Fuzzy learning vector quantization particle swarm optimization (FLVQ-PSO) and fuzzy neuro generalized learning vector quantization (FN-GLVQ) for automatic early detection system of heart diseases base.

2012 Proceedings of SICE Annual Conference

http://www.sice.or.jp/sice2012/

Akita University, Akita, Japan
August 20-23, 2012

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Murata, Atsuo (12)

Fuzzy learning vector quantization particle swarm
optimization (FLVQ­PSO) and fuzzy neuro generalized
learning vector quantization (FN­GLVQ) for automatic early

detection system of heart diseases based on real­time
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Rachmadi, M.F. ; Ma'sum, M.A. ; Setiawan, I.M.A. ; Jatmiko, W.

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SICE Annual Conference 2012
August 20-23, 2012, Akita University, Akita, Japan

Fuzzy Learning Vector Quantization Particle Swarm Optimization (FLVQ-PSO) and Fuzzy
Neuro Generalized Learning Vector Quantization (FN-GLVQ) for Automatic Early Detection
System of Heart Diseases based on Real-time Electrocardiogram
M. Febrian Rachmadi1, M. Anwar Ma’sum1, I Made Agus Setiawan2, and Wisnu Jatmiko1
1

Faculty of Computer Science, Universitas Indonesia, Depok, Indonesia
(E-mail : muhammad.febrian@ui.ac.id, wisnuj@cs.ui.ac.id)
2
Computer Science Department, Udayana University, Bali, Indonesia

Abstract: Automatic heart beats classification has attracted much interest for research recently and we are interested to
determine the type of arrhythmia from electrocardiogram (ECG) signal automatically. This paper will discuss
thoroughly about study and implementation of FLVQ-PSO, an extension from FLVQ algorithm which use MSA and
PSO method, and FN-GLVQ, an extension from GLVQ algorithm which use fuzzy logic concept, to classify ECG
signals. By using 10-Fold Cross Validation, the algorithm produced an average accuracy 84.02%, 98.25%, 99.00%, and
97.70%, respectively for FLVQ, FLVQ-PSO, GLVQ, and FN-GLVQ.
Keywords: Arrhythmia Classification, Biomedical Signal Processing, FLVQ, FLVQ-PSO, FN-GLVQ, GLVQ.

1. INTRODUCTION

Learning Vector Quantization (FN-GLVQ) to classify
arrhythmia beat types [10] using data from MIT-BIH
arrhythmia database [11].
This system implements some of neural network
algorithms, including Fuzzy Learning Vector
Quantization (FLVQ) and Generalized Learning Vector
Quantization (GLVQ). Furthermore, we also implement
and use two neural network algorithms which are
developed based on FLVQ and GLVQ, they are Fuzzy
Learning Vector Quantization Particle Swarm
Optimization (FLVQ-PSO) and Fuzzy Neuro
Generalized Learning Vector Quantization (FN-GLVQ).
These four algorithms will classify any ECG signals
detected by ECG sensor into classes which describe
cardiac health. This paper will also discuss thoroughly
about the study and implementation of FLVQ-PSO and
FN-GLVQ to classify ECG signals.
The contribution of this research is an
implementation of smart portable device for early
detection system of heart diseases. Furthermore, this
research also implements some learning algorithms such
as FLVQ, GLVQ, FLVQ-PSO, and FNGLVQ for
heartbeat classification. We also used real-time data
from patient simulator which can generate human’s
heartbeat signals.
The rest of this paper is organized as follows. Section
2 discusses how our early detection system of heart
diseases is formed. The explanation in this section
includes system’s architecture, system’s modules, and
heartbeat data processing. Section 3 discusses
algorithms which are used in the system. They are
FLVQ-PSO and FNGLVQ. Section 4 shows all of
experiments and results in this research, and section 5
draws a conclusion.

Coronary heart disease is currently listed as the most
life-threatening disease in the world. Over 80%
Cardiovascular Disease (CVD) occur in developing
countries. In particular, the percentage of deaths caused
by heart diseases and blood vessels in Indonesia
increased from 9.1% in 1986 to 26.3% in 2001. Lack of
proper medical devices for cardiac signal detection,
such as cardiograph, was indicated as a cause for CVD
to become the deadliest disease. In addition, limited
number of cardiovascular specialists also contributes in
this problem. As an illustration, the ratio between
number of cardiologists in Indonesia and Indonesia’s
total population reached 1:665.730 in 2011.
Furthermore, medical devices from abroad make the
cost of health care services become expensive, hence
most of the people cannot get proper services.
The main objective in this research is to develop an
automatic early detection system for heart diseases. This
system can detect heart disease by its symptoms based
on electrocardiogram (ECG) signal. It will be attached
in a portable device, hence it can be brought along
anywhere by people to monitor their current cardiac
health. Android smartphone, which is connected to
mini-ECG sensor, will be used as a hardware module in
this portable device.
Many algorithms have been proposed for automatic
classifier of life-threatening arrhythmia based on ECG
data. There are a lot of works applying artificial neural
network (ANN) and its variant as an arrhythmia
detection based on ECG and some of them are
combining wavelet transform, Principal Component
Analysis, or Fuzzy C-Mean with ANN or LVQ-NN for
classifying the signal [1], [2], [3]. Some researchers are
also applying fuzzy theory on arrhythmia detection [4],
[5], [6]. There are also others who use Support Vector
Machine (SVM) as a classifier [7], or combining SVM
with Genetic Algorithm [8] or combining SVM with
Particle Swarm Optimization (PSO) [9]. In our previous
study we applied Generalized Learning Vector
Quantization (GLVQ) and Fuzzy Neuro Generalized

2. STATE OF THE ART: EARLY DETECTION
SYSTEM OF HEART DISEASES
2.1 System architecture
Early detection system of heart diseases is composed
of hardware module and software module. The

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PR0001/12/0000- 0465¥ 400 ©2012 SICE

sent continuously without any separator. These integer
data will be converted to floating point format number
which data ranges from -1 to 1. This conversion process
uses Eq. (1).

hardware module is composed of an electrocardiograph
device, a digital circuit of microcontrollers, and a serial
bluetooth adapter. This module has a function to capture
human heartbeat signal and convert it to digital data
whereas the software modules of this system are built
based on Java platform and Android platform. Each of
these software modules, either Java platform or Android
platform, can visualize the human heartbeat wave which
is captured by hardware module and perform
classification to the heartbeat data into several classes of
health condition of the heart. Both hardware module and
software module are working together as a system.

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ଶହହ

ቁെͳ

(1)

Continuous heartbeat data will be separated from
each other, so each data will represent a human
heartbeat. The separation process is conducted by
searching for the culmination of human heartbeat or
R-point. Because of a human heartbeat has 850 sample
points, we search and approximate the R-point for every
beat and get 424 points to the left of R-point and 425
points of the right of the R-point.
After the separation process, each heartbeat will be
transformed by using wavelet algorithm. Wavelet
algorithm is used to simplify heartbeat data so each of
human heartbeat just has 55 sample points, but it does
not change the shape of the heartbeat wave. Mother
wavelet that we used in this research is Daubechies
order 4 level 4. Heartbeat data that have been obtained
after 4 level wavelet processes will be the data input for
training process of artificial neural network algorithms.

2.2 Hardware Module
As described before, hardware module in this system
is composed of an electrocardiograph device, a digital
circuit of microcontrollers for analog to digital converter,
and a serial bluetooth adapter. Electrocardiograph in this
hardware module consists of several types of electronic
circuits including two amplifiers (INA118 and OP07),
three filters (one high pass filter and two low pass filter),
and one adder. This hardware module is responsible for
reading heartbeat from human body, converting
heartbeat analog data to digital data, and passing all
digital data to software module using serial bluetooth
adapter.

3. ALGORITHM

2.3 Software Module
Software module in this system is built for computers
and mobile devices. In the first version of software
module, we use Java platform for computers and
Android platform for mobile devices. Software module
is used to visualize heartbeat wave taken from hardware
module and to classify heart’s health condition.
Software module also provides some information about
classes of heart diseases, classifying methods, and user
guide on how to use the application.

3.1 Fuzzy Learning Vector Quantization Particle
Swarm Optimation (FLVQ-PSO)
Fuzzy Learning Vector Quantization (FLVQ) is a
pattern recognition algorithm which is developed from
Learning Vector Quantization (LVQ) algorithm. FLVQ
uses fuzzy theory in initialization process of initial
reference vectors, training process, and determination of
winning reference vectors. Using these two methods,
LVQ and fuzzy, FLVQ has advantages such as fast
computation and high rate of pattern recognition just
like backpropagation.
Fuzzy Learning Vector Quantization Particle Swarm
Optimization (FLVQ-PSO) is an algorithm which is
developed from FLVQ and combines main concept from
Matrix Similarity Analysis (MSA) and Particle Swarm
Optimization (PSO). Differences between FLVQ and
FLVQ-PSO happen when these two algorithms are
doing the training process. In the training process,
reference vectors in FLVQ-PSO are updated using both
of FLVQ training method and PSO method respectively.
FLVQ has several clusters rather than has several hidden
layers. These clusters are used as particles in PSO
algorithm.
FLVQ-PSO has several advantages from additional
applied methods. The advantages are the ability to do
fast computation from FLVQ method, to determine
fitness value with MSA, and to determine optimal
solution with PSO. In subsections follow, we will
discuss about combining FLVQ with MSA and
combining FLVQ with PSO.

2.4 Heartbeat Signals Processing
In this research, we use The PS400 Patient Simulator
from Fluke Biomedical Corporation to get real-time
heartbeat data. This patient simulator can generate up to
12 classes of arrhythmia and 5 classes of normal
heartbeat, which are based on the beat per minute (bpm).
In this research, we use 10 classes of heartbeat data,
they are;
1) Right Bundle Branch Block (RBBB),
2) Premature Atrial Contraction (PAC),
3) Premature Ventricular Contraction (PVC),
4) Ventricular Tachycardia (V-Tach),
5) Ventricular Fibrillation (V-Fib),
6) Paced (P),
7) Atrial Fibrillation (A-Fib),
8) Normal beat with 120 bpm,
9) Normal beat with 180 bpm, and
10) Normal beat with 240 bpm.
Heartbeat data that have been caught by the hardware
module have 8 bits integer data format and range in
value from 0 up to 255. Each of these human heartbeat
data has 850 sample points. All of heartbeat data are

3.1.1 FLVQ with MSA
In FLVQ training process, the algorithm stops when

-466-

so we can get a good initial reference vectors.
FLVQ-PSO uses fitness value to determine local best
and global best for each cluster. Fitness value is
obtained from MSA where the fitness value is sum of
value in the main diagonal of matrix similarity of MSA
minus sum of value in the non-main diagonal of
similarity matrix of MSA. Suppose a similarity matrix
of MSA is formed of mij elements where i and j is
integer from 1 to n, and size of similarity matrix of
MSA is n x n, so fitness value for the k-th cluster is
obtained from Eq. (5) below.

maximum number of epoch is reached. Unfortunately,
there are some probabilities where FLVQ yields
non-optimal solution at the end of final epoch or FLVQ
has reached optimal solution when the maximum
number of epoch is not reached yet. To optimize number
of epoch, we need an analysis method to determine
when the algorithm should stop the training process.
MSA can be used to determine average value of
reference vectors in each of epochs. The average value
of reference vectors in matrix similarity will determine
how well the reference vectors that are yielded by the
training process in a particular epoch. An ideal
condition for FLVQ to stop its training process is when
the value of MSA is as close as an identity matrix. We
can also use a specific condition value in matrix
similarity to make a threshold, so training process will
stop when the specific condition value of MSA is
reached.
Similarity matrix in MSA is formed by adding
similarity value from FLVQ algorithm for each of
clusters into an n x n size of matrix, where n is the
number of output classes. Each of clusters in
FLVQ-PSO has a similarity matrix of MSA. All of
similarity matrixes will be computed by every
completion of epoch. The value of similarity matrix can
be obtained by using Eqs. (2) ~ (3) below,
ଵ

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ே

ͳ

݂݅‫ܥ߳ݔ‬௜ ݈ܽ݊݀ܿܽ‫ݕ݂݅ݏݏ‬ሺ‫ݔ‬ሻ ൌ ‫ܥ‬௝
Ͳ ‫݁ݏ݅ݓݎ݄݁ݐ݋‬

‫ ڮ‬୬ଵ
‫ڰ‬
‫ ڭ‬൩
‫ ڮ‬୬୬

(5)

‫ ܩ‬ൌ ƒšሺ‫ܮ‬ሻ
‫ ܮ‬ൌ ƒšሺ݂݅‫ݏݏ݁݊ݐ‬ଵ ǡ ݂݅‫ݏݏ݁݊ݐ‬ଶ ǡ ǥ ǡ ݂݅‫ݏݏ݁݊ݐ‬௞ ሻ

(6)
(7)

In PSO algorithm, each of particles has local best and
global best, so has FLVQ-PSO. Local best and global
best is used to update reference vectors. Local best in
FLVQ-PSO is the best reference vector from each of
clusters, whereas global best is the best reference vector
from local best which has the best fitness value. If the
old fitness value of reference vector in one cluster is
better than the new one, the old one is preserved as a
reference vector rather than using the new one. Whereas
the new fitness value of reference vector in one cluster
is better than the old one, the new one will substitute the
old one. Global best and local best can be obtained by
using Eqs. (6) ~ (7) below,

(2)
(3)

where G is the global best and L is a group of local best
from each of clusters.

where i is input class, j is output class, N is number of
input vectors for one class, x is one input vector, and Cj
is a member of class j.
All of reference vectors will be computed using Eq.
(2) and yield a similarity matrix for FLVQ. Eq. (4)
shows the form of similarity matrix of MSA,
ଵଵ
 ൌ൥ ‫ڭ‬
ଵ୬

݂݅‫ݏݏ݁݊ݐ‬௞ ൌ  σ௡௜ୀଵ ݉௜௜ െ  ൣσ௡௜ୀଵ σ௡௝ୀଵ ݉௜௝ ݂݅݅ ് ݆൧

3.1.3 Reference Vectors Update Processes
As described at the previous section, reference
vectors in FLVQ-PSO are updated using both of FLVQ
training method and PSO method. First of all, we update
the reference vectors using Eqs. (8) ~ (9) below,
‫ݓ‬௜௝ ሺ‫ ݐ‬൅ ͳሻ ൌ ‫ݓ‬௜௝ ሺ‫ݐ‬ሻ ൅ ‫ݒ‬௜ ሺ‫ ݐ‬൅ ͳሻ

(4)

(8)

‫ݒ‬௜ ሺ‫ ݐ‬൅ ͳሻ ൌ
(9)
ܺሺ‫ݒ‬௜ ሺ‫ݐ‬ሻ ൅ ܿଵ ‫ܴ݀݊ܽ כ‬ሺሻ ‫ כ‬ሺ‫݌‬௟ ሺ‫ݐ‬ሻെ‫ݓ‬௜௝ ሺ‫ݐ‬ሻ
ሺ‫ݐ‬ሻ
െ ‫ݓ‬௜௝ ሺ‫ݐ‬ሻሻሻ
൅ܿଶ ‫ܴ݀݊ܽ כ‬ሺሻ ‫ כ‬ሺ‫݌‬௚

where M is similarity matrix with ݊ ൈ ݊ of size and ݊
is number of output classes.
3.1.2 FLVQ with PSO
Particle Swarm Optimization (PSO) was introduced
by R. C. Eberhart and J. Kenndey (1995) [12]. PSO is
an algorithm to search optimum solutions from a
particular problem. There are two key elements in PSO,
they are particles and solutions. In FLVQ-PSO
algorithm, particles are clusters and the solutions are
reference vectors.
FLVQ-PSO is developed to reduce FLVQ algorithm
dependency on initialization of initial reference vectors.
Initialization of initial reference vectors in FLVQ-PSO
is conducted by creating initial reference vectors as
much as the clusters. This initialization is conducted
randomly based on the output class of the input vector,

where ‫ݓ‬௜௝ ሺ‫ݐ‬ሻ is the average value of reference vectors
before update, ‫ݓ‬௜௝ ሺ‫ ݐ‬൅ ͳሻ is the average value of
reference vectors after update, ‫݌‬௟ ሺ‫ݐ‬ሻ is the local best,
‫݌‬௚ ሺ‫ݐ‬ሻ is the global best, ܿଵ is the acceleration factor of
cognitive value, ܿଶ is the acceleration factor of social
value, Rand() is a random value between 0 and 1, X is a
construction value between 0 and 1, ‫ݒ‬௜ ሺ‫ݐ‬ሻ is the
velocity vector before update, and ‫ݒ‬௜ ሺ‫ ݐ‬൅ ͳሻ is the
velocity vector after update. Fig. 1 also shows us the
update process which is experienced by reference
vectors.
Velocity vector of particle affects how big particle
will move from its initial position. Some other aspects

-467-

that affect velocity value of particle are cognitive value
and social value. Suppose cognitive value of a particle is
greater than social value, then the particle tends to move
closer to its local best. If social value is greater than
cognitive value, then the particle tends to move closer to
its global best.
After average value of reference vectors are updated,
minimum value and maximum value of reference
vectors can be updated using Eqs. (10) ~ (12) below,
݀௜௝ ൌ ‫ݓ‬௜௝ ሺ‫ݐ‬ሻ െ ‫ݓ‬௜௝ ሺ‫ ݐ‬൅ ͳሻ

(10)

‫ݓ‬ሺ‫ݎ‬ሻ௜௝ ሺ‫ ݐ‬൅ ͳሻ ൌ ‫ݓ‬ሺ‫ݎ‬ሻ௜௝ ሺ‫ݐ‬ሻ ൅ ݀௜௝

(12)

‫ݓ‬ሺ݈ሻ௜௝ ሺ‫ ݐ‬൅ ͳሻ ൌ ‫ݓ‬ሺ݈ሻ௜௝ ሺ‫ݐ‬ሻ ൅ ݀௜௝

Fig. 2 Illustration of FN-GLVQ algorithm for ECG
classification.
applied to the average of membership degree or
similarity value for each reference vector. The
membership function define as ݄௜௝ ሺ‫ݔ‬ሻ with ݅ ൌ
݂݁ܽ‫ ݁ݎݑݐ‬and ݆ ൌ ܿܽ‫ݕݎ݋݃݁ݐ‬.

(11)

ߤ௜௝ ൌ ݄௜௝ ሺ‫ݔ‬ሻ

where ‫ݓ‬ሺ݈ሻ௜௝ is the minimum value of a reference
vector, ‫ݓ‬ሺ‫ݎ‬ሻ௜௝ is the maximum value of a reference
vector, ‫ ݐ‬is a state before update process, ‫ ݐ‬൅ ͳis a
state after update process, and ݀௜௝ is the difference
value between old average value and new average value
of reference vector.

(13)

The similarity for each reference vector (ߤ௝ ) then
propagated to next neuron using average operation as
shown in Eq. 14
ଵ

ߤ௝ ൌ  σ௞௜ୀଵ ߤ௜௝

(14)

‫ݓ‬௣ ൌ  ƒš௝ ሺߤ௝ ሻ

(15)

௞

To determine the winner (‫ݓ‬௣ ) in winner-take-all rule,
we choose maximum of similarity value (ߤ௝ ) using Eq.
15.

In FNGLVQ, the update process of the reference
vector is not defined by the winner vector, but it is
defined by minimum classification error (MCE) as
pointed out in Eq. 16.

Fig.1 Illustration of the velocity vector calculation in
FLVQ-PSO.

ௗభ ିௗమ

߮ሺ‫ݔ‬ሻ ൌ 

ௗభ ାௗమ

߮ሺ‫ݔ‬ሻ ൌ 

ଶିఓభ ିఓమ

(16)

We need to complement similarity value into
݀ ൌ ͳ െ ߤ, in which ݀ is dissimilarity. Later on, we
substitute it into Eq. 16 and we will obtain Eq. 17.

3.2 Fuzzy Neuro Generalized Learning Vector
Quantization (FNGLVQ)
On previous study [10], I Made Agus et al. introduce
an extension of GLVQ, which employed fuzzy theory as
discriminant function. This method did not use crisp
value but fuzzy membership function and as the
reference vector. This algorithm approach adopting
Fuzzy-Neuro LVQ that developed by Kusumoputro
Budiarto and Jatmiko W[13]. The conceptual
architecture of FNGLVQ as described on Fig. 2.
The result value of discriminant function replaced
with similarity value on fuzzy concept. Each of crisp
input value is feed into the network. Reference vector is
formed by membership function that represents the
distribution for each feature. We use triangular function
as membership function. The similarity value between
each crisp input and reference vector are calculated by
seeking the degrees of membership of each feature to
each membership function. GLVQ's winner-take-all rule

ఓమ ିఓభ

(17)

where ߤଵ is similarity value between input vector (‫)ݔ‬
with reference vector from the same category (‫ܥ‬௫ ൌ ‫ܥ‬௪ ),
ߤଶ is the greatest similarity value between ‫ ݔ‬with
reference vector that are not from the same category as
input vector (‫ܥ‬௫ ് ‫ܥ‬୫ୟ୶ೕ ሺ௪ೕ ሻ ). Adjustments are made by
similarity term and based on steepest descent method,
so we have the derivative of ܵ as shown in Eq. 18.
ఋௌ

ఋ௪೔

ൌ

where

obtain

ఋௌ

Ǥ

ఋఝ ఋఓ೔ 

Ǥ

ఋఝ ఋఓ೔ ఋ௪೔
ఋఝ

ఋఓభ
ఋఝ

ఋ௪೔

and

ǡ ݅ ൌ ͳǡ ʹ

ఋఝ

ఋఓమ

(18)

are the derivative of MCE. To

depends on the chosen membership function.

In case of triangular function with reference vector

-468-

‫ݓ‬௜௝ ൌ ሺ‫ݓ‬௠௜௡೔ೕ ǡ ‫ݓ‬௠௘௔௡೔ೕ ǡ ‫ݓ‬௠௔௫೔ೕ ሻ ,the
function can be defined as Eq. 19.

• If ߤଵ ൐ Ͳߤଶ ൐ Ͳ , at least one of two
reference vectors recognize the input, so
- if recognize correctly (߮ ൏ Ͳ) then increase the
fuzziness using Eqs. (28) ~ (29).
‫ݓ‬௠௜௡  ՚ ‫ݓ‬௠௘௔௡ െ ሺ‫ݓ‬௠௘௔௡ െ  ‫ݓ‬௠௜௡ ሻ
ൈ ሺͳ ൅ ሺߚ ൈ ߙሻሻ (28)

membership

ߤ ൌ ݄ሺ‫ݔ‬ǡ ‫ݓ‬௠௜௡ ǡ ‫ݓ‬௠௘௔௡ ǡ ‫ݓ‬௠௔௫ ሻ
Ͳ
ǡ ‫ ݔ‬൑ ‫ݓ‬௠௜௡
‫ ۓ‬௫ି௪೘೔೙
ۗ
ǡ ‫ݓݔ‬௠௜௡ ൑ ‫ ݔ‬൑  ‫ݓ‬௠௘௔௡ ۖ
ۖ௪
ି௪
೘೔೙
ൌ  ೘೐ೌ೙
௪೘ೌೣ ି௫
‫۔‬
ۘ
ǡ ‫ ݔ‬൑ ‫ݓ‬௠௜௡
ۖ௪೘ೌೣ ି௪೘೐ೌ೙
ۖ
ǡ
‫ݔ‬
൒
‫ݓ‬
௠௘௔௡
‫ە‬
ۙ
Ͳ

(19)

‫ݓ‬௠௔௫  ՚ ‫ݓ‬௠௘௔௡ ൅ ሺ‫ݓ‬௠௔௫ െ  ‫ݓ‬௠௘௔௡ ሻ
ൈ ሺͳ ൅ ሺߚ ൈ ߙሻሻ (29)

- if recognize wrongly (߮ ൒ Ͳ) then decrease the
fuzziness using Eqs. (30) ~ (31).
‫ݓ‬௠௜௡  ՚ ‫ݓ‬௠௘௔௡ െ ሺ‫ݓ‬௠௘௔௡ െ  ‫ݓ‬௠௜௡ ሻ
ൈ ሺͳ െ ሺߚ ൈ ߙሻሻ (30)

Therefore, the derivative of the triangular function
against the average weight ( ‫ݓ‬௠௘௔௡ ) lead to three
conditions and hence the learning rules can be described
as Eqs. (20) ~ (24).
• For ‫ݓ‬௠௜௡ ൏ ‫ ݔ‬൑ ‫ݓ‬௠௘௔௡
ఋ௙
‫ݓ‬ଵ ሺ‫ ݐ‬൅ ͳሻ  ՚ ‫ݓ‬ଵ ሺ‫ݐ‬ሻ െ ߙ ൈ   ൈ 
ൈ  ቀሺ௪

ଶሺଵିఓమ ሻ

ఋఝ
ሺଶିఓభ ିఓమ ሻమ
௫ି௪೘೔೙

మ
೘೐ೌ೙ ି௪೘೔೙ ሻ

‫ݓ‬ଶ ሺ‫ ݐ‬൅ ͳሻ  ՚ ‫ݓ‬ଶ ሺ‫ݐ‬ሻ ൅ ߙ ൈ 
ൈ  ቀሺ௪

ఋ௙

ൈ

• For ‫ݓ‬௠௘௔௡ ൏ ‫ ݔ‬൑ ‫ݓ‬௠௔௫
ఋ௙
‫ݓ‬ଵ ሺ‫ ݐ‬൅ ͳሻ  ՚ ‫ݓ‬ଵ ሺ‫ݐ‬ሻ ൅ ߙ ൈ   ൈ 

ቁ

మ
೘ೌೣ ି௪೘೐ೌ೙ ሻ

ൈ  ቀሺ௪

ఋ௙

ൈ

ቁ

(21)

మ
೘ೌೣ ି௪೘೐ೌ೙ ሻ

ቁ

4. EXPERIMENT AND RESULT
(23)

In this experiment, we use a dataset which consist of
100 heartbeat data from each of 10 classes, so in total
we use 1000 heartbeat data. These 1000 data are
generated from The PS400 Patient Simulator from Fluke
Biomedical Corporation and processed in heartbeat
signals processing which are discussed in Section 2.
Comparison was performed by using FLVQ,
FLVQ-PSO, GNLVQ, and FN-GLVQ. We configured
the classifier with the training parameters as can be seen
in Table 1.

(24)

where ݅ is feature, ݆ is category, ‫ݓ‬ଵ is reference
vector from same category with input vector (‫ܥ‬௫ ൌ ‫ܥ‬௪ ),
and ‫ݓ‬ଶ is reference vector that have the greatest
similarity value that are not from the same category as
input vector (‫ܥ‬௫ ് ‫ܥ‬୫ୟ୶ೕ ሺ௪ೕ ሻ ). All of update procedures
above is performed to ‫ݓ‬௠௘௔௡ whereas update
procedures for ‫ݓ‬௠௜௡ and ‫ݓ‬௠௔௫ are based on the new
‫ݓ‬௠௘௔௡ using Eqs. (24) ~ (25) below.

Table 1. Parameters for the learning process.
Algorithm
FLVQ
FLVQ-PSO
GLVQ
FN-GLVQ

‫ݓ‬௠௜௡  ՚  ‫ݓ‬௠௘௔௡ ሺ‫ ݐ‬൅ ͳሻ െ ሺ‫ݓ‬௠௘௔௡ ሺ‫ݐ‬ሻ െ  ‫ݓ‬௠௜௡ ሺ‫ݐ‬ሻሻ (25)
‫ݓ‬௠௔௫  ՚  ‫ݓ‬௠௘௔௡ ሺ‫ ݐ‬൅ ͳሻ െ ሺ‫ݓ‬௠௔௫ ሺ‫ݐ‬ሻ െ  ‫ݓ‬௠௘௔௡ ሺ‫ݐ‬ሻሻ (26)

The value of ߙ, which has value between 0 and 1, in
iteration ‫ ݐ‬can be computed using Eq. 26, so the value
of ߙ will be decreasing along with iteration.

ߙሺ‫ ݐ‬൅ ͳሻ ൌ ߙሺ‫ݐ‬ሻ  ൈ  ቀͳ െ 

௧

௧೘ೌೣ

ቁ

If ߤଵ ൌ Ͳ‫ߤܦܰܣ‬ଶ ൌ Ͳ, it means that both
reference vectors cannot recognize the input,
so all of reference vectors fuzziness are
increased by using Eqs. (32) ~ (33) where ߛ
in between [0,1]. The value of ߛ in our
research is ߛ ൌ ͲǤͳ.
‫ݓ‬௠௜௡  ՚ ‫ݓ‬௠௘௔௡ െ ሺ‫ݓ‬௠௘௔௡ െ  ‫ݓ‬௠௜௡ ሻ
ൈ ሺͳ െ ሺߛ ൈ ߙሻሻ (32)

‫ݓ‬௠௔௫  ՚ ‫ݓ‬௠௘௔௡ ൅ ሺ‫ݓ‬௠௔௫ െ  ‫ݓ‬௠௘௔௡ ሻ
ൈ ሺͳ ൅ ሺߛ ൈ ߙሻሻ (33)

(22)

ଶሺଵିఓభ ሻ

ሺଶିఓభ ିఓమ ሻమ
ఋఝ
௪೘ೌೣ ି௫

• For ‫ ݔ‬൑ ‫ݓ‬௠௜௡ ‫ ݔܦܰܣ‬൒  ‫ݓ‬௠௔௫
‫ݓ‬௜ ሺ‫ ݐ‬൅ ͳሻ ՚  ‫ݓ‬௜ ሺ‫ݐ‬ሻǡ݅ ൌ ͳǡ ʹ

•

ଶሺଵିఓమ ሻ

ఋఝ
ሺଶିఓభ ିఓమ ሻమ
௪೘ೌೣ ି௫

‫ݓ‬ଶ ሺ‫ ݐ‬൅ ͳሻ  ՚ ‫ݓ‬ଶ ሺ‫ݐ‬ሻ െ ߙ ൈ 

(20)

ଶሺଵିఓభ ሻ

ఋఝ
ሺଶିఓభ ିఓమ ሻమ
௫ି௪೘೔೙

మ
೘೐ೌ೙ ି௪೘೔೙ ሻ

ൈ  ቀሺ௪

ቁ

‫ݓ‬௠௔௫  ՚ ‫ݓ‬௠௘௔௡ ൅ ሺ‫ݓ‬௠௔௫ െ  ‫ݓ‬௠௘௔௡ ሻ
ൈ ሺͳ െ ሺߚ ൈ ߙሻሻ (31)

ߙ
0.005
0.005
0.05
0.05

Max epoch
5
1
250
250

In order to evaluate all of learning methods, we tested
them with 10-Fold Cross Validation. From Table 2, we
can see that MSA method and PSO method in
FLVQ-PSO (98.18%) make a huge impact to the FLVQ
(84.02%) learning method in term of accuracy. In the
other side, we can see in Table 3 that FN-GLVQ has
better error rate in training process (0.007590056) rather
than GLVQ (0.02666667).

(27)

To gain a better recognition performance, we perform
additional adjustment in term of the width of reference
vector fuzziness through following rules.

-469-

arrhytihemias using artificial neural networks,” in
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[3] R. Ceylan and Y. Ozbay, “Comparison of fcm, pca
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[5] B. Anuradha and V. C. V. Reddy, “Cardiac
arrhythmia classification using fuzzy classifiers,”
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Technology, 2008.
[6] C. C. Yeh Y.-C., Wang W.-J., “Heartbeat case
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signals, ”International Journal of Fuzzy Systems,
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Table 2.
Performance result using 10-Fold Cross Validation.
Fold
1
2
3
4
5
6
7
8
9
10
AVG

FLVQ
67.70
82.90
85.60
87.90
86.80
88.80
85.60
85.80
83.60
85.50
84.02

FLVQ-PSO
97.85
90.65
100.00
96.00
99.00
100.00
99.00
100.00
100.00
100.00
98.25

GLVQ
99.00
99.00
99.00
99.00
99.00
99.00
99.00
99.00
99.00
99.00
99.00

FN-GLVQ
98.00
97.00
98.00
98.00
98.00
98.00
98.00
96.00
98.00
98.00
97.70

Table 3. Error rate of GLVQ and FN-GLVQ.
Algorithm
GLVQ
FN-GVLQ

Error Rate In Training
0.026666667
0.007590056

5. CONCLUSION
We have presented in this paper an extension of
FLVQ and an extension of GLVQ, which are
FLVQ-PSO and FN-GLVQ to improve capability of the
system for determining arrhythmia category. We train
our dataset using FLVQ, FLVQ-PSO, GLVQ, and
FN-GLVQ. From our experiment we found that MSA
method and PSO method in FLVQ-PSO can increase the
accuracy of classifier compared with original FLVQ. In
other hand, FN-GLVQ has better error rate in training
proses compared with GLVQ. By using 10-Fold Cross
Validation, the algorithm produced an average accuracy
84.02%, 98.25%, 99.00%, and 97.70%, respectively for
FLVQ, FLVQ-PSO, GLVQ, and FN-GLVQ.

ACKNOWLEDGMENT
This work is supported by Competitive Research
Grant 2010 University of Indonesia No. DRPM/Hibah
Riset Kompetensi Universitas Indonesia/2010/I/10246.
Besides that, this research is also supported by Grant of
Joint Research for Foreign Affairs and International
Publication No. 1495/E5.2/PL/2011 by the Ministry of
Education, Republic of Indonesia.

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