Comparison of selected clustering algorithms of raw data obtained by interferometric methods using artificial neural networks

Full text

Comparison of Selected Clustering Algorithms of
Raw Data Obtained by Interferometric Methods
Using Artificial Neural Networks
Marta Wlodarczyk-Sielicka
Institute of Geoinformatics
Maritime University of Szczecin
Szczecin, Poland
m.wlodarczyk@am.szczecin.pl
Jacek Lubczonek
Institute of Geoinformatics
Maritime University of Szczecin
Szczecin, Poland
j.lubczonek@am.szczecin.pl
Andrzej Stateczny
Marine Technology Ltd.
Szczecin, Poland
a.stateczny@marinetechnology.pl
Abstract— The article presents a particular comparison of
selected clustering algorithms of data obtained by interferometric
methods using artificial neural networks. For the purposes of the
experiment original data from Szczecin Port have been tested.
For collecting data authors used the interferometric sonar system
GeoSwath Plus 250 kHz. GeoSwath Plus offers very efficient
simultaneous swath bathymetry and side scan seabed mapping.
During the use of Kohonen's algorithm, the network, during
learning, use the Winner Take All rule and Winner Take Most
rule. The parameters of the tested algorithms were maintained at
the level of default. During the research several populations were
generated with number of clusters equal 9 for data gathered from
the area of 100m². In the subsequent step statistics were
calculated and outcomes were shown as spatial visualization and
in tabular form.
Index Terms— interferometric system; artificial neural
network; clustering algorithm; bathymetry
I.
I
NTRODUCTION
The most important data for maritime and inland navigation
are Electronic Navigational Charts (ENC). Some aspects of
Electronic Navigational Charts using in navigation process was
discussed in [1-5].
Data essential to chart production are gathering during
hydrographical works. Usually, the most important are the
bathymetric data. This data are gathered by synchronous
registration of geographical coordinates (φ,λ) obtained most
often by means of system GPS in RTK mode and hydrographic
measurement of depths (h), converted to data sets of XYZ
points. This data are a very big sets of bathymetric points.
During post processing data should be reduced for presentation
bathymetric data on charts. Clustering is the first step of the
proposed reduction algorithm.
Spatial clustering is the task of grouping a set of points in
such a way that points in the same cluster are more similar to
each other than to those in other groups clusters [6].
Bathymetric data very often are collected used multibeam
echosounders (MBES), among them interferometric systems
are popular. For collecting data authors used the interferometric
sonar system GeoSwath Plus 250 kHz. GeoSwath Plus offers
very efficient simultaneous swath bathymetry and side scan
seabed mapping with accuracies much better then specified in
the IHO Standards for Hydrographic Surveys. The applied
phase measuring bathymetric sonar technology provides data
coverage of up to 12 times the water depth, giving unsurpassed
survey efficiency in shallow water environments. The
GeoSwath Plus turn-key solution comprises a dual transducer
head with versatile mounting options as well as a deck unit
containing the complete sonar electronics together with a high
spec PC with hydrographic software. The software provides
full acquisition, calibration and data processing capabilities for
producing the final bathymetry map and side scan mosaic data
products. All customary ancillary sensors can be directly
interfaced. The measurement profiles maintaining 100%
coverage of the measured body of water were realized. Some
problem of multibeam echosounders data processing was
described in [7-11]. Similar to MBES problems are with
LIDAR data [12] as well other navigational data processing
[13-16]. Another interesting problem is multisensory data
fusion [17-21].
The main goal of this paper is to compare of selected
clustering algorithms of raw data obtained by interferometric
methods. Some aspects of data reductions was described in
previous authors works [22-23].
II.
ARTIFICIAL NEURAL NETWORKS
Artificial neural networks (ANN) can be treated as a
certain kind of data structure, which changes in the course of
978-1-5090-2518-3/16/$31.00 ©2016 IEEE

the learning process adapting to the kind of problem to be
solved. This structure is constituted by single neurons
performing simple arithmetic functions bound into a network.
The first and basic neuron model defined as early as in 1943 by
McCulloch and Pitts is the nerve cell, the function of which
consists in the weight sum of neuron entrances, and next
subjecting the sum thus obtained to the action of non-linear
activation function. ANN are very often used to solve
navigational problems like sea bottom shape modeling [24-26]
and others tasks [27-35].
For clustering problems solution especially useful are self-
organizing ANN. Kohonen's networks are one of basic types of
self-organizing neural networks. The ability to self-organize
provides new possibilities - adaptation to formerly unknown
input data. It seems to be the most natural way of learning,
which is used in our brains, where no patterns are defined.
Those patterns take shape during the learning process, which is
combined with normal work.
Kohonen's networks are a synonym of whole group of
networks which make use of self-organizing, competitive type
learning method. At the beginning, signals on network's inputs
were set up and then winning neuron is chosen, the one which
corresponds with input vector in the best way. Precise scheme
of competition and later modifications of synaptic wages may
have various forms. There are many sub-types based on rivalry,
which differ themselves by precise self-organizing algorithm.
During the use of Kohonen's algorithm, the network, during
learning, use the Winner Takes All rule (further referred to as
WTA) and Winner Takes Most rule (further referred to as
WTM). In case of WTA rule neural adaptation relates only to
the winner neuron. Neurons lose competition neurons do not
modify their weights. While, WTM rule modifies not only the
weight of the winner, but also its neighbors. The radius of the
neighborhood decreases with learning time. In this case winner
neuron and all neuron within a radius of its neighborhood
subject to adaptation [36].
III. T
HE SPECIFICATION OF GEODATA REDUCTION METHOD
Spatial data obtained by interferometric methods is a large
set of points. The essential purpose of the authors’ research is
the implementation of a new reduction algorithm for spatial
data (XYZ points) to be used for the creation of bathymetric
map. In short reduction of data is a procedure by which the
number and hence size of a data set is reduced, in order to
make the analysis easier and more efficient. In many cases,
hydrographic systems generate a grid of bathymetric data by
using means or weighted means. The authors aim to create a
new reduction algorithm for bathymetric data using artificial
neural networks. The clustering of data is the first part of the
search algorithm and the next stage is the generalization of
bathymetric data. Schema of the search algorithm is shown in
Fig. 1.
Figure 1. Schema of proposed reduction algorithm.
The goal of the authors is to classify a set of XYZ points
into clusters and then represent each group by a single point
with minimum depth depending on the compilation scale. It
needs to be highlighted that, in this method the points of
minimum depth will remain in their true position, and they will
be visualized irrespective of the scale used on bathymetric
map. For safety associated with navigation it is very important
to retain points of minimum depth. The main objective of new
reduction algorithm is that, the position of point and the depth
at this point will not be an interpolated value.
IV. E
XPERIMENT
For the purposes of the experiment original data from
Szczecin Port have been tested. Artificial neural networks were
used for data clustering. During the use of Kohonen's
algorithm, the network, during learning, use the WTA rule and
WTM rule. The parameters of the tested algorithms were
maintained at the level of default. During the research several
populations were generated with number of clusters equal 9 for
data gathered from the area of 100m². In the subsequent step
statistics were calculated and outcomes were shown as spatial
visualization and in tabular form. The final step was their
analysis. The test algorithms were implemented using Matlab
software, developed by MathWorks.
A. Test area
During the bathymetric survey a large amount of data was
gathered. When using a standard computer, very high-density
data present the main operational limitation. For solve this
problem, the authors separated the primary data point sets into
smaller subsets. During the studies, test data gathered from the
area of 100m² was used and this set contains 3 760 samples of
XYZ elements. Test data was collected within Szczecin Port,
near the Babina Canal. This area at the scale 1:25000 is
presented in Fig. 2.

Figure 2. Partial view of Szczecin Port.
Several point has three attributes: latitude (X), longitude
(Y) and depth at a given point (Z). The minimum depth within
this area is 3.60 meters and the maximum depth is 5.23 meters.
B. Parameters of algorithms
For data gathered from the area of 100m², over the tests
several populations were generated with number of clusters
equal 9. For the purpose of clustering self-organizing map was
applied. The authors selected the hexagonal network topology,
where each of the hexagons represents a neuron. The numbers
of rows and columns was set to 3×3, which provided 9 clusters.
During each trainings the number of iteration was set at 1000.
Distances are calculated from their positions by means of a link
distance function, which is default function in software used.
The link distance from one neuron is the number of links or
steps that must be taken to get to the neuron under
consideration. During the training the network applies the
WTA rule and WTM rule. Consequently using the WTN rule
the initial neighborhood size was set at 3 and the number of
training steps for initial coverage of the input space was set at
100. During this phase, the neighborhood is gradually reduced
from a maximum size of neighborhood down to 1, where it
remains from then on.
C. Results
The results for 9 clusters are presented in this article. All sets
of received clusters were analyzed. During the research the
authors adopted the precision of two decimal places.
In this research the authors adopted the following
evaluation criteria: time taken for calculations and distribution
of data in each cluster. The authors focused on depth values,
which are of significant importance for the safety of
navigation. Tab. 1 introduces the results for 9 clusters.
TABLE I. C
OMPARISON OF STATISTICS FOR
9
CLUSTERS
Clusters
1 2 3 4 5 6 7 8 9
WTA
Min
a
4.09 4.16 3.93 3.66 3.96 4.00 3.60 3.67 4.08
Max
b
5.22 5.20 5.04 4.67 5.04 4.92 4.75 4.60 5.23
Mean
c
4.65 4.71 4.46 4.17 4.42 4.46 4.25 4.15 4.69
SD
d
0.22 0.20 0.19 0.18 0.17 0.17 0.19 0.17 0.22
NoP
e
355 368 348 467 484 518 416 478 326
WTM
Min 4.09 4.11 3.93 3.67 3.96 3.94 3.60 3.70 4.17
Max 5.22 5.20 4.94 4.67 4.94 5.04 4.74 4.60 5.23
Mean 4.64 4.69 4.48 4.17 4.39 4.47 4.21 4.17 4.72
SD 0.22 0.20 0.17 0.18 0.17 0.19 0.19 0.17 0.22
NoS 304 446 524 478 443 430 421 434 280
a. Minimum value of depth
b. Maximum value of depth
c. Mean value of depth
d. Standard deviation
e. Number of samples in each cluster
The results for different method in clusters are comparable.
Minimum values of depth in each cluster are at a similar level.
For four clusters they are the same. The major differences are
in cluster designated as 9 and cluster marked 2. The differences
range from 5 centimeters to 9 centimeters. The differences
between minimum and maximum depth in each clusters for
WTA range 0.92 meter to 1.15 meter. While, for WTM they
range 0.90 meter to 1.14 meter. The mean values of depth are
slightly different in each cluster, which is shown in Fig. 3. The
biggest difference between the methods occurs for cluster
designated as 7 and it is only 4 centimeters.
Figure 3. Comparison of the mean values of depth in each cluster.
A high standard deviation is in cluster marked 1 and 9 – at a
level equal 0.22. It indicates that the data points are spread out
over a wider range of values.

Fig. 4 presents spatial representation of the results for the for 9
clusters. It can be noticed, that results for WTA and WTM are
close to each other.
Figure 4. Spatial representation of results for a) WTA and b)WTM.
The final analyzed value is number of samples in each cluster.
Fig. 5 presents distribution numbers of points in each clusters
for tested methods. The axis X represents the number of
clusters and the axis Y shows number of samples.
Figure 5. Distribution of the number of samples in each cluster.
The greatest difference can be seen for cluster designated as 3.
However, it should be noted that for this cluster the minimum
depth is the same and it assumes a value of 3.93 meters.
During tests the authors also paid attention on the time taken
for calculations. It was shorter by about 5 seconds, when
WTM rule was tested.
V. C
ONLUSION
Self-organizing networks have the ability to divide spatial
data areas. They accumulate together data with similar values.
The authors aim to create a new reduction algorithm for
bathymetric data. The main criterion for evaluating each
method for reduction of bathymetric maps is the legibility of
the maps. After analysis of the above results it can be used both
tested methods. The statistics related to depth values were
taken into account and the results in particular clusters are
comparable. Minimum values of depth in each cluster are very
similar. However, it should be noted that the time taken for
calculations was shorter when WTM rule was used. High-
density data obtained by interferometric methods present the
main operational limitation when using a standard computer.
So, the original data point have to be divided into smaller
subsets, which could be trained separately. In this case
computing time is very important. Regular distribution of data
in each cluster is important in case of a small slope bottom. In
the next stages of the research, the authors will use the selected
method over several different test areas. These areas will be
characterized by varying the inclination and by a diverse
distribution of samples.
R
EFERENCES
[1] A. Stateczny, I. Bodus-Olkowska, “Hierarchical Hydrographic Data
Fusion for Precise Port Electronic Navigational Chart Production”.
Mikulski J.(ed.) Telematics in the Transport Environment, Book Series:
Communications in Computer and Information Science 471, pp. 359-
368. Ustron, 2014.
[2] N. Wawrzyniak, T. Hyla, „Managing Depth Information Uncertainty in
Inland Mobile Navigation Systems”. Proceedings of the Joint Rough Set
Symposium, Granada and Madrid, Spain, Kryszkiewicz et al. (Eds),
Lecture Notes in Artificial Intelligence, 8537, pp. 343–350, 2014.
[3] W. Kazimierski, A. Stateczny, “Radar and Automatic Identification
System track fusion in an Electronic Chart Display and Information
System”. The Journal of Navigation vol. 68, issue 6, pp 1141 - 1154
2015.
[4] W. Kazimierski, A. Stateczny, “Fusion of Data from AIS and Tracking
Radar for the Needs of ECDIS”, IEEE Conference: Signal Processing
Symposium (SPS), Jachranka 2013.
[5] M. Wlodarczyk-Sielicka, M., A. Stateczny, “Clustering Bathymetric
Data for Electronic Navigational Charts”. The Journal of Navigation (in
press), 2016
[6] Z. Li, “Algorithmic Foundation of Multi-scale Spatial Representation”,
CRC Press, 2007
[7] W. Maleika, “The influence of track configuration and multibeam
echosounder parameters on the accuracy of seabed DTMs obtained in
shallow water”. Earth Science Informatics, vol. 6, issue 2, pp. 47-69,
2013.
[8] W. Maleika, “Development of a Method for the Estimation of
Multibeam Echosounder Measurement Accuracy”. Przeglad
Elektrotechniczny, 88 (10B), 205–208, 2012.
[9] W. Maleika, M. Palczynski, D. Frejlichowski, “Effect of Density of
Measurement Points Collected from a Multibeam Echosounder on the
Accuracy of a Digital Terrain Model”. 4th International Scientific Asian
Conference on Intelligent Information and Database Systems (ACIIDS).
Edited by: Pan, JS., Chen, SM., Nguyen, NT., Book Series: Lecture
Notes in Artificial Intelligence, vol. 7198, pp. 456-465. Kaohsiung,
Taiwan 2012.
[10] W. Maleika, “Moving Average Optimization in Digital Terrain Model
Generation Based on Test Multibeam Echosounder Data”. Geo-Marine
Letters, 35, 61–68, 2015.
[11] W. Maleika, “The Influence of the Grid Resolution on the Accuracy of
the Digital Terrain Model Used in Seabed Modelling”. Marine
Geophysical Research, 36, 35–44, 2015.
[12] P. Burdziakowski, A. Janowski, A Kholodkow et al. “Maritime Laser
Scanning as the Source For Spatial Data” Polish Maritime Research, vol.
22, issue 4, pp.9-14, 2015.
[13] A. Stateczny, N. Wawrzyniak, “Method for determining stationary
position of scanning sonar, involves determining head position based on
sonar search for actual sonar image with set of synthetic images
generated by performing ray tracing process based on model of bottom”.
Patent Number: PL406523-A1. Patent Assignee: Marine Technology Sp.
z o.o. 2015.

[14] A. Stateczny, “Methods of comparative plotting of the ship's position”.
Book Editor(s): Brebbia, CA., Sciutto, G. Maritime Engineering & Ports
III. Book Series: Water Studies Series vol. 12, pp. 61-68, Rhodes 2002.
[15] M. Przyborski, “Possible determinism and the real world data”. Physica
A-Statistical Mechanics and its Applications, vol. 309, issue 3-4, pp.
297-303, 2002.
[16] M. Przyborski, J. Pyrchla, “Reliability of the navigational data”.
International Intelligent In-formation Systems/Intelligent Information
Processing and Web Mining Conference (IIS: IIPWM 03). Edited by:
Klopotek, MA., Wierzchon, ST., Trojanowski, K., Book Series: Ad-
vances in Soft Computing, pp. 541-545. Zakopane, 2003.
[17] J. Łubczonek, M. Borawski, “Comparative analysis of radar image
compression methods”, Proceedings of 16th International Radar
Symposium (IRS), International Radar Symposium Proceedings, H.
Rohling (Ed.), pp. 1117 - 1122, Dresden, Germany (2015).
[18] A. Stateczny, W. Kazimierski, “Sensor Data Fusion in Inland
Navigation”. Book Editor(s): Rohling, H. 14th International Radar
Symposium (IRS), vols. 1 and 2. Book Series: International Radar
Symposium Proceedings pp. 264-269. Dresden 2013.
[19] W. Kazimierski, “Problems of Data Fusion of Tracking Radar and AIS
for the Needs of Integrated Navigation Systems at Sea”. 14th
International Radar Symposium (IRS), vol.1 and 2, Book Series:
International Radar Symposium Proceedings, pp. 270-275, Dresden,
2013.
[20] T. Hyla, W. Kazimierski, N. Wawrzyniak, „Analysis of Radar
Integration Possibilities in Inland Mobile Navigation. Proceedings of the
16th International Radar Symposium (IRS), International Radar
Symposium Proceedings, Dresden, Germany, H. Rohling (Ed.), pp. 864-
869, 2015.
[21] A. Stateczny, I. Bodus-Olkowska, “Sensor Data Fusion Techniques for
Environment Modelling”. Proceedings of 16th International Radar
Symposium (IRS), International Radar Symposium Proceedings, H.
Rohling (Ed.), pp. 1123-1128. Dresden, 2015.
[22] A. Stateczny, M. Wlodarczyk-Sielicka, “Self-Organizing Artificial
Neural Networks into Hydrographic Big Data Reduction Process”. 2014
Joint Rough Set Symposium, Granada-Madrit, Lecture Notes in
Computer Science, vol. 8537, pp. 335-342, Granada-Madrit, 2014.
[23] M. Wlodarczyk-Sielicka, A. Stateczny, “Selection of SOM Parameters
for the Needs of Clusterisation of Data Obtained by Interferometric
Methods”. Proceedings of 16th International Radar Symposium (IRS),
International Radar Symposium Proceedings, H. Rohling (Ed.), pp.
1129-1134. Dresden, 2015.
[24] J. Lubczonek, “Hybrid neural model of the sea bottom surface”. Edited
by: Rutkowski, L., Siekmann, J., Tadeusiewicz, R. et al. 7th
International Conference on Artificial Intelligence and Soft Computing -
ICAISC 2004. Book Series: Lecture Notes in Artificial Intelligence, vol.
3070, pp.: 1154-1160. Zakopane, 2004.
[25] J. Lubczonek, A. Stateczny, “Concept of neural model of the sea bottom
surface”. Book Editor(s): Rutkowski, L., Kacprzyk, J. Neural Networks
and Soft Computing Book Series: Advances in Soft Computing, pp. 861-
866. Zakopane 2003.
[26] A. Stateczny, “The neural method of sea bottom shape modelling for the
spatial maritime information system”. Book Editor(s): Brebbia, CA.,
Olivella, J. Maritime Engineering and Ports II. Book Series: Water
Studies Series vol. 9, pp. 251-259. Barcelona 2000.
[27] A. Stateczny, “Neural manoeuvre detection of the tracked target in
ARPA systems”. Book Editor(s): Katebi, R. Control Applications in
Marine Systems 2001 (CAMS 2001). Book Series: IFAC Proceedings
Series, pp. 209-214, Glasgow 2002.
[28] A. Stateczny, W. Kazimierski, “Selection of GRNN network parameters
for the needs of state vector estimation of manoeuvring target in ARPA
devices”. Book Editor(s): Romaniuk, RS. Photonics Applications in
Astronomy, Communications, Industry, and High-Energy Physics
Experiments IV. Book Series: Proceedings of the Society of Photo-
Optical Instrumentation Engineers (SPIE) vol. 6159, pp. F1591-F1591.
Wilga 2006.
[29] A. Stateczny, W. Kazimierski, “A comparison of the target tracking in
marine navigational radars by means of GRNN filter and numerical
filter”. 2008 IEEE Radar Conference, vols. 1-4. Book Series: IEEE
Radar Conference, pp. 1994-1997. Rome 2008.
[30] A. Stateczny, W. Kazimierski, “Determining Manoeuvre Detection
Threshold of GRNN Filter in the Process of Tracking in Marine
Navigational Radars”. Book Editor(s): Kawalec, A., Kaniewski, P. 2008
Proceedings International Radar Symposium, pp. 242-245. Wroclaw
2008.
[31] A. Stateczny, “Artificial neural networks for comparative navigation”.
Book Editor(s): Rutkowski, L., Siekmann, J., Tadeusiewicz, R., et al.
Artificial Intelligence and Soft Computing - ICAISC 2004. Book Series:
Lecture Notes in Artificial Intelligence vol. 3070, pp. 1187-1192,
Zakopane 2004.
[32] J. Balicki, Z., Kitowski, A. Stateczny, “Extended Hopfield Model of
Neural Networks for Combinatorial Multiobjective Optimization
Problems”. 2th IEEE World Congress on Computational Intelligence,
pp. 1646-1651. Anchorage 1998.
[33] A. Stateczny, W. Kazimierski, “Method and system of determining the
vector of traced objects”. Patent Number: PL212560-B1. Patent
Assignee: Akademia Morska w Szczecinie, 2012.
[34] W. Kazimierski, G. Zaniewicz, “Analysis of the Possibility of Using
Radar Tracking Method Based on GRNN for Processing Sonar Spatial
Data”, Proceedings of the Joint Rough Set Symposium, Spain,
Kryszkiewicz et al. (Eds), Lecture Notes in Artificial Intelligence, 8537,
pp. 319-326. Granada and Madrid, 2014.
[35] A. Stateczny, Method for determining control parameters of collision
avoidance floating units of watercraft, involves detecting objects that
threaten collision, cascading modules in appropriate manner, and
determining parameters for optimal maneuver. Patent Number:
PL408536-A1. Patent Assignee: Marine Technology Sp. z o.o. 2016.
[36] S. Osowski, “Sieci neuronowe do przetwarzania informacji”, Oficyna
Wydawnicza Politechniki Warszawskiej, 2013.