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ТЕСТИРОВАНИЕ МНОГОСЛОЙНОГО ПЕРСЕПТРОНА ДЛЯ ПРОСТРАНСТВЕННОЙ ИНТЕРПОЛЯЦИИ
Вероника Невтипилова
Университет Палацкого в Оломоуци, 17, Листопаду 50, 771 46 Оломоуц, Чешская Республика, магистр, кафедра геоинформатики, тел./факс:+420585634519(Р), e-mail: pastwa.justyna@gmail.com
Юстына Паства
Университет Палацкого в Оломоуци, 17, Листопаду 50, 771 46 Оломоуц, Чешская
Республика, кандидат наук, кафедра геоинформатики, тел./факс:+420585634519(Р), e-mail: pastwa.justyna@gmail.com
Мукеш Сингх Бури
Университет Палацкого в Оломоуци, 17, Листопаду 50, 771 46 Оломоуц, Чешская Республика, кандидат наук, доцент, кафедра геоинформатики, тел./факс:+420585634519(Р), e-mail: msboori@gmail.com
Вит Возенилек
Университет Палацкого в Оломоуци, 17, Листопаду 50, 771 46 Оломоуц, Чешская Республика, кандидат наук, профессор, зав. кафедрой геоинформатики,
тел./факс:+420585634519(Р), e-mail: vit.vozenilek@upol.cz
Целью данного исследования является тестирование пакета программ ANN (искусственная нейронная сеть), входящего в программное обеспечение GRASS 6.4 для пространственной интерполяции, и сравнение с общими методами интерполяции IDW и обычного кригинга. Этот пакет программ сравнивали также с пакетами программ Nnet и neuralnet для нейроных сетей, доступными в программном обеспечении R Project. Все пакеты используют модель многослойного персептрона (MLP) вместе с алгоритмом обратного распространения. Методы оценки, главным образом, основаны на методе наименьших квадратов. Все тесты выполнялись по моделированным данным, созданным в программном обеспечении R Project. По ним строились три поверхности с различными характеристиками. Для того, чтобы найти оптимальную конфигурацию для многослойного персептрона, тестировались различные сетевые параметры (метод проб и ошибок). Основным тестируемым параметром является число нейронов в скрытых слоях. Результаты показывают, что многослойная модель персептрона в модуле ANN, встроенного в GRASS, может быть использована для пространственной интерполяции. Тем не менее, результирующая среднеквадратическая ошибка оказалась больше СКО, полученной методами интерполяции IDW и обычного кригинга. При сравнении пакетов программ в GRASS GIS для искусственной нейронной сети с пакетами программ R Project выяснилось, что лучшими оказались пакеты из R Project. Создание модели многослойного персептрона (MLP) выполняется быстрее и полученные результаты лучше.
Ключевые слова: ANN, IDW, кригинг, интерполяция, персептрон, GRASS ГИС, Nnet, Neuralnet.
TESTING MULTILAYER PERCEPTRON (MLP) FOR SPATIAL INTERPOLATION
Veronika Nevtipilova
Palacky University Olomouc, 17. listopadu 50, 771 46 Olomouc, Czech Republic, MSc, Department of Geo-informatics, tel./fax:+420585634519(0), e-mail: pastwa.justyna@gmail.com
Justyna Pastwa
Palacky University Olomouc, 17. listopadu 50, 771 46 Olomouc, Czech Republic, PhD, Department of Geo-informatics, tel./fax:+420585634519(O), e-mail: pastwa.justyna@gmail.com
Mukesh S. Boori
Palacky University Olomouc, 17. listopadu 50, 771 46 Olomouc, Czech Republic, PhD, Assistant Professor, Department of Geo-informatics, tel./fax:+420585634519(O), e-mail: msboori@gmail.com
Vit Vozenilek
Palacky University Olomouc, 17. listopadu 50, 771 46 Olomouc, Czech Republic, PhD, Professor, Head of Department of Geo-informatics, tel./fax:+420585634519(O), e-mail: vit.vozenilek@upol.cz
The aim of this research is to test Artificial Neural Network (ANN) package in GRASS 6.4 software for spatial interpolation and to compare it with common interpolation techniques IDW and ordinary kriging. This package was also compared with neural networks packages nnet and neuralnet available in software R Project. All the packages uses multi-layer perceptron (MLP) model trained with the back propagation algorithm. Evaluation methods were based mainly on RMSE. All the tests were done on artificial data created in R Project software; which simulated three surfaces with different characteristics. In order to find the best configuration for the multilayer perceptron many different settings of network were tested (test-and-trial method). The number of neurons in hidden layers was the main tested parameter. Results indicate that MLP model in the ANN module implemented in GRASS can be used for spatial interpolation purposes. However the resulting RMSE was higher than RMSE from IDW and ordinary kriging method and time consuming. When compared neural network packages in GRASS GIS and R Project; it is better to use the packages in R Project. Training of MLP was faster in this case and results were the same or slightly better.
Key words: ANN, IDW, Kriging, Interpolation, GRASS GIS, Nnet, Neuralnet.
1. INTODUCTION
Spatial interpolation is quite frequently used method for working with spatial data. Currently there are many interpolation methods, each of which has its own application. The level of accuracy of these methods is limited, and therefore the spatial interpolation looking for new techniques and methods. One of these techniques is the use of neural networks. The principle of neural networks is known for a very long time, the first artificial neuron was constructed in 1943 (Volna, 2008). However their use in the field of geo-informatics only started recently. From the available literature, it is evident that neural networks are using the spatial interpolation with good results, comparable with other interpolation methods, in some cases even better (Snell, 2000; Bhaskaran, 2010; Chowdhury, 2010). Using neural networks for spatial interpolation is not yet very widespread issue among regular users of GIS, since most of the available GIS software is not implemented itself a neural network models. GRASS GIS software is one of the
few for which there is a module to work with neural networks, namely the multilayer perceptron model (MLP). This work is engaged in testing of this module and its comparison with two the mostly used in spatial analysis interpolation methods: IDW and simple kriging.
The aim of this research is to use MLP model for normal interpolation and determine whether the quality of the resulting interpolation comparable with other conventional methods. In this paper, first we mention objectives of the research work. Second summarizes the methods used and work progress. In third part we briefly describe the theoretical basis used in interpolation methods - that is, neural networks, IDW and kriging. This part also deals with the implementation of neural networks in two software; used in this work. Briefly assesses and compare examples from the literature on the use of neural networks for spatial interpolation. Fourth describe - data creation, selection of best MLP parameters, process, steps of used commands and settings for custom interpolation in the GRASS 6.4 software and R Project. The last part summarized results. This part present and evaluate outcomes of previously used interpolation methods; compare and evaluate their quality. Also compare MLP method in GRASS 6.4 software and R Project.
2. METHODOLOGY AND DATA PROCESSING
A simple neuron model shown in Fig. 1 :
Figure 1: Formal neuron (http://www.root.cz/clanky/biologicke-algoritmy-4-
neuronove-site/)
The sum of all weighted inputs y in indicates the internal potential of the neuron:
(1)
The weighted sum is passed through a neuron activation function y = f (y_in) and produce the final output of the neuron. Which turn can become stimulus for neurons in the next neural network layer. The simplest type of activation function is threshold function:
This simple model of neuron is known as perceptron (Vozenilek, 2011). The interconnection of neurons create neural network. Connection method is such that the output from one neuron is the input of other neurons (Volna, 2008). Neurons in the network are organized into layers (Fig. 2). An important feature of neural network is to change the weights between neurons. Multilayer perceptron is multilayer neural network in which each neuron is modeled as a perceptron. Activation functions of neurons in multilayer perceptron is differentiate continuous function, most used is a sigmoid function (Tarassenko, 1998):
Back-propagation algorithm: The MLP is trained using back-propagation algorithm. This is a supervised learning and it takes two stages. First is the feedforward propagation. The second phase is back-propagation. For each neuron in input layer is calculated gradient of the error function at each iteration step, which is the part of error transmitted to the left of the unit (to previous layer) according to formula:
8k = (tk-yk)fXy-ink) (4)
Where tk is the expected output of neuron, yk is the calculated output and y ink is the internal potential of a neuron Yk.
Input layer Hidden (internal) layer Output layer
Figure 2: Example of a neural network; freely adapted from Volna, 2008. Topology of neural networks: First several MLP neural networks with different number of neurons in hidden layers were created. Then trained on training dataset
using back propagation algorithm and tested on smaller (testing) dataset, which was not used while training. The mean square error (RMSE) was calculated from trained MLP on test data and few of the best MLP configurations were selected for later calculations.
Custom Interpolation: Using three distinct datasets representing terrain with different characteristics, the interpolation was performed in software's GRASS 6.4 and R. The interpolation method IDW, krigig and MLP were used. Interpolation was done for each simulated terrain. In software GRASS 6.4; 12 raster's were created while analysis (three from MLP trained on raster data, six from MLP trained on vector data and three from IDW); in R software; 12 raster's were created (six by MLP from each package (nnet and neuralnet), six by methods IDW and simple kriging).
Evaluation results of interpolation: For all interpolation results was calculated RMSE. In order to visually compare applied methods, results were subtracted and the difference between them was calculated. Each time raster created by IDW and simple kriging was subtracted from raster generated MLP.
3. IMPLEMENTATION IN GIS
GRASS 6.4: MLP was trained with the back-propagation algorithm using 5 scripts written in Python programming language invoking Fast Artificial Neural Network (FANN) library (Netzel, 2011). This script works with raster data. Scripts and their functions are: ann.create creates ANN; ann.info displays information about defined ANN; ann.datarast prepares the learning datasets using raster layer data. ann.learn perform learning and ann.run.rast run the trained ANN to create output raster layer (Netzel, 2011).
R Project: The R Project software work with MLP by nnet and neuralnet packages.
The nnet package (Venables a Ripley, 2002) allow for training feed forward networks using back-propagation algorithm. This network has only one hidden layer. The possible setting parameters are: the number of input and desired output of neurons, number of neurons in hidden layer, weight parameter and maximum number of epoch. Learning of the network is relatively fast and the quality of the result is comparable with other methods.
The neuralnet package (Fritsch et al., 2012) in many respects resemble nnet package, but provide more setting parameters. In opposition to the previous package, it is possible to design more than one hidden layer with any number of neurons; additionally user can choose between few available learning algorithms as well as activation function. The training of network is slower than in case of nnet package, but resulting total error is usually smaller.
TESTING INTERPOLATION METHODS
Creating Data: To provide interpolation using MLP, three artificial datasets were created in R Project. The dataset simulate different roughness of the terrain. The model with higher roughness was signed as 1, with less roughness - as 3. The datasets were randomly generated using functiion grf (Gaussian random fields) from package geoR that create points and randomly assign values to them. These values are influenced by other parameters of the function. grf(pocetBodu, grid = "reg", cov.pars = c(sill, range), nug = nugget, cov.model = covModel, aniso.pars = c(anisotropyDirection, anisotropyRatio), xlims = xlims, ylims = ylims)
Parameter grid="reg" indicate that points are generated in a regular grid. Parameter cov.model determines the type of variogram, here spherical. Values xlim and ylim were set in interval 0 - 1. There were 1024 points generated in a regular grid for each dataset. These points had three attributes: coordinates x and y from range 0 -1 and value z which represented elevation. Parameters value describing roughness, used while creation of datasets is given in Table 4.1.
Table 1: Parameter values for all surface contours
Sill Range Nugget Anisotropy ratio
Roughness 1 0.12 0.3 0.00001 0.8
Roughness 2 0.08 0.5 0.00001 0.8
Roughness 3 0.01 1.2 0.00001 0.3
The range of value z was different for each roughness. Data with lower roughness presented smaller range of value.
Roughness 1: Roughness 2: Roughness 3 :
■0.7396643 to 1.090838 ■0.534922 to 0.8930179228 ■0.2012766 to 0.1411988275
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Figure 5: Distribution of points of articulation 1, 2 and 3.
Figures 5 are shown in the distribution of points in different datasets. Larger diameter wheels indicate higher z. Training data consist of 724 randomly selected
points and was used for learning MLP. Testing data contained remaining 300 points and were used to calculate RMSE.
Selecting optimal configuration of MLP using nnet package: The configuration of MLP was determined using test-and-trial method. To make the work more effective, a script gradually creating datasets for all surface topography was created. For each roughness of terrain 10 datasets were created and these datasets were divided into training and testing part. In next step 10 MLP was learned using training data from each existing datasets. Later, for all testing sets RMSE was calculated. This procedure was carried out a total of fifteen times, each time through the varied number of neurons in hidden layer in the range 15 to 30. For each roughness RMSE was calculated. In the last step average RMSE was calculated for all roughness for each MLP configuration. Results are listed in Table 2. Best setting is found MLP with 28 neurons in the hidden layer.
Table 2: Average RMSE for testing network setting (nnet)
Number of neurons Segmentation average
Articulation 1 Articulation 2 Articulation 3
28 0.148758 0.096397 0.017947 0.087701
24 0.151135 0.096007 0.018192 0.088444
25 0.149176 0.099806 0.018237 0.089073
26 0.154605 0.095057 0.017955 0.089206
22 0.152875 0.097339 0.018894 0.089703
30 0.157484 0.095408 0.018022 0.090304
19 0.154560 0.097975 0.018826 0.090454
20 0.157060 0.097911 0.018621 0.091197
18 0.156477 0.098647 0.019657 0.091594
29 0.163756 0.095861 0.018037 0.092551
21 0.161621 0.097511 0.019381 0.092838
16 0.161058 0.099874 0.019209 0.093380
23 0.167908 0.095541 0.019640 0.094363
27 0.158991 0.106556 0.018620 0.094722
17 0.166058 0.100206 0.019149 0.095138
15 0.164467 0.103390 0.019708 0.095855
Selecting optimal configuration of MLP using neuralnet package: this is similar to nnet package. The difference is that neuralnet package allows trained networks with more hidden layers. Gradually networks were tested with one to four hidden layers. The number of neurons in the first hidden layer is always moved in the interval of 15 to 30. The number of neurons in other hidden layers has been fixed and was selected from a number of 5, 10, 15, 20, and 25. Average RMSE test set was again calculated for all datasets. 24, 15, 10, 5 number of neurons were selected as the best network with four hidden layers. Results of testing networks are in Table 3.
Table 3: Average RMSE for testing network settings (neuralnet)
Number of neurons Segmentation average
Articulation 1 Articulation 2 Articulation 3
24 0.149159 0.098706 0.029940 0.092602
16 0.153596 0.098004 0.029210 0.093603
15 0.148941 0.100402 0.032237 0.093860
22 0.150838 0.097616 0.033587 0.094014
20 0.149615 0.098070 0.035774 0.094486
30 0.150110 0.098537 0.035594 0.094747
17 0.152036 0.100431 0.031792 0.094753
23 0.152735 0.099836 0.031717 0.094763
27 0.155015 0.096519 0.033971 0.095169
29 0.150820 0.098389 0.036693 0.095301
26 0.152207 0.099028 0.034765 0.095333
28 0.151465 0.098248 0.038276 0.095996
21 0.153177 0.099907 0.036171 0.096418
19 0.150610 0.102501 0.036541 0.096551
18 0.152551 0.101085 0.038194 0.097277
25 0.156908 0.101286 0.033683 0.097292
Selecting optimal configuration of MLP using GRASS 6.4: The module ANN allows training network with multiple hidden layers. As well as in previous methods, an optimal configuration for MLP was found using test-and-trial method. The network with three hidden layers and the number of neurons 32, 38, 27 was selected as most successful MLP setting.
IDW: This method is implemented in R Project software in several packages; in this work gstat package was used with the function idw.
idw_result <- idw (z ~ x + y = train.set locations, NewData = grid, nmax = 18, idp = 1.0
Function idw use parameter formula to distinguish coordinates and values which will interpolated. Parameter locations define data used for interpolation and newdata parameter specifies the new coordinates. Number of points that are used in interpolation is set with the parameter nmax (the chosen is 18). Number p (power) is specified in parameter idp.
Kriging: The method of kriging is implemented very extensively in R Project -there are plenty of packages and functions available. From purposes of this work package automap with function autoKrige was used because it allows for ordinary kriging. To generate variogram function autofitVariogram was used.
Calculation of RMSE and visual comparison: To assess the quality of interpolation RMSE was calculated and compare tested interpolation methods. Assessment was carried out in R Project. When estimating RMSE for surfaces interpolated in GRASS 6.4 from raster data, the vector layer of randomly located points was created by command v.random. To this points the value of original and interpolated raster were added. After these preparations, the data were exported to CSV format using command v.out.ogr. In the next step, the CSV file was imported to R Project where elevation values z were normalized and RMSE was calculated. When estimating RMSE for surfaces interpolated in GRASS 6.4 from vector data, at first the points from test.set were imported to GRASS 6.4. Using command v.what.rast the corresponding values from interpolated raster were added. Next, the file with points were imported to R Project, than the normalized values were transformed to real ones and RMSE was calculated. The steps while analyzing outputs from IDW method was analogous but the values after interpolation was real and there was not need to convert it. The calculation of RMSE was carried out in R Project in the same way for each interpolation methods. The RMSE was calculated for interpolation results coming from test data. The interpolation output from MLPs was transformed from normalized to real values. Next, the original values of elevation were added and finally the RMSE was calculated.
4. RESULTS Main results are following:
• Assessment of the quality of interpolation using ANN in GRASS GIS 6.4
• Comparison of ANN module and interpolation method IDW and kriging,
• Comparison of interpolation using neural networks in GRASS GIS and R Project,
5.1 Evaluation of the interpolation quality: first interpolation with the MLP trained on raster data was evaluated. RMSE values with decreasing roughness (falling range of values z) decreased. Learning time was longer with the increasing number of the vector points. Learning time was shorter with lower roughness data. The less iterations were required to train the networks when more vector points were used. Table 4 summarizes data about training the MLP.
The range of values z in the interpolated grid is lower than the range of values in the original grid (Table 5). This could be due to poor distribution of random vector points. RMSE value in this case was 0.0646. In case of roughness 1, MLP has missed extreme values. In roughness 2, difference in the rage is smaller; which means the random vector points were probably better distributed. However the extreme values are also omitted. The value of RMSE is 0.0427. In case of roughness 3, network behaviour is similar to the previous two cases and the value of RMSE is 0.0085. The value of RMSE was then expressed in percentage according to the range of value z. The difference between the values of RMSE is only 1%; for each roughness (Table 5).
Table 4: Ne
work training data for each segmentation
Roughness
Number of points
Time in minutes
Learning iterations
RMSE
Roughness 1
500
1000
2000
3000
12
22
25
39
13292
11675
7901
7618
0.099482
0.106778
0.088307
0.064648
Roughness 2
500
1000
2000
3000
10
18
25
23
10729
10014
6998
3903
0.068894
0.056571
0.039702
0.042661
Roughness 3
500
1000
2000
3000
4
13
14
11
4863
9534
3403
1717
0.010265
0.009793
0.009272
0.008466
Table 5: Range of value z in original and interpolated data and comparison of __RMSE for all roughness.__
Original data range Interpolated grid RMSE %
Segmentatio n 1 -0.6924255 -1.034648 -0.6198587 to 0.8887726 4.2852
Segmentatio n 2 -0.5086115 -0.863945 -0.4962887 to 0.7969054 3.2989
Segmentatio n 3 -0.1734903 -0.124689 -0.1563402 to 0.1131727 3.1412
Interpolation quality was further evaluated by visual comparison of resulting raster's. MLP module trained on raster data was able to adapt quite well and resulting grid was very similar to the original grid. Figure 6 shows the original and interpolated grid for roughness 1.
Fig. 7 shows differences in the z values between the new and original grid. Original grid was subtracted from the new grid. Grid created with MLP has z values, usually lower than the original bitmap. The average value of the difference was -0.03145 and highest differences were -0.32560 and 0.18220. MLP trained on vector data file had a similar behaviour as the MLP trained on raster data file. It was necessary to change learning coefficient, when training the network on vector data. Table 6 summarizes the data about training the MLP with the numbers of 32, 38, 27 neurons and the MLP with the numbers of 20, 25, 17 neurons for each roughness.
(A) Original Bitmap (B) Interpolated grid
Figure 6: Comparison of the original grid with grid interpolated
using neural network.
Figure 7: Difference between new and original screen z values (broken one).
During interpolation MLP again omitted extreme values. In roughness 2, the lower boundary of the interval z values in a new grid was lower than in the original data. Range of z values in the original and newly interpolated data can be found in Table 7. Which show values for a grid created with MLP with the number of 20, 25, 17 neurons. RMSE value was 0.1407 in case of roughness 1, 0.0982 in roughness 2 and 0.0252 in case of roughness 3.
Table 6: Data on training networks for each roughness.
learning Iterations learning
time in Coefficient RMSE
minutes
Network 32, 38, Roughness 1 42 32494 0.7 0.212881
27
Roughness 2 47 36136 0.4 0.126754
Roughness 3 14 3403 0.1 0.017628
Network
Roughness 1
20, 25, 7 10504 0.4 0.140651
17
Roughness 2
3 5021 0.4 0.098192
Roughness 3
2 3104 0.4 0.025206
Table 7: Range of values z original and interpolated data on (20 25 17) network _and comparison of RMSE for all roughness._
Original data range Interpolated grid RMSE %
Roughness 1 -0.7396643 - 1.090838 -0.6786178 to 0.9450067 8.6658
Roughness 2 -0.5203077 - 0.893018 -0.6193843 to 0.6952054 7.4700
Roughness 3 -0.2012766 - 0.141199 -0.1532334 to 0.0899525 10.3624
5.2 Comparison of ANN, IDW and kriging method: The input data selected for input neurons is same as used in IDW and ordinart kriging. The criterion for comparison was RMSE value, time demand and user friendliness.
Comparison by RMSE: Figure 8 (A) compares the RMSE values of resulting raster's. The network used in this comparison was the one with number of 38, 32, 27 neurons. RMSE values of raster generated by the network were in case of segmentation 1 and 2, higher than value of other two methods. This was due to the wrong setting of network parameters; may be network probably got over-trained. Table 8 is recorded RMSE values with four decimal accuracy places.
Fig. 8 (B) compare all methods, the network used in this comparison is one with number of 20, 25, 17 neurons. In this case RMSE values were comparable for all methods, but in case of roughness 2 and 3; values of RMSE for raster interpolated using neural network were higher. This was probably caused by network parameter settings that did not fit the data from this segmentation. Table 8 records the RMSE values with accuracy of four decimal places.
Table 8: RM SE values for all segmentation for GRASS GIS
n network(32, 38, IDW kriging
27)
n network (32, 38, 27) articulation 1 0.2221 0.1398 0.1240
articulation 2 0.1285 0.0874 0.0770
articulation 3 0.0172 0.0177 0.0158
n network (20, 25, 17)
articulation 1 0.1407 0.1398 0.1240
articulation 2 0.0982 0.0874 0.0770
articulation 3 0.0252 0.0177 0.0158
surfacejypel suiface_type2 surface_type3 surface_type1 surface_type2 surface_type3
surfaceJype surface Jype
Figure 8: Comparison of RMSE for all contours of the GRASS GIS (A: 32, 38, 27
and B: 20, 25, 17 network).
The RMSE value of raster's interpolated by MLP were higher than the values of raster created by IDW and kriging. Although it was assumed that neural networks would have better results. There are several reasons: Despite the testing of neural networks settings. It is possible that inappropriate parameters were chosen to fit the nature of data and networks were trained poorly. The other reason for worse results of the neural networks might be insufficient number of input parameters - only two were used: coordinates and elevation (z). Figure 9 shows comparison of the RMSE value for all methods in R Project. RMSE values of raster's by neural networks from both packages were higher than values of raster's by IDW and kriging methods.
surfacetypel surface_type2 surface_type3
surface_type
Figure 9: Comparison of RMSE for all the methods in R Project.
Table 9: RMSE values for all the contours of the R Project.
nnet NeuralNet IDW Kriging
Articulation 1 0.1418 0.1427 0.1325 0.1240
Articulation 2 0.0843 0.1002 0.0828 0.0770
Articulation 3 0.0177 0.0264 0.0176 0.0158
RMSE values for the nnet package for segmentation 2 and 3 are most similar to the RMSE value for the other methods. Table 9 shows the RMSE values with an accuracy of four decimal places. Figure 10 shows the resulting raster interpolated with neural networks, IDW and kriging in GRASS GIS for the segmentation 1.
Fig. 11 show the differential bitmap for segmentation 1. Sub-figures (a) and (b) show the difference in z values between raster's created by neural network (32, 38, and 27) and other methods. Maximum values of difference between the network and the IDW were -0.784100 and 0.707100 and the average value was 0.006563. Values in raster interpolated using IDW was therefore lower than the values in raster interpolated using MLP. Maximal value of difference between the MLP and kriging were -0.666400 and 0.686100 and average value was 0.005321. Values in raster interpolated using kriging were also a bit lower than the values in raster interpolated using MLP.
Sub-figures (c) and (d) show the differences in z values between raster's created by MLP (20, 25, and 17) and other methods. The maximum value difference between the network and IDW were -0.3207000 and 0.3265000 and average value was 0.0030340. Maximal value of difference between the network and kriging were -0.272800 and 0.305600. The average value difference was -0.001977. Raster created by IDW and kriging methods has higher values. The differences between this network, IDW and kriging method is lower than in the first case.
icl IDW fdl krieinE
Figure 10: Comparison of interpolated grid for segmentation 1
Figure 11: The difference in the z values in resulting raster's for segmentation 1
Comparison by time-consuming: The time required to perform an interpolation is shown in Table 10. These values in case of MLP include the time needed to train the network and time required to perform the calculation. In case of other methods, only time required to perform the computation is shown. A neural network is time consuming due to the long training time. If wrong parameters were chosen; then training took a very long time (Table 10). With the better parameters, training time was distinctively shorter. With decreasing segmentation of the data the training time decreased as well. Calculation time was very short; once the networks were properly trained. The longest computation time had the kriging. The fastest
interpolation method was IDW. Interpolation with the neural network was the longest one, mainly because of the time needed to train the networks.
Table 10: Time required to performing interpolation (in ^ minutes).
n network (32, 38, 27) n network (20, 25, 17)
kriging IDW
articulation 1 42 7 3 0.5
articulation 2 47 3 3 0.5
articulation 3 14 2 3 0.5
Comparison by the user-friendliness: This review summarizes the work with availability methods to help and comprehensibility of used methods. IDW method and script v.surf.idw is part of the main installation of GRASS GIS. It can be used via the command line or the graphical interface. When working in the graphical interface a manual is available. It describes each setting that, what is the affect when used and in the last a short theoretical summary. Kriging method does not exist as a module in GRASS GIS. It can be used by connecting the GRASS GIS with R Project program. Only the command line is available for the user. Manual and instructions how to work with the kriging method is available in the R Project as well as in the internet. The ANN module is not a part of main installation of GRASS GIS and it's not stored in the repository modules accessible via the command g.extension. It can be downloaded from http://grasswiki.osgeo.org/wiki/AddOns web page. The ANN module can be operated both in command line and graphical interface, but manual is not included. It has to be opened separately. The manual describes necessary values for parameters but the effect to the outcomes is not mentioned. Unlike the IDW or kriging method, the use of ANN module is difficult for inexperienced users due to lack of knowledge of neural network.
Comparison of interpolation using neural networks in programs GRASS GIS and R Project: Comparisons were carried out in several respects. When compared by RMSE there was no significant difference between the MLP from GRASS GIS and R Project. Figure 12 compare the values of RMSE for the two MLP from the GRASS GIS, nnet and neuralnet package. For segmentation 1, values were almost equal, except the network (32, 38, and 27) of GRASS GIS, which was probably over-trained. This also happened in case of segmentation 2. Values of RMSE for other networks were again similar and best results were given by the nnet package. In case of the segmentation 3; values were again quite similar for (20, 25, and 17) network. MLP of neuralnet package showed signs of over-training. The best results for this segmentation were given by the MLP (32, 38, and 27) from GRASS GIS. Used MLP in both programs were chosen as one of the best possible for the available data. RMSE values for each segmentations is not much different. If the
MLP with different parameters were used. Results would have probably differed
more or less. Table 16 is recorded RMSE values from Fig. 12.
surface_type1 surface_type2 surface_type3
surface_type
Figure 12: Comparison of RMSE for all the contours of n network in GRASS GIS
and R.
The training speed of the networks in ANN module and R Project depends primarily on the number of neurons in the hidden layers, the segmentation of input data and size of training dataset. In case of the ANN module it also depends on appropriate parameter settings.
(c) sit 32, 38, 27 (<l) sit 20, 25, 17
Figure 13: Comparison of interpolated grid for segmentation
However the MLP implemented in packages in R Project train faster than the networks in the ANN module. Figure 13 shows the resulting bitmaps of the neural network for segmentation 1. The resulting raster in partial figure (a), (b) and (d) are visually quite similar and RMSE values is not much differ. Resulting raster in subfigure (c) differ significantly both in visually and RMSE value.
Table 11: RMSE values for all segmentation for GRASS GIS and R Project
n network (20, 25, 17) n network (32, 38, 27)
nnet neuralnet
Articulation 1 0.1407 0.2221 0.1418 0.1427
Articulation 2 0.0982 0.1285 0.0843 0.1002
Articulation 3 0.0252 0.0172 0.0177 0.0264
CONCLUSIONS
Evaluation and testing results shown that MLP available through GRASS 6.4 can be used for spatial interpolation, but if s not better than IDW and kriging method. The disadvantage of ANN module is work with raster data only (in present version). After comparing the neural networks from both software's for the purpose of normal interpolation the R Project is better than GRASS GIS, although neither network in the R Project had better results than the methods IDW and kriging. The use of MLP for spatial interpolation is an interesting option to classical methods. But it's requiring more knowledge of theory from the user and time consuming. The results are often uncertain and the training of MLP has to be repeated many times to reach satisfactory results. The ANN module is in its current form cannot yet be regarded as equivalent to the conventional methods; however future development of this module might make a difference.
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© V. Nevtipilova, Ju. Pastwa, M. S. Boori, V. Vozenilek, 2014
