Page 49 - Fister jr., Iztok, and Andrej Brodnik (eds.). StuCoSReC. Proceedings of the 2018 5th Student Computer Science Research Conference. Koper: University of Primorska Press, 2018
P. 49
ge size. The partitions into classes should maintain the In CS, exploration of the search space has been done by the
following properties: following expression:
1. Each cluster should have at least one data vector , = ( − ) ∗ (0, 1) + (8)
assigned i.e.,
≠ ∅ ∀ ∈ {1, 2, … . . , } Where, and are the upper and lower bound of the specific
variable. (0, 1) is the random variable drawn from the uniform
2. Two different clusters should have no data vector in
common i.e., distribution. But, this exploration ability of the CS algorithm
∩ = ∅, ∀ ≠ , ∈ {1, 2, … , }. crucially depends on the probability ∈ [0,1] as this fraction of
nests is abandoned.
3. Each data vector should definitely be attached to a
cluster i.e. Pseudo Code of the traditional CS is given as Algorithm 1.
∪−1 =
Algorithm 1: Cuckoo Search Algorithm
2.2 Cuckoo Search (CS) Algorithm
Step-1: Take objective function and generate initial
Cuckoo search (CS) algorithm is a powerful
optimization algorithm proposed by Xin-she Yang and Suash Deb population of solution randomly using Eq.8.
in 2009 under the inspiration of the obligate brood parasitism of
some cuckoo species by laying their eggs in the nests of other host Step-2: While termination condition does not meet Do
birds [27, 28].
A solution in the original cuckoo search algorithm corresponding Step-3: for =1 to Do
to cuckoo nests represents the position of the cuckoo egg within
the search space. Mathematically, this position is defined as: Step-4: Generate new solutions around with Lévy
Flight as per Eq.5
= {,}, for = 1, … . , and for = 1, … … . , (4) Step-5: = Suppose the new solution is and find the fitness
Step-6: values of
Where, n denotes the number of cuckoo nests in the population, d = [ (0, 1) ∗ + 1]
is the dimension of the problem to be solved, and t the generation
Step-7: if < then
number. Generation of new solution signifies the exploitation of Step-8: = ; =
the current solutions is carried out by using the Lévy flight
Step-9: end if
distribution expressed as:
Step-10: if (0, 1) < then
Step-11: Do the initialization of worst nest according to Eq.8
+1 = + . é() (5) and
Step-12: end if
> 0 represents a scaling factor of the step size drawn from Lévy Step-13: if <
distribution i.e. é() . Lévy distribution has the ability of Step-14: = ; =; //replace the global best solution
exploring a large amount of search space. In this study, Step-15: end if
Mantegna’s algorithm [28] has been used to generate Lévy
Step-16: end for
distribution. It produces random numbers according to a
symmetric Lévy stable distribution as described below— Step-17: end While
= [(1 + ) (/2)/((1 + )/2)2(−1)/2)]1/ (6) 3. Experimental Results
Where, Γ is the gamma function, 0< β ≤ 2. σ is the standard The experiment has been performed over 40 colour breast
deviation. As per Mantegna’s algorithm, the step length v can be histopathology images with MatlabR2012b and Windows-7 OS,
x64-based PC, Intel(R) Pentium (R)-CPU, 2.20 GHz with 4 GB
calculated as, RAM. The proposed methods are tested on images taken from
UCSB Bio-Segmentation Benchmark dataset [29, 30]. Fig.1
= │1/ (7) represents the original images of different breast histopathology
⁄│ images.
Here, x and y are taken from normal distribution and = 3.1 Parameter Setting
, = 1 . Where is the standard deviation. The resulting
Parameter setting is very crucial for any Nature-Inspired
distribution has the same behavior of Lévy distribution for large Optimization Algorithm (NIOA) and most of the cases it is
values of the random variables. Mantegna’s algorithm associates performed from experience. The parameter setting of CS
with faster computational speed in the range 0.75 ≤ α ≤ 1.95 algorithm is as follows: = 0.2, = 1.5, = 0.01, population
[28].
StuCoSReC Proceedings of the 2018 5th Student Computer Science Research Conference 51
Ljubljana, Slovenia, 9 October
following properties: following expression:
1. Each cluster should have at least one data vector , = ( − ) ∗ (0, 1) + (8)
assigned i.e.,
≠ ∅ ∀ ∈ {1, 2, … . . , } Where, and are the upper and lower bound of the specific
variable. (0, 1) is the random variable drawn from the uniform
2. Two different clusters should have no data vector in
common i.e., distribution. But, this exploration ability of the CS algorithm
∩ = ∅, ∀ ≠ , ∈ {1, 2, … , }. crucially depends on the probability ∈ [0,1] as this fraction of
nests is abandoned.
3. Each data vector should definitely be attached to a
cluster i.e. Pseudo Code of the traditional CS is given as Algorithm 1.
∪−1 =
Algorithm 1: Cuckoo Search Algorithm
2.2 Cuckoo Search (CS) Algorithm
Step-1: Take objective function and generate initial
Cuckoo search (CS) algorithm is a powerful
optimization algorithm proposed by Xin-she Yang and Suash Deb population of solution randomly using Eq.8.
in 2009 under the inspiration of the obligate brood parasitism of
some cuckoo species by laying their eggs in the nests of other host Step-2: While termination condition does not meet Do
birds [27, 28].
A solution in the original cuckoo search algorithm corresponding Step-3: for =1 to Do
to cuckoo nests represents the position of the cuckoo egg within
the search space. Mathematically, this position is defined as: Step-4: Generate new solutions around with Lévy
Flight as per Eq.5
= {,}, for = 1, … . , and for = 1, … … . , (4) Step-5: = Suppose the new solution is and find the fitness
Step-6: values of
Where, n denotes the number of cuckoo nests in the population, d = [ (0, 1) ∗ + 1]
is the dimension of the problem to be solved, and t the generation
Step-7: if < then
number. Generation of new solution signifies the exploitation of Step-8: = ; =
the current solutions is carried out by using the Lévy flight
Step-9: end if
distribution expressed as:
Step-10: if (0, 1) < then
Step-11: Do the initialization of worst nest according to Eq.8
+1 = + . é() (5) and
Step-12: end if
> 0 represents a scaling factor of the step size drawn from Lévy Step-13: if <
distribution i.e. é() . Lévy distribution has the ability of Step-14: = ; =; //replace the global best solution
exploring a large amount of search space. In this study, Step-15: end if
Mantegna’s algorithm [28] has been used to generate Lévy
Step-16: end for
distribution. It produces random numbers according to a
symmetric Lévy stable distribution as described below— Step-17: end While
= [(1 + ) (/2)/((1 + )/2)2(−1)/2)]1/ (6) 3. Experimental Results
Where, Γ is the gamma function, 0< β ≤ 2. σ is the standard The experiment has been performed over 40 colour breast
deviation. As per Mantegna’s algorithm, the step length v can be histopathology images with MatlabR2012b and Windows-7 OS,
x64-based PC, Intel(R) Pentium (R)-CPU, 2.20 GHz with 4 GB
calculated as, RAM. The proposed methods are tested on images taken from
UCSB Bio-Segmentation Benchmark dataset [29, 30]. Fig.1
= │1/ (7) represents the original images of different breast histopathology
⁄│ images.
Here, x and y are taken from normal distribution and = 3.1 Parameter Setting
, = 1 . Where is the standard deviation. The resulting
Parameter setting is very crucial for any Nature-Inspired
distribution has the same behavior of Lévy distribution for large Optimization Algorithm (NIOA) and most of the cases it is
values of the random variables. Mantegna’s algorithm associates performed from experience. The parameter setting of CS
with faster computational speed in the range 0.75 ≤ α ≤ 1.95 algorithm is as follows: = 0.2, = 1.5, = 0.01, population
[28].
StuCoSReC Proceedings of the 2018 5th Student Computer Science Research Conference 51
Ljubljana, Slovenia, 9 October
