Int'l Conf. IP, Comp. Vision, and Pattern Recognition | IPCV'15 |
387
A Novel Trajectories Classification Approach for different
types of ships using a Polynomial Function and ANFIS
M. Elwakdy1, M. El-Bendary2, and M. Eltokhy3
Department of Electronic Technology, Helwan University, El-Amyria, Cairo, Egypt
2
Department of Electronic Technology / Helwan University, El-Amyria, Cairo, Egypt
3
Department of Electronic Technology / Helwan University, El-Amyria, Cairo, Egypt
1
Abstract - In this paper, a Trajectories Classification
Algorithm (TCA) is presented. The points of the tanker ship and
fishing boat were collected in the same environment. Each
trajectory of the tanker ship and fishing boat is partitioned to
many segments to extract the features from each trajectory by
using the polynomial function. The features extraction is used
as input of the subtractive clustering to put the data in a group
of clusters. Also it is used as an input of the neural network in
ANFIS.
The features extraction of each trajectory is represented with
the membership functions and group of the Fuzzy If-then rules.
The Initial Fuzzy Inference System (IFIS) is trained with
artificial neural network to get the Final FIS. The performance
of the TCA using a polynomial function and ANFIS is evaluated
by different trajectories. The proposed TCA is tested using
different trajectories obtaining a high classification accuracy
99.5%.
Keywords: Trajectories Classification; polynomial function;
Subtractive clustering; ANFIS.
1
Introduction
Pattern recognition is a section of machine learning which
aims to classify the trajectories of different kinds of objects.
Trajectories’ classification is important research topic for
predicting the type of moving objects (tanker ships and fishing
boats) based on their trajectories and other features [1-3].
Trajectories’ classification is one of the hot topics that
scientists are interested to work on. This study aims to
discriminate between two different types of ships [4]: Tanker
ship and fishing boat based on their trajectory data by using
ANFIS. In the classification task, we work on predicting with
the type of the object (fishing boat or tanker ship) that a
trajectory belongs to. There are different features that are
extracted from the tanker ship and fishing boat where the
fishing boat moves in bending trajectories (no limitation of the
movement of the fishing boat) and the tanker ship which moves
in specified trajectories (simple trajectories) at sea. This
presented innovative method that can be used widely in the
future for detecting any abnormal ship movements through
remote sensing, which can be an important assistance for
security and coastal safety in general.
Adaptive Neuro-Fuzzy Inference System is used for the
trajectories’ classification. ANFIS is not offered for all the
Fuzzy Inference System options [5]. Fuzzy logic was proposed
by Lotfi Zadeh [6]. Fuzzy logic concepts are contributed as an
effective tool in automatic decision making systems such as
pattern classification systems. In late 1980s, Neural Networks
(NNs) and Fuzzy Logic (FL) technologies developed as an
effective tool in many fields [7-11].
ANFIS is divided into two main groups: hybrid of neural
network and fuzzy logic which combine to enhance the
prediction capabilities so ANFIS merge both neural networks
and fuzzy logic principles to take advantage of both of them in
a single framework [5]. Artificial neural network performance
depends on the size of training samples [12]. This means that
the data must be prepared well before the training stage by
artificial neural network. When the size of training data is small
and doesn’t represent the possibility space, this preforms that
the network results are poor [13].
For preparing the data before the classification stage, each
trajectory is divided to many segments. A combination of
polynomial function [14] and ANFIS are efficiently extract the
features from each segment, and provide these features to
ANFIS for the classification purpose for getting high
classification accuracy and least average error.
This paper is organized as follows: Section 2 stated the
trajectories characterization of the fishing boat and tanker ship.
Section 3 stated the features extraction using the polynomial
function, subtractive clustering and ANFIS. Section 4 stated
training parameters using the ANFIS. The efficiency of the
proposed method for classification of the ships trajectories in
the proposed TCA through ANFIS is demonstrated in Section
4. In Section 5, the related work is discussed. In Section 6,
conclusions are presented. Finally, references are presented in
Section 7.
388
2
Int'l Conf. IP, Comp. Vision, and Pattern Recognition | IPCV'15 |
Trajectories
The Trajectories of both objects (tanker ship and fishing
boat) are represented as a sequence of 2-dimensional points
(vectors or trajectory elements) [3, 4] <x1; y1; t1>; …; < xn; yn;
tn> where xn and yn represent the position of the object at time
tn. In this paper, the temporal dimension is discarded, and each
trajectory of both objects is presented as T = < x1; y1 >; …; <
xn; yn >. The sample rate of all trajectories is not constant where
the temporal difference between the sequential samples is not
always the same. Generally, the trajectories of both objects are
different in temporal length, the number of data points and
distance traveled. Each trajectory of both objects is partitioned
to many line segments [1, 2, 4, 15], and the used real
trajectories database [4] is represented two different types of
ships in this study. This database is divided to two classes:
Tanker ship class and fishing ship class. The total number of
trajectories is 12 trajectories of both ships. The trajectories
number of the tanker ship (points) is 6 (530), and the
trajectories number of the fishing boat (points) is 6 (896).
3
Proposed Trajectories Classification
Algorithm (TCA)
TCA consists of three parts that are: features extraction,
subtractive clustering and ANFIS. The proposed algorithm is
used to carry the goal of this research.
The proposed algorithm is illustrated in Fig.1.
The following subsections are clarified in the above system's
block diagram.
3.1
Features Extraction
Polynomial function is used as a common base for
extracting the coefficients (discriminating features) [16] from
each trajectory of both objects (tanker ship and fishing boat).
The features extraction is the stage before the trajectories’
classification stage. For extracting the coefficients from each
trajectory, the polyfit function is used “polyfit (x, y, n)” in
MATLAB where ‘x ’ and ‘y ’ indicate the number of points of
each trajectory of both objects which are represented as a
Matrix and ‘n’ indicates the degree of the polynomial function
[14]. This function is used to return the coefficients for a
polynomial p(x) of degree n of each trajectory of both objects
that is a best fit (in a least-squares sense) for the trajectory data
in y. A polynomial with a degree n is represented as in Eq. (1):
‫݌‬ሺ‫ݔ‬ሻ ൌ ‫݌‬ଵ ‫ ݔ‬௡ ൅ ‫݌‬ଶ ‫ ݔ‬௡ିଵ ൅ ‫ ڮ‬൅ ‫݌‬௡ ‫ ݔ‬൅ ‫݌‬௡ାଵ
(1)
Fig.1. Proposed Algorithms of the Trajectories Classification (TCA)
using Features Extraction, Subtractive Clustering and ANFIS.
Where p1, p2,…, pn+1 indicate the coefficients for the
polynomial function. Because the coefficients don’t represent
the whole trajectories of both objects as shown in Fig.2 and
Fig.3, each trajectory is partitioned to equal number of
segments for getting a good representation of each segment by
using the polynomial function. The polynomial function is
used for extracting the same number of coefficients for each
segment of all trajectories where each segment consists of the
same number of points (three consecutive points) as much as
possible as shown in Fig.4 and Fig.5. When the segments
number in each trajectory of both objects is increased, the
coefficients can be represented all segments of all trajectories
of both objects well. This helps in getting real classification
accuracy by using an ANFIS. Note that, the number of points
of each trajectory depends on the type of object as we
mentioned before.
Int'l Conf. IP, Comp. Vision, and Pattern Recognition | IPCV'15 |
Fig.2. Blue line indicates the fishing boat trajectory
(bending trajectory) at sea. The Green line depicts to plot
Y through the constructed polynomial model evaluated
at each X- component values. The generic symbols X and
Y indicate the longitude and latitude coordinates
(projections of these coordinates to an x; y-plane).
389
Fig.5. Good representation of a segment is shown by
using a polynomial function. The segment of the tanker
ship trajectory consists of three consecutive points. The
generic symbols X and Y indicate the longitude and
latitude coordinates (projections of these coordinates to
an x; y-plane).
In simple and bending trajectories, when the coefficients
number is increased by using the “polynomial function”, this
will perform to “over-fitting problem” where the coefficients
don’t represent the ships' trajectories. For that, the increase of
segments number helps in getting a very good representation of
the sub-trajectories (all segments) of both objects, and
overcomes on the “over-fitting problem”. There are a lot of
experiments that are performed to specify the degree of the
polynomial function (the degree of a polynomial is ‘4’).
Fig.3. Blue line indicates the tanker ship trajectory
(simple trajectory) at sea. The Green line depicts to plot
Y through the constructed polynomial model evaluated
at each X- component values. The generic symbols X
and Y indicate the longitude and latitude coordinates
(projections of these coordinates to an x; y-plane).
Fig.4. Good representation of a segment is shown by
using a polynomial function. The segment of the fishing
boat trajectory consists of three consecutive points. The
generic symbols X and Y indicate the longitude and
latitude coordinates (projections of these coordinates to
an x; y-plane).
The dataset contains all coefficients of all segments of all
trajectories (both objects). The preparation of data is very
important to get high classification accuracy and least average
error so the coefficients extracted from all segments of all
trajectories of both objects are partitioned to equal number of
groups where the total number of groups is 22. The number of
coefficients in each group depends on the length of the
trajectories which include different number of points based on
the type of object. The ‘standard deviation’, ‘variance’, max
function’ and ‘bsxfun function’ in MATLAB [17, 18] are used
for all coefficients of each group to reduce the size of dataset
or to prepare the dataset well before the next stage (Subtractive
Clustering) as shown in Fig. 6. This helped on reducing the
number of rules which preformed to reduce the computational
cost and training time [5]. In this study, 50 % of the dataset of
each object is used for training by an artificial neural network,
and 50 % of the dataset of each object is used for testing.
390
Int'l Conf. IP, Comp. Vision, and Pattern Recognition | IPCV'15 |
3. The threshold δ is defined as the decision to continue or
stop in search about the cluster center. The search about
the cluster center will go on if the current maximum
potential remains greater than δ where δ is defined as δ
= (reject ratio) × (potential value of the first cluster
center) where η is the rejection ratio and ‫݌‬ሺଵሻ‫ כ‬is the
potential value of the first cluster center [20].
4. Remove the previous cluster center from further
consideration [20].
5. Revise the potential value of the remaining points
according to the Eq. (4) [20].
‫ʹ כ‬
‫݌‬௜ ൌ ‫݌‬௜ െ ‫݌‬௞‫݁ כ‬െߚ൫௭೔ ି௭ೖ൯ ሺͶሻ
Where ‫݌‬௞‫ כ‬is its potential value, ‫ݖ‬௞‫ כ‬is the point of the kth
ଶ
ଶ
cluster center, and β = 4/‫ݎ‬௕ and ‫ݎ‬௕ > 0 indicates the
radius of the neighborhood for which significant
potential reduction will occur [21].
Fig.6. Analysis Framework
3.2
Subtractive Clustering
The training and checking data is uploaded to ANFIS
EDITOR GUI of MATLAB. The training data is used in
training the Sugeno based ANFIS in next phases. The purpose
of the subtractive clustering is estimating the number of clusters
and the cluster centers through the training data. Through the
subtractive clustering, the training data is partitioned into
clusters [19]. The procedure for grouping 22 data point clusters
{z1, z2, z3,…., zn= 22} in the training set is described below
[20].
The work on generating the cluster centers is repeated until the
maximum potential value in the current situation is equal to less
than the threshold δ. We get different cluster center numbers
from 22 training samples (patterns) after using the subtractive
clustering (depending on the rejection ratio) [20]. The IFIS is
generated with number of rules and membership functions at
the end of clustering by using the subtractive clustering [19].
The training data is used to get the primary parameters of the
membership functions [5]. The center of each cluster is
projected to get the centers of the membership functions, and
the widths of the membership functions are obtained on the
basis of the radius [21].
ଶ
ଶ
α=4/‫ݎ‬௔ where ‫ݎ‬௔ is a positive constant
representing a normalized neighborhood data radius for
each cluster. Any point will have a little effect if it drops
out outside this encircling region. The point is
determined as a first cluster center if it has the highest
potential value. This temporarily defines the first cluster
center [20].
There are multiple parameters that are used for clustering:
Range Of Influence, Squash Factor, Accept Ratio and Reject
Ratio. Range of Influence indicates the radius of a cluster when
the data space is considered as a unit hypercube [22]. The goal
of the Squash Factor is that determines the neighborhood of a
cluster center by multiplying the radii values in that factor [22].
The Accept Ratio contributes in determining the cluster center.
When the value of Accept Ratio is high, this means that the data
points have a very strong potential for being cluster centers
[22]. The Reject Ratio contributes too in determining the
condition to reject a data point to be a cluster center [20]. The
criteria in determining the cluster center depends strongly on
the Accept and Reject ratios [20]. Based on these parameters
are mentioned before, the IFIS is constructed as shown in Fig.1.
2. When potential value (‫݌‬ሺଵሻ ) is equal to the maximum
The clustering parameters are used in this study are shown in
Table. I
1.
Calculate the initial potential value for each data point
(zi) as in Eq. (2) [20].
ܲ௜ ൌ ෍
݊
݆ൌͳ
݁െߙ൫௭೔ି௭ೕ൯ ሺʹሻ
of initial potential value (‫݌‬ሺଵሻ‫) כ‬, the point is qualified
as the first center as in Eq. (3) [15].
‫݌‬ሺଵሻ‫ כ‬ൌ ݉ܽ‫ݔ‬௜ ቀ‫݌‬ሺଵሻ ሺ‫ݖ‬௜ ሻቁሺ͵ሻ
Int'l Conf. IP, Comp. Vision, and Pattern Recognition | IPCV'15 |
TABLE.I. the clustering parameters are used in this study
Clustering
Parameters
3.3
Value
Range Of Influence
0.8
Squash Factor
1
Accept Ratio
0.5
Reject Ratio
0.15
Adaptive Neuro-Fuzzy Inference System
(ANFIS)
Adaptive Neuro- Fuzzy Inference System (ANFIS) is
used in many applications [5, 23-25]. In this study, ANFIS is
used for a classification purpose where it is used for predicting
the type of object: Tanker ship or fishing boat through their
trajectories. There are two kinds of fuzzy logic inference
system: Mamdani fuzzy logic inference system and TakagiSugeno fuzzy logic inference system. The ANFIS has a good
advantage where it merges artificial neural network and fuzzy
logic system [24]. The Artificial Neural Network works on
training the IFIS to access to least possible error between the
desired output and FIS output through the dataset to obtain
Final FIS as in Fig.1. The schematic of the architecture of
ANFIS based on Sugeno fuzzy model is shown in Fig.7.
391
The ANFIS works on classifying the data based on the features
extracted values [26] which represent the trajectories
characteristics which apply as inputs of ANFIS. The structure
of ANFIS [6] included input parameters, input membership
functions, Fuzzy rules, output parameters which represent
trajectories, output membership functions, and resultant
prediction of trajectories. The hybrid-learning algorithm [27,
28] is employed here where it is used to fit the input and output
membership parameters. The Hybrid learning rule is faster than
the classical back-propagation method [29]. The Hybrid FIS is
trained in 3 Epochs, and the Error tolerance is kept zero for the
process. The Hybrid FIS is a combination of back-propagation
algorithm and Least Squares [5]. The average error rate
depends strongly on the number of membership functions. In
addition, the average error rate and classification accuracy
depend on the difference between the FIS output curve and
checking data curve [5].
The ANFIS is evaluated with new input data (checking data)
where an ANFIS simulates the checking data with the stored
data [24]. After the training phase is successfully completed by
using an artificial neural network, the Final FIS is tested with
the checking data introduced where the training data is
converted to Fuzzy data. The fuzzy data has value between ‘0
to 1’ [23]. The ANFIS works on the basis of IF-Then rules [5]
where the IF-Then rules change if any change (modify)
happened in the membership functions. Based on the IF-Then
rules, the checking data (input data) is compared with the
trained data (output data). The ANFIS works on training the
fuzzy logic system by changing the membership functions [24].
The membership functions represent the training and checking
data which are uploaded from MATLAB workspace, and the
input membership functions are shown in Fig. 8. The total
number of IF-then rules is 4 rules where each IF-Then rule
contains six coefficients where five coefficients are multiplied
with five inputs in addition to the constant. IF-Then rules are
the core of fuzzy logic, and are related varies stages with input
parameters [5]. Each IF-Then rule explains some relationships
between the input and output variables [25].
(A)
Fig.7 the schematic of ANFIS architecture based on Sugeno fuzzy
model.
392
Int'l Conf. IP, Comp. Vision, and Pattern Recognition | IPCV'15 |
4
(B)
Experiment Results
In this study, the training and checking of the proposed
algorithm is done by using the ANFIS. There is 12 trajectories
of both ships is applied to the proposed algorithm where six
trajectories (three trajectories of both ships) is used as a training
data and the other six trajectories (three trajectories of both
ships) is used as a checking data for the proposed algorithm.
The tanker and fishing trajectories are correctly classified by
using the ANFIS. The ‘5’ input parameters are used for training
and checking aims and work on getting high classification
accuracy and least average error where the training and
checking data is uploaded to the ANFIS Editor. The input and
output parameters on FIS is shown in Fig.9. The Designer of
Neuro-Fuzzy shows the checking data appears as plus signs (+),
and the training data appears as circles (Ο) [19]. The Hybrid is
specified as an ANFIS model parameter optimization. The
number of training epochs is kept to the default value ‘3’, and
the training error tolerance is kept to the default value ‘0’.
(C)
Fig. 9. Input and Output parameters on Fuzzy Inference System
(D)
(E)
Fig.8 membership function plots of 5 inputs. (A) A typical initial MF
setting, where first input (in 1) range is between 6.147e-012 and
0.0002427, (B) a typical initial MF setting, where second input (in 2)
range is between 1.561e-008 and 0.02442, (C) a typical initial MF
setting, where third input (in3) range is between 1.487e-005 and 1,
(D) a typical initial MF setting, where fourth input (in 4) range is
between 0 and 0.0482, (E) a typical initial MF setting, where fifth
input (in 5) range is between 0 and 1.
The Sugeno ANFIS is implemented in MATLAB R2011a. 50%
of the dataset is used as a training data, and 50% of the dataset
is used as a checking data. In other words, the Sugeno ANFIS
is tested on 50 % of dataset. After IFIS is generated, it is trained
with 4 membership functions by using the Artificial Neural
Network. The input and output parameters are presented with
group of membership functions. The IFIS is trained many times
to get high classification accuracy and least average error. The
average testing error is very small which is near to the tolerance
limit. 99.5% correct classification is obtained at the ANFIS
training with checking data, which indicates (reflects) a good
discrimination of the trajectories of both ships. After the IFIS
is trained, the trained FIS is tested against the training and
checking data to notice the difference in average testing error
between both of them.
The output of the FIS appears on the plot as asterisks * * * * *
* * *. The plot indicates that there is very less contradiction
(conflict) between the training and checking data output and the
output of the FIS as shown in Fig 10, 11.
Int'l Conf. IP, Comp. Vision, and Pattern Recognition | IPCV'15 |
393
J. Lee, J. Han, X. Li and H. Gonzalez [4] worked on
trajectories’ classification of two difference types of ships:
Tanker ship and fishing boat by partition each trajectory of both
ships to number of segments which helped on discriminating
the parts of trajectories identifiable and explored two types of
clustering: region-based and trajectory-based which worked on
finding the features of the sub-trajectories and then used the
SVM for the classification purpose. The cooperation between
two types of clusters helped on discriminating the features of
sub-trajectories of both ships and got high classification
accuracy 98.2%.
Fig.10 trained FIS against the training data" Trajectories"
Fig.11. trained FIS against the checking data "Trajectories"
The average testing error is calculated by testing the training
and checking data against the trained FIS as shown in Table. II.
TABLE.II. The average testing error of training and
checking data
5
The average testing error
Value
Testing the training data against the
trained FIS
Testing the checking data against the
trained FIS
1.4426e-5
0.0051065
Related Works
In the field of pattern recognition, the trajectories
classification is used widely in many applications such as
automatic recognition of handwritten postal codes on postal
envelopes, signature, handwriting image and automatic speech
recognition. In many of proposed methods, the Hidden Markov
Model (HMM) classifier is used for the trajectories
classification. G. Vries, W. Hage and M. Someren [3] worked
on predicting with the type of the vessels through their
trajectories by clustering the trajectories into groups of similar
movement patterns and used the SVM for the classification
purpose. The trajectories haven’t been partitioned to many
segments before using the SVM classifier. They got
classification accuracy 75.4%.
R. Pelot and Y. Wu [1] worked on boats’ trajectories
classification of 4 different types of the recreational boats to
figure out the difference in the movements characteristics
across boat types. The samples of the boats’ trajectories were
accumulated in two environments. To discriminate between
different types of boats, there are 7 variables helped in that:
Mean Speed (MS), Max1/20 Speed, Mean Turning Angle
(MTA), Total Distance traveled (TD), Aspect Ratio (AR),
Coverage Index (CI) and furthest Distance from Shore (DFS),
but MS, MTA and DFS are most active variables in
discriminating the boat type. The statistical multivariate
approach helped in specifying the group to which an object
belongs by forming discriminate function for each boat group.
These functions, which include three active variables, played
important role in specifying the boat types. Based on the
forming discriminate functions, the highest classification
accuracy for discriminating between boat types is 99.7%.
We worked on extracting the coefficients from each segment of
all trajectories of two different types of ships using a
polynomial function. This helped in getting a good
representation of all segments in all trajectories. The used
database [4] contains fishing boat’s trajectories (bending
trajectories) and tanker ship’s trajectories (simple trajectories).
The training and checking datasets are prepared well before
uploading them to the ANFIS. ANFIS is used for the
classification purpose. In this study, we could obtain a high
classification accuracy (99.5%) compared with [3] and [4]. The
innovated method is a simple method for getting high
classification accuracy between two different types of ships
compared with previous study as in [4]. The trajectories of the
4 types of recreational boats [1] are simple trajectories
compared with the trajectories of fishing boat (bending
trajectories) which were used in this study and previous study
as in [4].
6
Conclusions
In this paper, a novel method for classifying the
trajectories of two different types of objects (fishing boat and
tanker ship) by using the Adaptive Neuro-Fuzzy Inference
System has been presented. This method enables us to classify
different types of objects that have different trajectories at sea.
There are lot of experiments, which are made using a real
database, for getting high classification accuracy (99.5%) and
lowest average error that is near the predefined tolerance limit.
394
Int'l Conf. IP, Comp. Vision, and Pattern Recognition | IPCV'15 |
The performance of the trajectories classification system is
evaluated through figuring out the average error where the
trained FIS is tested against the training and checking data.
The ANFIS is used for the classification purpose. The ANFIS
combines artificial neural network and fuzzy logic system
which help in getting a very high level of the classification
accuracy. Sugeno FIS is implemented to work on classifying
the trajectories. The tasks of features extraction and
classification were performed using polynomial function,
subtractive clustering and ANFIS. The trajectories of the two
ships are partitioned to many segments. The polynomial
function is used to extract the features from each segment of all
trajectories. These features make the system suitable for
trajectories classification. The subtractive clustering is an
effective tool to take the details of training data and place them
in a group of clusters. The subtractive clustering method is used
to estimate the number of clusters and cluster centers in a set of
data where each point supposed as a potential cluster center. In
other words, each data point is defined as a cluster center based
on the density of surrounding data and is computed by the
subtractive clustering.
The IFIS is generated by the subtractive clustering with
minimum number of rules. The Artificial Neural Network
works on training the IFIS for getting the Final FIS which
perform to increase the ability of ANFIS in trajectories
classification efficiently.
This study proves the ability of the trajectories classification
system in classifying different trajectories of two different
kinds of ships effectively by using the ANFIS.
7
References
[1] R. Pelot, Y. Wu. “Classification of recreational boat types
based on trajectory patterns”; ScienceDirect, Vol. 28, Issue
15, pp. 1987–1994, 2007.
[2] J. Lee, J. Han, K. Whang. “Trajectory Clustering: A
Partition-and-Group Framework”; Proceedings of the
ACM SIGMOD international conference on Management
of data, pp. 593-604, 2007.
[3] G. Vries, W. Hage, M. Someren. “Comparing Vessel
Trajectories using Geographical Domain Knowledge and
Alignments”; Data Mining Workshops (ICDMW), IEEE
International Conference, Sydney, NSW, pp. 209-216,
2010.
[4] J. Lee, J. Han, X. Li, H. Gonzalez. “TraClass: Trajectory
Classification Using Hierarchical Region-Based and
Trajectory-Based Clustering”; Proceedings of the VLDB
Endowment, Vol. 1, Issue 1, pp. 1081-1094, 2008.
[5] A. Abbas, A. Mazhar, S. Hassan. “Measuring Weather
Prediction Accuracy Using Sugeno Based Adaptive Neuro
Fuzzy Inference System, Grid Partitioning and Guassmf”;
Computing Technology and Information Management
(ICCM), 8th International Conference, pp. 214 – 219,
2012.
[6] A. T. Azar. "Adaptive Neuro-Fuzzy Systems"; Vienna,
Austria, 2010.
[7]Pakistan
Meteorological
Department's
web-site:
www.met.gov.pk.
[8] Wunderground web-site: www. wunderground.com.
[9] M.S.K. A wan, M.M. Awais. "Predicting weather events
using fuzzy rule based system"; Vol. 11, Issue 1, pp. 56–
63, 2011.
[10]P. Sallisl, M. Jarur, M. Koppen. "Frost Prediction
Characteristics and Classification Using Computational
Neural Networks"; (Eds.): ICONIP 2008, Part I, LNCS
5506, pp. 1211–1220, 2009.
[11]W. Myers, S. Linden, G. Wiener. "A data mining approach
to soil temperature and moisture prediction"; National
Center for Atmospheric Research, Boulder, CO, 2009.
[12]E. Visser, M. Otsuka, T.Lee “A spatio-temporal speech
enhancement scheme for robust speech recognition in
noisy
environments”;
Ingentaconnect,
Speech
Communication, vol.41, Issue 2, pp. 393-407, 2003.
[13]P. Nava, J. Taylor. “The Optimization of Neural Network
Performance through Incorporation of Fuzzy Theory”;
Proceedings of the Eleventh International Conference on
Systems Engineering, pp. 897-901.
[14]”Polynomial
Function,”
Mathimatics
Toolbox,
MathWorks, Matlab R2011a.
[15]H. Li, X. Wang. “Automatic Recognition of Ship Types
from Infrared Images Using Support Vector Machines”;
Computer
Science
and
Software
Engineering,
International Conference, Wuhan, Hubei, Vol. 6, pp. 483 –
486, 2008.
[16]B. Malakooti, Y. Zhou. “Approximating Polynomial
Functions by Feedforward Artificial Neural Networks:
Capacity Analysis and Design”; Applied Mathematics and
Computation, ScienceDirect, Vol. 90, Issue 1, pp. 27–51,
1998.
[17]”mathematics”, Statistics and Random Numbers,
Descriptive Statistics, MathWorks, Matlab R2011a.
[18]”Mathematics”, Linear Algebra, Matrix Functions,
MathWorks, Matlab R2011a.
[19] Fuzzy logic Matlab toolbox, Mathworks, Matlab R2011a.
[20]S. Nakkrasae, P. sophatsathit, W.R. Edwards. “Fuzzy
subtractive clustering based indexing approach for
software components classification”; Vol. 14D, Issue 1,
pp. 89-96, 2007.
[21]M. Eftekhari, S. D. Katebi. “Extracting compact fuzzy
rules for nonlinear system modeling using subtractive
clustering, GA and unscented filter”; Applied
Mathematical Modelling, ScienceDirect, Vol. 32, Issue 12,
pp. 2634–2651, 2008.
[22]S. Akbuluta, A.S. Hasiloglub, S. Pamukcu. “Data
generation for shear modulus and damping ratio in
reinforced sends using adaptive neuro-fuzzy inference
system”; ScienceDirect, vol. 24, Issue 11, pp. 805-814,
2004.
[23]R. Singh, W. Bailey. “Fuzzy logic applications to
multisensor-multitarget correlation”; IEEE transactions on
aerospace and electronic system, , Vol. 33, Issue 3, pp. 118, 1997.
Int'l Conf. IP, Comp. Vision, and Pattern Recognition | IPCV'15 |
[24]M. Shah, P. D. Mehta. “Classification of vehicles using
adaptive neuro fuzzy inference system”; Electrical,
Electronics and Computer Science (SCEECS), 2014 IEEE
Students' Conference, pp. 1-6, 2014.
[25]A. Pandey, N. Gupta. “Stage Determination of Oral Cancer
Using Neurofuzzy Inference System”; Electrical,
Electronics and Computer Science (SCEECS), 2014 IEEE
Students' Conference, pp. 1-5, 2014.
[26]A. Dufaux. “Detection and recognition of impulsive sound
signals”; Institute of microtechnology, Switzerland, pp.1209, 2001.
[27]J. Jang. “ANFIS: adaptive-network-based fuzzy inference
systems”. IEEE Trans Syst Man Cybern, 23, pp. 665- 685,
1993.
[28]J. Jang. “Fuzzy modeling using generalized neural
networks and Kalman filter algorithm”; Proc. Ninth Nat.
Conf. Artificial Intell, PP.762-767. 1991.
[29]E. Avci, Z. Akpolat. “Speech recognition using a wavelet
packet adaptive network based fuzzy inference system”;
SinceDirect, vol. 31, Issue 3, pp. 495- 503, 2006.
395