International Research Journal of Engineering and Technology (IRJET)
Volume: 06 Issue: 03 | Mar 2019
e-ISSN: 2395-0056
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p-ISSN: 2395-0072
Expert Independent Bayesian Data Fusion and Decision Making Model
for Multi-Sensor Systems Smart Control
Mumbere Muyisa Forrest1, Masivi Osée Muhindo2, Kasereka Masivi Samuel3
1School
of Software, Central South University, Changsha 410000, China.
d’Informatique de Gestion, ISP/Muhangi, Butembo, DRC.
3Departement of Computer Science, Invertis University, India.
----------------------------------------------------------------------***--------------------------------------------------------------------2Département
Abstract- Internet of Things (IoT) and its applications
have increased the number of multi-sensors computer
applications. Then, the necessity of multi-sensor data
merging and expert independent decision algorithms is
real. This paper proposes a novel multi-sensor system
smart control model based on Bayesian. Proposed “study
on intelligent” algorithms are expect-dependent trainable
predicting the system only from anterior and actual data.
Simulations test on a three sensors system (sol
temperature, air temperature, and moisture) an overall
prediction precision of more than 96%. However, a real
life customizable implementation of the proposed
algorithm is needed.
system was able to stand between the source data and
the human and helped him to make decisions based on
the fused output. The big challenge with these methods
is the amount of data and processing need for training
the decision making algorithm.
Therefore, Bayesian approach, including Bayesian
analysis, Statistic, and recursive operators stood as one
of reliable alternatives. Used already for data fusion [7]
Bayesian approach is being accepted to be one of the
most classical fusion approach. Furthermore, the authors
in [8] demonstrated that the data fusion based on Bayes
estimation can weaken the possible sensor errors,
resulting from the sensor faults and noise inference. The
most appealing advantage of Bayes parameters
estimation algorithms is the small amount of training
needed for classification [9] [10] and its impendence
toward system experts.
Keywords: Naïve Bayes, Data fusion, Multi-sensor,
System smart control, Expert independent training.
1. INTRODUCTION
This paper introduces the Naïve Bayes theorem in the
decision algorithm from merged data collected from
sensors with different characteristics. The algorithm
should to make decision in control systems under multisensor context. The proposed method includes system
parameters learning and time-based system state
prediction and is expected [11] (a) to easy design
process with less free parameters to set, (b) to easy
result application to a large variety of tasks, (c) to use a
small amount of data for learning process (d) to be
computationally fast when making decisions.
The meteoric rise of Internet of Things (IoT) has
increased the number of sensors in almost all computer
applications and hence increases the necessity of multisensor systems smart control algorithms. These
algorithms are not only required to merge sensed data
from a good number of sensors into a common
representational format, but also to make relevant
decisions. Despite the fact that suggested principles,
procedures, theories and tools are approximately the
same [1], decision algorithms depend on the number of
sensors [2] [3] in the application context [4].
Furthermore,
sensors
characteristics
increase
exponentially the complexity of the system decision
algorithm.
3. PROPOSED MATHEMATICAL METHOD
In this paper, Bayesian inference is used to draw
conclusions about features (parameters) in system
control based on a sample from the same system. Both
parameters and sample data are treated as random
quantities [12]. The proposed algorithm computes the
distribution for the system parameters from the
likelihood function which defines the random process
that generates the data, and a prior probability
distribution for the parameters.
2. RELATED WORKS AND OBJECTIVES
Data fusion and decision making and related challenges
[4] have been addressed by researchers for decades.
Since then, two major approaches have emerged:
artificial intelligence methods and probabilistic based
methods. Artificial approaches, with the main focus on
machine learning, fuzzy logic, have been reputed to yield
higher accuracy compared to other techniques [2][5]. In
this line, [6] proposed a generic data fusion system
which established a relationship between the source of
data and the type of processing in order to extract
maximum possible information from data collected. The
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By assuming that all the variables are observed with no
missing data and that all classes have equal prior
probabilities [13], the proposed method estimates the
probability of a system feature by the frequency of
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Volume: 06 Issue: 03 | Mar 2019
occurrence of the same feature
database
{
}.
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in the feature
| )
(
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(
): Posterior probability of class
membership.
(
| ) : Likelihood which is the
probability of the predicator given class.
: class prior probability
Using (9), any new case X can be labeled by a class level
with the highest posterior probability. Then after
normalization, the decision distribution is :
(
)
(10)
(
)
-
The conditional likelihood of this feature is computed by
(1) and the density probability of the set of data D is
computed by (2). Since
occurs whenever
and
, (3) is deducted from (2), then the
logarithmic notation of (3) gives (4).
(
e-ISSN: 2395-0056
| )
√
Where :
∏
(1)
∏
4. PROPOSED COMPUTATIONAL MODEL
∏
(2)
∏∏
∏∏
The proposed computational protocol sketched in Figure
1, uses the following steps: (a) getting data from sensors
(b) split training set from test data (c) learning/training
the model (d) predict class using Naive Bayes model.
(3)
∏∏∏
Naive
Bayes
Model
(4)
∑∑∑
Since [6] demonstrates that (4) formula can be
simplified to (5), the Maximum Likelihood (ML)
approach used in this paper is expressed by (6).
̂
̂(
{
∑
|
)
̂
}
∑
Sensors
data
capturing
g
(5)
Figure 1: Naïve Bayes protocol for state estimation
A.
∏ (
(
| )
Table 1. Adequate range values for the system C.
(7)
Sensor S1
Values
(8)
| )
B.
( | )
( )∏ (
| )
(9)
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S2
S3
Learning & training the model
The proposed model is “study on intelligent” say it was
trained from data collected from sensors [15]. Hence, the
state of the system depends on values provided by
Where:
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Collecting data from sensors
During this step, the system collects data from a given
number of sensors. Each sensor can be in one of the
three states: low, adequate or high. Each sensor is
assumed to be independent in terms of data types and
collecting rate [14] [15]. The example provided in Table
1 gives the ranges for the training system of three
sensors.
This classifier was improved by Naive Bayes to handle an
arbitrary number of independent variables by
constructing the posterior probability for the feature
{
} among a set
given a set of variables,
{
} by (7). Assuming
of possible outcomes
that the variables are statistically independent, the
likelihood is decomposed to a product of terms in (8).
Then from (8) the estimation computed by (9).
)
Posterior
probability
Predicted
State
(6)
With
being the number of features in the database
whose variable
is in the state
and parents are in the
configuration .
(
Training
data
Test data
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D. Decision
different sensors: at time t, Ct depends on the state of S1t,
S2t, S3t, Snt. From example (Table 1), the System State
had 27 different probable classes. Each class is
composed by 3 different states provide by the 3 sensors.
The class C1can be represented by: S1low, S2adequate,
S3high, meaning that at a given time t, sensor 1 sent a
value lower than 16, sensor 2 sent a value between 20
and 25 and sensor 3 sent a value higher than 120. The
learning process used it this paper can be summarized
by algorithm 1 as follow:
The proposed Bayesian classifier (Algorithm 2) is a
probabilistic model based on the Bayes rule [17] in
which each element
) is associated to a
class with a maximum a posteriori.
( |
)
( )
( | )
Algorithm 1: Training process
Input: K (Training set)
For each class c in K do
Compute mean(k) and std(k)
End for
Output: mean, std
( | )
(15)
( | )
Algorithm 2: Testing
Input: k(Learned features)
For each class li do
Calculate P(li|k)
End for
{
Output:
class)
During the training stage, the mean and standard
deviation values of the features for each class were
computed.
C.
e-ISSN: 2395-0056
}(estimated
The probabilities for the objective existing in each class
are computed and the highest is chosen as the estimated
class.
Classification
5. SIMULATION RESULTS
Assuming that system parameters are distributed
according to the Gaussian density, two parameters were
computed. First the parent node without parents . It
probability
is the frequency of the
class in the
training database. Since all the classes have the same
probability at this stage:
The proposed computational model was evaluated and
its goodness was tested using the following evaluation
parameters: accuracy, precision, recall, f1 score drawn
from a confusion matrix. Furthermore, imbalanced data
set results were compared to balanced data set results
( )
A.
Confusion matrix
( )
∑
(11)
( )
∑ ( )
Where:
: The size of the database
( ): The number of observation belonging to the class
Second, the probability of the children nodes were
computed by using the Normal law in conditional
probability of node
considering the parent
(12)
then combine the different values computed in the
previous step (13).
in (13) being constant
hence easy to compute, (13) was rewritten as (14).
Figure 2. Confusion matrix for imbalanced data set
Figure 2, shows a confusion matrix, with an accuracy
rate of 87% for imbalanced data. In Figure 3, the false
negative and the false positive have been minimized by
balancing the data in the training set; the result shows
that the accuracy of the model has improved from
87.33% to 96.33%.
(12)
( |
( |
( )
(
)
)
( | )
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|
| )
( | )
( | )
(13)
(14)
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96.33%. Accuracy is misled by the class with high
support, thus reducing the overall accuracy as shown in
(a).
Precision, recall, f1-score
Precision
120
precision
100
80
60
Precision
40
20
Cl
as
s
Cl 1
as
s
Cl 2
as
s
Cl 3
as
s
Cl 4
as
s
Cl 5
as
s
Cl 6
as
s
Cl 7
as
s
Cl 8
as
Cl s 9
as
s
Cl 10
as
s
Cl 11
as
s
Cl 12
as
s
Cl 13
as
s
Cl 14
as
s
15
0
Figure 3. Confusion matrix with balanced data sent.
classes
Comparative Accuracy
(a)
After varying the percentage of the learning set and the
test set, we create 9 different set of data. Figure 3 show
the relationship between the size of the learning set and
the test set.
Precision
105
100
95
Precision
90
Accuracy
85
87.5
Cl
a
ss
Cl 1
as
s
Cl 2
as
s
Cl 3
as
s
Cl 4
as
s
Cl 5
as
s
Cl 6
as
s
Cl 7
as
s
Cl 8
as
Cl s 9
as
s
Cl 10
as
s
Cl 11
as
s
Cl 12
as
s
Cl 13
as
s
Cl 14
as
s
15
80
Accuracy %
87
(b)
86.5
Accuracy
Figure 5: Precision (a) Precision for imbalance data set
(b) Precision for balanced data set.
86
85.5
Figure 5 shows that the balanced data set achieves high
precision than the imbalance data set, reaching 6 times a
precision of 100%, on the other hand, the highest
precision for classes in the imbalance data set reached
hardly reached 100%. Figure 5 represents the sensitivity
of balanced and imbalance data set.
85
10%
20%
30%
40%
50%
60%
70%
80%
90%
Training set
(a)
Accuracy
100
Accuracy %
95
In term of sensitivity, the balanced data set, produce a
higher rate of sensitivity than the imbalance data set.
F1-score conveys the balance between the precision and
the recall, when dealing with imbalance classes,
classification alone cannot be trusted to select a well
performing model. Figure 8, shows the relationship
between precision, recall and f1-score.
90
85
Accuracy
80
75
70
10%
20%
30%
40%
50%
60%
70%
80%
90%
Training set
(b)
Figure 4: Relation between the size of the
learning set and accuracy. (a) Imbalance data
set (b) Balanced data set.
Better result are obtained when the size of the training
set ranges between 40 to 65 % as shown in (a) and (b) in
Figure 4. On the other hand taking the same number of
data for each class in the training set (balanced data set)
can improve the accuracy of the system from 87.3% to
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Precision,Recall,f1-score
Recall
120
120
100
Score in %
100
80
Score
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60
Recall
80
Precision
60
Recall
f1-score
40
40
20
20
0
Cl
a
ss
Cl 1
as
s
Cl 2
as
s
Cl 3
as
s
Cl 4
as
s
Cl 5
as
s
Cl 6
as
s
Cl 7
as
s
Cl 8
as
Cl s 9
as
s
Cl 10
as
s
Cl 11
as
s
Cl 12
as
s
Cl 13
as
s
Cl 14
as
s
15
C
la
ss
C 1
la
ss
C 2
la
ss
C 3
la
ss
C 4
la
ss
C 5
la
ss
C 6
la
ss
C 7
la
ss
C 8
la
s
C s9
la
ss
C 10
la
ss
C 11
la
ss
C 12
la
ss
C 13
la
ss
C 14
la
ss
15
0
Classes
classe
(a)
(a)
Precision, recall, f1-score
Recall
105
102
100
Classes
100
Score
98
Precision
95
Recall
90
96
f1-score
Recall
94
85
92
80
Cl
a
ss
Cl 1
as
s
Cl 2
as
s
Cl 3
as
s
Cl 4
as
s
Cl 5
as
s
Cl 6
as
s
Cl 7
as
s
Cl 8
as
Cl s 9
as
s
Cl 10
as
s
Cl 11
as
s
Cl 12
as
s
Cl 13
as
s
Cl 14
as
s
15
90
88
Cl
a
ss
Cl 1
as
s
Cl 2
as
s
Cl 3
as
s
Cl 4
as
s
Cl 5
as
s
Cl 6
as
s
Cl 7
as
s
Cl 8
as
Cl s 9
as
s
Cl 10
as
s
Cl 11
as
s
Cl 12
as
s
Cl 13
as
s
Cl 14
as
s
15
score %
(b)
Classe
Figure 8: Precision (a) Precision for imbalance data
set (b) Precision for balanced data set.
(b)
Figure 6: Recall (a) Precision for imbalance data set (b)
Precision for balanced data set.
For imbalance class in the training set, the support of a
class has a positive impact on the precision of the class;
however, classes with a very high accuracy can create an
accuracy paradox problem by predicting the value of the
majority class for all predictions and achieve high
classification accuracy.
The support of the class in the training set has a positive
impact on the precision of the class, especially when we
have imbalance class in the training set. Figure 7 shows
the relationship between the support and the precision.
C
al
ss
lC
a
ss
2 lC
a
ss
3 lC
a
ss
4 lC
a
ss
5 lC
a
ss
6 lC
a
ss
7 lC
a
ss
8 lC
a
ss C
9 al
ss
01 alC
ss
11 alC
ss
21 alC
ss
31 alC
ss
1
4 alC
ss
51
Classes
1
f1-score
0
100
80
70
60
200
50
40
30
20
erocS
Score
100
90
f1-score
Precision
300
Support
400
500
600
10
0
Cl
a
ss
Cl 1
as
s
Cl 2
as
s
Cl 3
as
s
Cl 4
as
s
Cl 5
as
s
Cl 6
as
s
Cl 7
as
s
Cl 8
as
Cl s 9
as
s
Cl 10
as
s
Cl 11
as
s
Cl 12
as
s
Cl 13
as
s
Cl 14
as
s
15
Support & Precision
(a)
Classe
Support & Precision
(a)
30
f1-score
25
102
20
Score
100
score
98
96
support
10
94
f1-score
5
92
0
Cl
as
s
Cl 1
as
s
Cl 2
as
s
Cl 3
as
s
Cl 4
as
s
Cl 5
as
s
Cl 6
as
s
Cl 7
as
s
Cl 8
as
Cl s 9
as
s
Cl 10
as
s
Cl 11
as
s
Cl 12
as
s
Cl 13
as
s
Cl 14
as
s
15
90
88
86
Cl 1
as
s
Cl 2
as
s
Cl 3
as
s
Cl 4
as
s
Cl 5
as
s
Cl 6
as
s
Cl 7
as
s
Cl 8
as
Cl s 9
as
s
Cl 10
as
s
Cl 11
as
s
Cl 12
as
s
Cl 13
as
s
Cl 14
as
s
15
Classes
ss
Cl
a
Precision
15
(b)
classe
Figure 9: Relationship between the support and the precision.
(a) Relationship between the support and precision for
imbalance data set (b) Relationship between the support and
precision for balanced data set.
(b)
Figure 7: f1 score (a) Precision for imbalance data set (b)
Precision for balanced data set.
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6. DISCUSSIONS AND CONCLUSION
Since the trained and proposed model is “study on
intelligent”, the algorithm reduces the reliance on
experts. It is a “previous system data” dependent model.
This means that any non-expert can train and use the
system. A few expertise is only required during the
training step of the system. However, a real life
customizable implementation of the proposed algorithm
is needed.
7. REFERENCES
[1] H. Mitchell, Multi-Sensor Data Fusion: An
Introduction, Berlin: Springer.
[2] D. Hall and J. Llinas, Handbook of Multisensor Data
Fusion, New York, 2001.
[3] M. Wang and all, "City Data Fusion: Sensor Data
Fusion in the Internet of Things," International
Journal of Distributed Systems and Technologies,
June2015.
[4] F. Aiam and All, "Data Fusion and IoT for Smart
Ubiquitous Environments: A Survey. ,," IEEE.
[5] B. Yang, X. Liu and X. Z. Y. Li, "Stochastic
Blocmodeling and variational Bayes Learning for
Signed Network Analysis," in IEEE Transactions on
Knowledge and Data Engineering, May 2017.
[6] D. Hall and A. Garga, "Pitfalls in data fusion(and how
to avoid them)," Proceedings of the Second
International Conference on Information Fusion
(Fusion ’99), vol. 1, pp. 429-439, 1999.
[7] H. Holzapfel, K. Nickel and R. Stiefelhagen,
"Implementation and evaluation of a constraintbased multimodal fusion system for speech and 3D
pointing gestures," Proc. 6th Int. Conference
Multimodal interfaces- ICMI ’04, p. 175, 2004.
[8] F. Shen and R. Yan, "A Thermostatic Control
Strategy Based on Multi-sensor Data Fusion and
Fuzzy PID Method," in Tenth Internation
Conference on Sensing Technology, 2016.
[9] J. He, S. Bai and X. Wang, "An Unobtrusive Fall
Detection and Alerting System Based on Kalman
Filter and Bayes Network Classifier," Sensors 2017,
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[10] R. Mahler, Unified Bayes Multi target Fusion of
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Ambigous Data Sources, Boston, USA: Kimasi, 2003.
[11] A. Ashari, I. Paryudi and A. Tjoa, "Performance
Comparison between Naive Bayes, Decision tree
and K-Nearest Neighbor in Searching Alternative
Design in an Energy Simulation Too," IJACSA,
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[12] X. Meng, G. Bai, X. Shu and D. Bao, "A study of
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[13] G. Myburgh and A. V. Niekerk, "Impact of training
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[14] D. J. Hand and K. Yu, "Idiot’s bayes : Not so stupid
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[15] M. Godec, C. Leistner, A. Saffari and H. Bischof, "OnLine Random Naïve Bayes for Tracking," IEEE,
Pattern
Recognition
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20th
International Conference, 2010.
A novel multi-sensor system smart control model based
on Bayesian data was proposed. The proposed algorithm
is able to predict the state of a system taking into
account the actual and the anterior data collected from
different types of sensors. For test seek, a three sensors
system (sol temperature, air temperature, and moisture)
was set and the algorithm performance was measured.
Simulation tests have proved that the proposed
algorithm can predict at an overall rate of more than
96% the actual state of the system.
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BIOGRAPHIES
Mumbere Muyisa Forrest is a MSc
holder in Information Technology
and a Lecturer of IT courses at
Université Adventiste de Lukanga
and Institut de Commerce de Beni in
RDC. He is currently preparing his
PhD in Software Engineering in
School of Software at Central South
University, Changsha 410000, China.
Dr MASIVI is a Computer Science
PhD holder from University of the
Philippines Los Banos. He is
currently
Associate
Professor
lecturing IT and Computer Science
courses at Rusangu University
(Zambia) and ISP/Muhangi (RDC).
Kasereka Masivi Samuel is a MSc
holder in Information Technology
and a Lecturer of courses at
Université Adventiste de Lukanga
and Université de Bunia in DRC. He
is currently preparing his PhD in
Computer Science at Invertis
University, India.
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