A hybrid immune-estimation distribution of algorithm for mining thyroid gland data

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A hybrid immune-estimation distribution of algorithm for mining thyroid

gland data

Wei-Wen Chang

a,*

_{, Wei-Chang Yeh}

a

_{, Pei-Chiao Huang}

b

a

Department of Industrial Engineering and Engineering Management, National Tsing Hua University, 101, Section 2, Kuang-Fu Road, Hsinchu, Taiwan, ROC b

Department of Industrial Engineering and Management, National Chiao Tung University, 1001 University Road, Hsinchu 300, Taiwan, ROC

a r t i c l e

i n f o

Keywords:

Estimation of distribution algorithms Immune algorithms

Genetic algorithms Classiﬁcation rules

a b s t r a c t

In this paper we combine the main concepts of estimation of distribution algorithms (EDAs) and immune algorithms (IAs) to be a hybrid algorithm called immune-estimation of distribution algorithms (IEDA). Both EDAs and IAs are extended from genetic algorithms (GAs). EDAs eliminate the genetic operation including crossover and mutation from the GAs and places more emphasis on the relation between gene loci. It adopts the distribution of selected individuals in search space and models the probability distri-butions to generate the next population. However, the primary gap of EDAs is lock of diversity between individuals. Hence, we introduce the IAs that is a new branch in computational intelligence. The main concepts of IAs are suppression and hypermutation that make the individuals be more diversity. More-over, the primary gap of IAs is to pay no attention to the relation between individuals. Therefore, we com-bine the main concepts of two algorithms to improve the gaps each other. The classiﬁcation risk of data mining is applied by this paper and compares the results between IEDA and general GAs in the experi-ments. We adopt the thyroid gland data set from UCI databases. Based on the obtained results, our research absolute is better than general GAs including accuracy, type I error and type II error. The results show not only the excellence of accuracy but also the robustness of the proposed algorithm. In this paper we have got high quality results which can be used as reference for hospital decision making and research workers.

1. Introduction

In this paper, we attempt to propose the hybrid algorithm that considers the advantage of estimation of distribution algorithms (EDAs) and immune algorithms (IAs). The EDAs was ﬁrst intro-duced byLarranaga and Lozano (2001). It is a search method that eliminates crossover and mutation from the genetic algorithms (GAs) and places more emphasis on the relation between gene loci. More precisely, it generates the next generation based on probabil-ity distribution of N superior population samples. In this way, the probability distribution estimated at each generation is progres-sively converted into a probability distribution that generates more superior individuals (Chen & Zhao, 2008). In addition, many combinatorial optimization algorithms have no mechanism for capturing the relationships among the variables of the problem (Inza, Larranaga, & Sierra, 2001). The EDAs considers the interac-tions between individuals that are performed by probability distri-bution, hence, this is main improvement from general GAs.

IAs emerged in the 1990s as a new branch in computational intelligence. The biological immune system is a complex adaptive system that has evolved in vertebrates to protect them from invad-ing pathogens (Dipankar, 2006). The operative mechanisms of im-mune system are very efficient from a computational standpoint. The immune system mostly consists of the immune cells that most are lymphocytes. We can summarize the two main concepts of IAs; first, the immune response to secondary encounters could be con-siderably enhanced by storing some high affinity antibody produc-ing cells from the first infection (memory cells), so as to form a large initial clone for subsequent encounters. Second, the process of hypermutation that means the mutation processes in lympho-cytes. Random changes (mutations) take place in the variable re-gion genes of antibody molecules. These random changes are mutational events and cause structurally different cells (Engin & Döyen, 2004). According to the above, we known the major ideas of two algorithms were the representation of probability model in EDAs and the mechanism of physiological immune systems in IAs. In addition, the main drawback in IAs is not to consider the interaction of variables that causes the phenomenon of local opti-mal. Therefore, we combined the two major ideas to be a hybrid algorithm called immune-estimation of distribution algorithms

*Corresponding author.

E-mail address:changwerwen@gmail.com(W.-W. Chang).

Contents lists available atScienceDirect

Expert Systems with Applications

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(IEDA) that was proven much effective and efﬁcient in the experiments.

With the rapid growth of databases, data mining has become an increasingly important approach for data analysis (Yeh, Chang, & Chung, 2008). The operations research community has contrib-uted significantly to this field, especially through the formulation and solution of numerous data mining problems such as optimi-zation problems. Several operations research applications have also be addressed using data mining methods. One of the impor-tant tasks in data mining is classification (Olafsson, Li, & Wu, 2008). In classification, there is a target variable which is parti-tioned into predefined groups or classes. The classification system takes labeled data instances and generates a model that deter-mines the target variable of new data instances. The discovered knowledge is usually represented in the form of if – then predic-tion rules, which have the advantage of being a high level, sym-bolic knowledge representation, contributing to the comprehensibility of the discovered knowledge (Mohamadi, Hab-ibi, Abadeh, & Saadi, 2008).

The health care related data mining is one of the most reward-ing and challengreward-ing area of application in data minreward-ing and knowl-edge discovery. The challenges are due to the data sets which are large, complex, heterogeneous, hierarchical, time series and of varying quality. The available healthcare data sets are fragmented and distributed in nature, thereby making the process of data inte-gration is a highly challenging task (Delen & Patil, 2006). Moreover, data classiﬁcation method has been applied in problems of medi-cine, social science, management, and engineering (Ryu, Chandr-asekaran, & Jacob, 2007). In this paper, we adopt IEDA to discover the classiﬁcation rules that the thyroid gland data from UCI database is applied. We will compare the effectiveness be-tween IEDA and general GAs in experiments.

2. Literature review

2.1. Estimation of distribution algorithms

The EDAs emerged as a generalization of genetic algorithms (GAs), for the purpose of overcoming the two main problems: poor performance in certain deceptive problems and the difficulty of mathematically modeling a huge number of algorithm variants (Sun, Zhang, & Tsang, 2005). The primary concept was to extracts directly the global statistical information about the search space from the search so far and builds a probability model of promis-ing solutions. New solutions are sampled from the model thus built (Gonzalez, Lozano, & Larranaga, 2002). Hence, the represen-tation of probability model was a crucial process in EDAs. An appropriate probability model could ensure the effectiveness and efficient of algorithm. However, it was difficult and compli-cated to build an appropriate probability model. From now, many references had proposed various methodologies to build an appropriate probability model. The concept of EDAs was first introduced by Muhlenbein and Paas (1996) in 1996 and was later termed by Larranaga and Lozano (2001) in 2001. EDAs derive optimal solutions by developing probability models of each pop-ulation. Compared with GAs, EDAs do not require genetic opera-tions such as crossover and mutation to estimate the next generation. Instead, EDAs rely on selected individuals to model the joint probability distribution that can reflect the important feature of EDAs—precise description of the association between variables. General evolutional algorithms are not equipped with any mechanism that can correctly capture the global statistics in the previous search as a basis for future searches. EDAs develop probability distributions and use sampling and estimation to generate new generation solutions and improve the above

draw-backs. Besides, the absence of crossover and mutation operators in EDAs can avoid the problem of prematurity and is thus an important contribution.

2.2. Immune algorithms

IAs also extend from GAs and use ideas gleaned from immunol-ogy to develop intelligent systems capable of learning and adapt-ing, and have been widely applied to the various areas (Zuo & Fan, 2006). IAs is evolutionary algorithms based on physiological immune systems that have mechanisms to enable them to elimi-nate foreign substances. The mechanisms work by ﬁrst recognizing foreign substances known as antigens. The immune systems then generate a set of antibodies to eliminate the antigens. These anti-bodies interact with the antigens to produce different results. The mechanisms are able to recognize which antibodies are better at eliminating the antigens and produce more variations of those antibodies in the next generation of antibodies (Alisantoso, Khoo, & Jiang, 2003).Fig. 1shows the ﬂowchart of a typical immune net-work algorithm (Timmis, 2007).

Therefore, in this paper we combine the main viewpoint of two algorithms to be a hybrid algorithm. This algorithm not only con-siders the interaction between individuals but also maintain the diversity between individuals.

3. The procedure of IEDA

We described the detailed steps of IEDA in the following: Step 0: Set the three number TL;TC and TU where 0 < TL<

TC<TU<1.

Step 1: Generate an initial solution randomly labeled by P1.

Step 2: Evaluate the ﬁtness of individuals and arranged in an order.

Calculate affinity of each member of P with objective

function or pattern

Generate a clone set C, and mutate each clone Remove individuals With an

affinity below certain threshold

Select j highest Affinity clones from C and place in

P

Perform network Interactions in P and remove

I low affinity members

Insert n number of Random individuals into P Met Termination condition? Output P Randomly intialize population P Yes No

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Step 3: Select individuals of the best d%; M-inds and put them into the memory pool. We adopt each dimension of indi-viduals in memory pool to build a probability model; Mi Probjwhere i = 1, . . . , m, j = 1, . . . , n.

Step 4: Select individuals of the worst d%; S-inds and put them into the suppress pool. We adopt each dimension of individuals in suppress pool to build a reverse probabil-ity model; Si Probjwhere i = 1, . . . , m, j = 1 . . . , n.

Step 5: Generate a random number; f where 0 < f 6 1. Step 6: If 0 < f 6 TLthen kept the present variable.

Step 7: If TL<f 6 TCthen generate a variable via Mi Probj.

Step 8: If TC<f 6 TUthen generate a variable via Si Probj.

Step 9: If TU<f 6 1 then generate a random variable; n where

the domain of n depended on the problem.

Step 10: Weather the criterion of stopping is reached or not? If not then goto Step 2.

Step 11: End algorithm.

In the step 4, we not only achieve the effect of suppression but also maintain the diversity between individuals. Since, we still keep the worse individuals and build the reverse probability mod-el. The different combination of variables may create better indi-viduals, therefore in proposed IEDA does not eliminate worse individuals to maintain the diversity between individuals. We adopt the reciprocal of original probability and recalculate new probability of each dimension. Afterward we build the new proba-bility model called reverse probaproba-bility model. The example ofTable 1shows this process in detail. We assume the domain of dimen-sion j to be 1, 2 and 3. At ﬁrst, we sum up the number of each var-iable, and then we derive the original probabilities; 0.5, 0.333 and 0.167, respectively. Second, we transform the original probabilities into the type of reciprocal; 2, 3 and 6, respectively. Finally, we use these reciprocals to build the new probability model called reverse probability model. Hence, this process not only improves the diver-sity between individuals but also considers the mechanism of sup-pression.Fig. 2shows the process of IEDA in detail.

4. IEDA for mining thyroid data set 4.1. Introduction of data set

This paper adopts the thyroid gland data from UCI database. Number of instances is 215 and includes ﬁve features and one class that is showed byTable 2. The data set contains 150 to be Normal (class = 1), 70 Hyper (class = 2), and the reminders is Hypo (class = 3).

4.2. Data preprocessing

We rearrange the conﬁguration of data set according to the or-der. Since the original type of data set is ﬂoating point in part. The

way of transformation is to convert the original data set to be inte-gers according to order. For example, the feature of f1 that the ﬁrst value is ‘‘65”, and we convert ‘‘65” to be ‘‘1” and so on. It is conve-nient to be executed by IEDA.Table 3shows parts of new data set via transformation.

4.3. Encoding

This paper adopts the Yeh et al.’s (2008) approach that the method of encoding is showed byFig. 3. We deﬁne the feasible

Table 1

The process of reversing probability distribution. Dimension j Individual 1 2 Individual 2 3 Individual 3 2 Individual 4 1 Individual 5 1 Individual 6 1 Variable 1 2 3 Count 3 2 1 Original probability 0.5 0.333 0.167 Reciprocal 2 3 6 New probability 0.182 0.273 0.545 Generate initial population

Evaluate fitness of each individual

Suppression pool Memory pool

Build the reverse probability model

Build the probability model

Generate a random number ζ

ζ Via the probability model in memory pool Via the reverse

probability model in suppression pool

Randomly generate new variable

Keep the present variable

Update the population

Terminate ? End TC ζ TU TL ζ C TU ζ 1₀ _{ζ T L} Yes No ≤ ≤ _≤

Fig. 2. The ﬂowchart of IEDA.

Table 2

The features of thyroid gland dataset.

Feature name Domain Simpliﬁed form

T3-resin uptake test 65—144 f1

Total serum thyroxin 0:5—25:3 f2

Total serum triiodothyronine 0:2—10 f3

Basal thyroid-stimulating hormone 0:1—56:4 f4 Maximal absolute difference of TSH value 0:7 to 56:3 f5

Class 1, 2, 3 Y

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solution like that is a 1_{(3m + 1) array called an ‘‘individual” and}

the grids called ‘‘dimensions”. The ﬁrst dimension represents the amounts of features that are chosen by IEDA. The second dimen-sion represents the variable 1, third dimendimen-sion that uses ‘‘1” repre-sents ‘‘>”, ‘‘2” reprerepre-sents ‘‘=” and ‘‘3” reprerepre-sents ‘‘<” and forth dimension represents threshold.

4.4. Fitness function

We can calculate the accuracy that represents the fitness value of each individual. The equation of accuracy, sensitivity and spec-ificity are showed by the following. In terms of relative reference, we define the TP, TN, FP and FN rate parameters to show in the Ta-ble 4. The calculation of accuracy is the amount of the ‘‘class<> 1” to be select correctly plus the amount of the ‘‘class = 1” to be not select that divide the amount of data (Yeh et al., 2008).

Accuracy ¼ TP þ TN TP þ TN þ FP þ FN Sensiti

v

ity ¼ TP TP þ FN Specificity ¼ TN TN þ FP

4.5. The process of IEDA

We divide the raw data set into training data set and testing data set. The number of training data set is 142, and the remain-ders are testing data set. We adopt the method of 10-fold-valida-tion (Chen & Hsu, 2006) to perform the robustness and reliability of algorithm. The process of mining thyroid gland data set by IEDA shows inFig. 4.

5. Experiment

In our experiment, we want to classify between ‘‘Normal” and ‘‘Hyper” and between ‘‘Normal” and ‘‘Hypo”. Hence, we divide the two parts that the purpose of first part is to find rules to classify between ‘‘Normal” and ‘‘Hyper”, and the second part is to find rules to classify between ‘‘Normal” and ‘‘Hypo”. Table 5shows the re-sults of first part that classify between ‘‘Normal” and ‘‘Hyper”. We find the best and average accuracy of classification by IEDA to be better than by GAs. The best and average accuracy by IEDA are 0.9839 and 0.96775, respectively. Besides, the best and average accuracy by GAs are 0.9516 and 0.90805, respectively. In the sec-ond part, we want to find the classification rules between ‘‘Nor-mal” and ‘‘Hypo”. Similarly, both the best and average accuracy

Table 3

Parts of results via transformation.

Original dataset Transformed dataset

1 f1 f2 f3 f4 f5 f1 f2 f3 f4 f5 2 65 25.3 5.8 1.3 0.2 1 88 47 12 8 3 65 18.2 10 1.3 0.1 1 101 42 12 9 4 67 23.3 7.4 1.8 0.6 2 98 45 17 2 5 68 14.7 7.8 0.6 0.2 3 76 46 5 5 6 76 25.3 4.5 1.2 0.1 4 101 37 11 6 7 79 19 5.5 0.9 0.3 5 90 41 8 10 8 80 23 10 0.9 0.1 6 97 47 8 6 9 84 21.5 2.7 1.1 0.6 7 89 36 10 4 10 84 18.5 4.4 1.1 0.3 7 94 26 10 2 Domain 65—144 0:5—25:3 0:2—10 0:1—56:4 0:7 to 56:3 1—54 1—101 1—47 1—47 1—85 Number of Feature Variable

Variable 1 > or = or < Threshold … Variable k > or = or < Threshold

Fig. 3. The form of encoding.

Table 4

The TP, TN, FP and FN rate parameters.

Actual state Predicted patient state Classiﬁed as ‘‘true” (Positive)

Classiﬁed as ‘‘false” (Negative)

Class is ‘‘true” (Positive) TP FN

Class is ‘‘false” (Negative) FP TN

Thyroid Data Set

Training Data Set Testing Data Set

IEDA for Mining Classification Rule Classification Rules Achieve the Predefined Accuracy? The Unclassified Data End No Yes

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Table 5

The results of ﬁrst part.

Rule Accuracy of training Accuracy of testing Type I error Type II error

The results of IEDA

1 f2>69 and f5>3 0.8943 0.9839 0 1 2 f2>59 and f5<21 0.9675 0.9355 4 0 3 f2>55, f4<21 and f5<15 0.9675 0.9839 1 0 4 f2>77; f3<47 and f4<19 0.9106 0.9516 0 3 5 f2>68 and f5<20 0.9675 0.9839 0 1 6 f2>75 and f5>3 0.9106 0.9516 0 3 7 f2>70 and f5<24 0.9593 0.9839 0 1 8 f2>76 and f3<48 0.9268 0.9516 0 3 9 f2>70 and f3>15 0.9675 0.9677 0 2 10 f2>68 and f5<20 0.9675 0.9839 0 1 Average 0.94391 0.96775 0.5 1.5 Std. 0.0298 0.018639

The results of GAs

1 f2>87 and f5>1 0.9187 0.8387 0 10 2 f3>27 and f5>3 0.935 0.8871 1 6 3 f2>38, f 3 < 45and f5<11 0.9187 0.8548 7 2 4 f3>26 0.935 0.9032 1 5 5 f3>27 and f5>3 0.935 0.8871 1 6 6 f2>75 and f5>3 0.9106 0.9516 0 3 7 f2>77; f3<47 and f4<19 0.9106 0.9516 0 3 8 f2>74 and f3<44 0.9024 0.9516 0 3 9 f3>26 0.935 0.9032 1 5 10 f2>75 and f5>3 0.9106 0.9516 0 3 Average 0.92116 0.90805 1.1 4.6 Std. 0.012757 0.042369 Table 6

The results of second part.

Rule Accuracy of training Accuracy of testing Type I error Type II error

The results of IEDA

1 f2<22 0.9667 0.9833 0 1 2 f2<21 and f5<83 0.95 0.95 2 1 3 f3>0 and f5>63 0.9417 0.9333 3 1 4 f4>25 0.9667 0.9667 2 0 5 f2<20 and f4<45 0.9333 0.9667 2 0 6 f2<22 and f3<28 0.9667 0.9833 0 1 7 f2<28 and f5>45 0.9667 0.9833 1 0 8 f2<63 and f4>24 0.9667 0.95 2 1 9 f1>13 and f4>25 0.9667 0.9667 2 0 10 f2<22 0.9667 0.9833 0 1 Average 0.94391 0.96775 1.5 0.5 Std. 0.0298 0.018639

The results of GAs

1 f2<46; f3<9 and f5<83 0.8917 0.9167 5 0 2 f3<11; f4>29 and f5<85 0.8917 0.9333 4 0 3 f4<47 and f5>69 0.9083 0.9167 5 0 4 f2<21 and f5<84 0.9583 0.95 2 1 5 f2>2 and f5>61 0.9167 0.9167 4 1 6 f2<63 and f4>24 0.9667 0.95 2 1 7 f3<13; f4<48 and f5>55 0.925 0.9333 4 0 8 f3<21; f4>20 and f5>26 0.9583 0.9333 2 2 9 f2<16; f3<28 and f4<46 0.9083 0.9333 4 0 10 f1>18; f3>5 and f4>23 0.9333 0.9 5 1 Average 0.92116 0.90805 4.6 1.1 Std. 0.012757 0.042369 Table 7

The comparisons of IEDA and GAs.

Algorithm Best rule Best accuracy Type I error Type II error

Part 1 IEDA f2> 55, f4< 21 and f5< 15 0.9839 1 0

GAs f2>75 and f5>3 0.9516 0 3

Part 2 IEDA f2< 28 and f5> 45 0.9833 1 0

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of classiﬁcation by IEDA are better than by GAs. The details of re-sult are showed inTable 6.Table 7lists the best results in IEDA and GAs, respectively. In addition,Table 8shows the best type I er-ror and type II erer-ror of IEDA are better than GAs.Table 9shows the average type I error and type II error of IEDA are also better than GAs.

6. Conclusion

Data mining is the search for valuable information in large vol-umes of data (Xiong, Kim, Baek, Rhee, & Kim, 2005). In this paper, we propose the hybrid algorithm that combines the immune algo-rithm and estimation distribution of algoalgo-rithm called immune-estimation distribution of algorithm; IEDA and successfully applied to the classiﬁcation risk of UCI thyroid gland data set. We compare the results between IEDA and traditional GAs. Based on the ob-tained results, our research absolute is better than GAs including accuracy, type I error and type II error. The results show not only the excellence of accuracy but also the robustness of the proposed algorithm. In this paper we have got high quality results which can be used as reference for hospital decision making and research workers. In future research, we will improve the effectiveness

and efﬁciency of IEDA and make it apply more domains. Hence, we will draw the concept of estimation distribution of algorithm for continuous problems to our IEDA, and consider the conditional probability in establishing probability distribution of the IEDA. It will improve the IEDA to be more effective.

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The type I and type II error of IEDA and GAs.

Actual class Classiﬁed class

I(Normal) II(Hyper) Part 1 I(Normal) IEDA 49(98.00%) 1(2.00%) GAs 50(100.00%) 0(0.00%) II(Hyper) IEDA 0(0%) 12(100.00%) GAs 3(0.25%) 9(0.75%) Part 2 I(Normal) IEDA 49(98.00%) 1(2.00%) GAs 49(98.00%) 1(2.00%) II(Hypo) IEDA 0(0%) 10(100.00%) GAs 2(0.20%) 8(0.80%) Table 9

The average type I and type II error of IEDA and GAs.

Average type I error (%) Average type II error (%) Part 1 IEDA 1 12.5 GAs 2.2 38.3 Part 2 IEDA 3 5 GAs 9.2 11