwards to each neuron in the output layer, then the hidden layer. At the end of the second step, the weights and the biases are recomputed. These two steps are alternately used until the network's overall error is less than a predefined rate, or until the number of maximum epochs is reached.

3.2. Generalized Regression Neural Networks (GRNN) GRNN networks have four layers; input, hidden, pattern (summation) and decision (Fig. 2). Like FFBP, number of input neurons in the input layer is equal to the total number of parameters. Input neurons standardize input values and feed the standardized values to the neurons in the hidden layer. Hidden layer has one corresponding neuron for each case in the training data set. For the current problem, there are 104 neurons in the hidden layer of GRNN since data from 104 crews are used for training purposes as discussed in Section 4. Each neuron stores the values of the predictor variables together with the target value and computes the Euclidean distance of the test case from the neuron's center point and then applies the RBF kernel function using the sigma value(s). The Sigma value determines

Input Layer

Output Layer

Experience Crew Size

Table 1 Distribution characteristics of productivity values for plastering crews.

Hidden Layers

Productivity

Age

Plastering (mh/m2) Mean productivity Standard deviation Coefficient of Variation Skewness coefficient Kurtosis coefficient

0.5 0.23 0.47 1.08 2.53

Fig. 1. The architecture a FFBP Neural Network with two hidden layers.

M. Oral et al. / Automation in Construction 22 (2012) 271–276

Input Layer

Hidden Layer

Experience

Pattern Layer

273

Input Nodes

Decision Layer

Weights

Output Nodes

N

Crew Size

÷

Age

Productivity

D

Experience

Crew Size Fig. 2. Schematic diagram of GRNN.

Age

the spread of RBF kernel function. The output value of a hidden neuron is passed to the two neurons in the pattern layer where one neuron is the denominator summation unit and the other is the numerator summation unit. The denominator summation unit adds up the weight values coming from each of the hidden neurons and the numerator summation unit adds up the weight values multiplied by the actual target value for each hidden neuron. The decision layer then divides the value accumulated in the numerator summation unit by the value in the denominator summation unit and uses the result as the predicted target value [49–50]. The prediction performance of a GRNN strongly relies on the sigma value. It is the only parameter that needs to be tuned by the user. 3.3. Self Organizing Maps (SOM) Unlike FFBP and GRNN, SOM uses groups of similar instances, i.e. input/output patterns, instead of a predefined classification, i.e. pairs consisting of an input and the desired output for training. The training data set contains only input variables and SOM attempts to learn the structure of the data in order to arrive at solutions. It organizes and clusters unknown data into groups of similar patterns according to a similarity criterion (e.g. Euclidean distance) resulting in reduction in the amount of data and organization of the data on a low dimensional display. Thus, when the process is complete, each node in the ‘Output Layer’ has a topological position where similar clusters position close to each other [51]. Fig. 3 shows the current problem as an example, which adapts 4 dimensional input vector into a 6 × 6 dimensional map. Contrary to its common usage for; clustering, classification or displaying multidimensional data, SOM can be modified to make accurate predictions from which the data model is unknown. A typical SOM has an input vector which has as many dimensions as the number of independent parameters, and no target vector. By feeding experience of the crew on the particular site, crew size, age of the crew members and productivity as input vector, the relationships between these attributes can be displayed in two dimensional maps produced by SOM. The maps are, in fact, visual representations of the weight values that connect input and output nodes. The weight values originating from ‘crew size’ input node, for example, form ‘crew size map’. As seen in Fig. 3, the output nodes do not produce any output. Any output has to be derived from the weights. During the training phase of SOM, similar input instances are approximated and grouped together topologically. While some of the output nodes correspond to the input vectors of the data set, some of them are the estimation of the possible vector instances that lay between these input vectors. This feature allows SOM to predict the outcome of the instances that is not in the training data set. For the prediction of crew productivity, FFBP and GRNN require input vectors that have three components; experience, crew size and age, and target vectors

*

Productivity

Fig. 3. SOM structure.

that have only one component; productivity. SOM, on the other hand, requires only input vectors. The input vectors of SOM have four components; experience, crew size, age, and productivity. The weights of the output nodes are calculated according to these inputs. After the training process, prediction is achieved as follows: an input vector is fed into the input layer. Since one of the input components – for the current problem that is the productivity value – is unknown and to be estimated, that component of the input vector would be missing. Then, the Best Matching Unit (BMU), which is the output node with the weight vector best matching to the current input vector, is identified. The weight originating from the missing input node is not considered for the calculation of BMU. The weight connecting the BMU to the missing component of the input vector is the normalized prediction value. Thus, after de-normalization, prediction process is completed. 4. Prediction performance of the models FFBP, GRNN and SOM neural networks were configured and tuned with different network structures and parameters in order to achieve the best prediction performances. The input data set contains three independent parameters; crew size, experience of the crew on the particular site and age of the crew members, and one dependent variable; crew productivity for 117 crews. Nine fold cross validation was carried out for each configuration in order to compare the prediction results obtained from the three methods. The input data set was divided into nine sub-groups containing 13 crews each. Eight sub-groups were used to train the models and the remaining sub-group was used as test data. The cross-validation process was repeated nine times by using each of the nine sub-groups as test data. Three standard error measures; Mean Squared Error (MSE), Mean Absolute Error (MAE) and Mean Absolute Percentage Error (MAPE), were then calculated for each data set by using Eqs. 2–4. MAPE, MAE and MSE values for the data sets are given for FFBP, GRNN and SOM in Table 2. MAPE values together with Coefficient of Variation (CV) were considered to be the determinants in arriving to the conclusions about the accuracy of each model as both MSE and MAE have the disadvantages of heavily weighting outliers and MSE accentuating large errors. CV values

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Table 2 Validation results for FFBP for different transfer functions. FFBP Configuration

TSig

PLin

PLin–PLin

PLin–TSig

TSig–PLin

TSig–TSig

Nodes MSE MAE MAPE

7 0.07 0.2072 49.99

9 0.0614 0.1896 46.83

7-6 0.0593 0.1882 45.97a

10-9 0.0699 0.1988 46.61

6-6 0.0699 0.201 48.31

6-5 0.0672 0.2027 47.37

a

Best result.

(Eq. 5), on the other hand, presented the measure of dispersion, meaning that the smaller the CV value, the more reliable the model was in terms of stableness in predicting values. Fig. 4. Initial neighborhood radius vs MAPE values.

MSE ¼

1 n 2 ∑ ðA −Pi Þ n i¼1 i

ð2Þ

MAE ¼

1 n ∑ jA −Pi j n i¼1 i

ð3Þ

MAPE ¼

CV ¼

  1 n Ai −Pi  100% ∑ n i¼1 Ai 

ð4Þ

σ  100% μ

ð5Þ

where; n Ai Pi σ μ

number of data sets used for estimation actual value of the ith element of the data set. predicted value of the ith element of the data set. standard deviation mean

Two different network structures were tested for FFBP. In the first structure, FFBP had a single hidden layer with “Tan-sigmoid” (TSig) transfer function. The number of neurons in the hidden layer was changed from five to ten, and the best prediction performance was obtained for the network structure with seven neurons in the hidden layer with 49.99, 0.07 and 0.2072, for MAPE, MSE and MAE, respectively (Table 2). Then the transfer function is changed to “Purelinear” (PLin) and better prediction accuracy was obtained for nine neurons in the hidden layer with 46.83, 0.0614 and 0.1896, for MAPE, MSE and MAE, respectively. Finally, number of hidden layers was increased to two and both the number of

neurons in the hidden layers and the transfer functions were changed as in the first structure. The best result was obtained as 45.97, 0.0593 and 0.1882 for MAPE, MSE and MAE, respectively when transfer functions in both layers were set to “Purelinear” with the number of neurons equal to seven for the first layer and six for the second layer (Table 2). The GRNN algorithm, on the other hand, needs only one parameter to be tuned up; spread of radial basis function (σ). σ parameter was changed from 0 to 5 with 0.01 steps in order to seek the most suitable value to achieve the best prediction performance. The best result was obtained when σ was 0.3, and MAPE, MAE and MSE values were 45.87, 0.117 and 0.023, respectively (Table 3). SOM, however, requires many parameters to be tuned up; output map size, initial learning rate, initial neighborhood radius, even seed of random generator. Instead of using systematic parameter search as in FFBP and GRNN, random twelve different configurations were tested for SOM. The best results were obtained with output map size of 50 by 50 and initial learning rate of 0.1. It was observed that initial neighborhood radius has a significant effect on the prediction accuracy. Further experiments were carried on by changing initial neighborhood radius from 70 to 300 with step size 1. Fig. 4 shows the effect of initial neighborhood radius on the prediction accuracy. The best result was obtained when the radius was set to 237. MAPE, MAE and MSE values were obtained as 41.27, 0.193 and 0.069 respectively, with these parameters (Table 3). Results in Table 3 show that the prediction accuracy of SOM is superior to GRNN and FFBP with respect to MAPE values. “Best” and “Worst” rows in Table 3 – which display the best and the worst

Table 3 Validation results. GRNN

Fold 1 Fold 2 Fold 3 Fold 4 Fold 5 Fold 6 Fold 7 Fold 8 Fold 9 Best Worst μ σ. CV (%) a

Best result.

FFBP (PLin–PLin)

SOM

MSE

MAE

MAPE

MSE

MAE

MAPE

MSE

MAE

MAPE

0.022 0.013 0.019 0.020 0.055 0.036 0.019 0.011 0.012 0.011 0.055 0.023 0.014 61

0.118 0.100 0.112 0.120 0.153 0.166 0.116 0.084 0.080 0.080 0.166 0.117 0.029 25

47.85 31.15 82.12 51.07 33.59 43.88 51.74 39.91 31.56 31.15 82.12 45.87 15.78 34

0.066 0.031 0.053 0.057 0.129 0.089 0.043 0.028 0.040 0.028 0.129 0.059 0.032 54

0.175 0.155 0.199 0.204 0.234 0.264 0.170 0.134 0.158 0.134 0.264 0.1882 0.0412 22

36.87 31.02 85.50 59.52 31.63 44.71 47.50 39.74 37.29 31.02 85.50 45.97 17.23 38

0.068 0.028 0.040 0.070 0.183 0.120 0.046 0.021 0.051 0.021 0.183 0.07 0.051 74

0.199 0.123 0.168 0.212 0.298 0.278 0.158 0.120 0.182 0.120 0.298 0.193 0.062 32

42.93 21.25 66.12 49.96 39.52 40.59 43.50 29.30 38.23 21.25 66.12 41.27a 12.53 30

M. Oral et al. / Automation in Construction 22 (2012) 271–276

275

Table 4 Sensitivity analysis. FFBP

GRNN

SOM

10-8 0.0725 0.2057 46.98

0.0586 0.1879 46.50

0.027 0.120 41.41a

5-5 0.0658 0.1929 45.82

6-5 0.0592 0.1872 44.50

0.0588 0.1857 45.67

0.0761 0.2085 45.82

9-7 0.0619 0.1867 43.56

5-6 0.0661 0.1968 46.97

10-5 0.0652 0.1923 45.46

0.0587 0.1871 46.06

0.0660 0.043 40.69a

8-8 0.0608 0.1831 42.79a

7-10 0.058 0.1833 44.52

8-10 0.0828 0.2115 47.79

9-8 0.0745 0.1953 43.20

0.0586 0.1874 46.40

0.0651 0.1860 43.96

(e) Sensitivity analysis 5: (independent variable: experience) Nodes 5 6 MSE 0.0574 0.0675 MAE 0.1848 0.1946 MAPE 45.44 46.57

8-8 0.0613 0.1856 43.68a

7-8 0.0681 0.1934 43.94

7-6 0.0654 0.1954 44.61

9-9 0.0622 0.1888 44.40

0.0585 0.187 46.02

0.0645 0.1939 44.56

(f) Sensitivity analysis 6: (independent variable: crew size) Nodes 10 6 MSE 0.0618 0.0613 MAE 0.1892 0.1881 MAPE 45.67 44.82

8-8 0.0605 0.1825 42.86

9-7 0.0602 0.1863 44.71

10-5 0.0614 0.1872 44.83

6-9 0.0616 0.1892 43.51

0.0585 0.1866 45.70

0.0581 0.1858 40.54a

Configuration

PLin–TSig

TSig–PLin

TSig–TSig

(a) Sensitivity analysis 1: (independent variables: age/crew size) Nodes 9 5 5-7 MSE 0.0599 0.0861 0.0607 MAE 0.1883 0.2131 0.1881 MAPE 47.09 48.89 45.55

8-5 0.0791 0.2073 45.91

9-5 0.0636 0.1955 44.86

(b) Sensitivity analysis 2: (independent variables: age/experience) Nodes 9 6 5-8 MSE 0.0597 0.0668 0.0626 MAE 0.1892 0.1954 0.1918 MAPE 46.43 47.78 45.08

5-9 0.0605 0.1865 44.63a

(c) Sensitivity analysis 3: (independent variables: experience/crew size) Nodes 9 6 6-8 MSE 0.0619 0.0652 0.0585 MAE 0.1909 0.1941 0.1836 MAPE 45.21 46.55 45.26 (d) Sensitivity analysis 4: Nodes MSE MAE MAPE

a

PLin

TSig

PLin–PLin

(independent variable: age) 5 6 0.0637 0.0719 0.1923 0.2027 46.93 49.16

Best result.

prediction performances amongst the nine folds – together with CV values additionally show that SOM provides the most stable model for predicting plastering crew productivity when the crew size, experience of the crew on the particular site, age of the crew members are known. SOM displays an excellent performance for Fold 2 as 21.25, 0.123 and 0.028 for MAPE, MAE and MSE, respectively. Fold 2 also gives the best results for both GRNN and FFBP. Meanwhile the worst results – with very high MAPE values – are obtained for Fold 3 for all of the models; giving the hint of outliers in the training data set used for that fold.

When the results are compared by considering the MAPE values, SOM's prediction accuracy is better than both FFBP and GRNN for three cases with independent variables; experience/crew size, age/ crew size and crew size; and prediction results for independent variable combinations of; age/experience, age, and experience are better for FFBP. When overall performances of the prediction models are considered, prediction accuracy of SOM is superior for 4 out of 7 combinations with an average MAPE value of 42.89. Table 5 additionally summarizes sensitivity analyses of SOM's performance in itself. The results show that best prediction values were obtained when data sets included crew size data.

4.1. Sensitivity analysis 5. Conclusions Sensitivity analyses were additionally undertaken in order to observe how the prediction performances changed by ignoring one or more of the independent variables. Table 4 (a)–(f) shows the results.

Artificial neural network models based on supervised learning have proved to be successful in predicting construction crew productivity

Table 5 Sensitivity results of SOM. Independent variable

Age/experience/crew size Age/experience Age/crew size Experience/crew size Age Experience Crew size a

Best result.

MSE

MAE

MAPE

μ

σ

CV (%)

μ

σ

CV (%)

μ

σ

CV (%)

0.07 0.0761 0.0680 0.0660 0.0651 0.0645 0.0581

0.051 0.0437 0.0400 0.0304 0.0501 0.0345 0.0320

74 57.4244 58.8235 46.0606 76.9585 53.4884 55.0775

0.193 0.2085 0.1889 0.1926 0.1860 0.1939 0.1858

0.062 0.0551 0.0443 0.043 0.0772 0.0614 0.0518

32 26.4267 23.4516 22.3261 41.5054 31.6658 27.8794

41.27 45.82 43.41 40.69 43.96 44.56 40.54a

12.53 15.70 19.21 12.49 10.93 9.58 11.77

30 44.2525 30.6955 24.8635 21.4991 29.0331 30.3853

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M. Oral et al. / Automation in Construction 22 (2012) 271–276

significantly better than statistical methods like regression. Meanwhile applications in various areas other than construction showed that if the causal relation between input and output has a complex variability, learning task is often easier with unsupervised learning. Thus, current research focused on application of both supervised and unsupervised learning based methods to plastering crew productivity data in order to compare the prediction results. Results show that SOM has a superior performance than FFBP and GRNN for plastering crew productivity prediction. SOM's performance has also been tested for concrete, reinforcement and formwork crews and superior prediction performance, in comparison to the previous models has been reported [29]. However, future work is required in order to compare the results with the performance of FFBP and GRNN for concrete, reinforcement and formwork crews. Positive effect of crew size related data on the model's performance is also an additional point which can guide future data collections and which can be investigated by the future applications. Finally, it can be concluded that the current research proved SOM to be an alternative tool to the supervised learning based tools and SOM can be used in various prediction applications.

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Acknowledgment Data used in this paper has been collected during the research project 106M055 which is supported by TÜBİTAK (The Scientific and Technical Research Council of Turkey). The authors would like to thank G. Mıstıkoglu, E. Erdis, E.M. Ocal, and O. Paydak for their invaluable support during data collection.

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