An Improved Fuzzy ISODATA Algorithm for Credit Risk Assessment of the EIT Enterprises

doi:10.4236/me.2012.35088

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Modern Economy, 2012, 3, 686-689

http://dx.doi.org/10.4236/me.2012.35088 Published Online September 2012 (http://www.SciRP.org/journal/me)

An Improved Fuzzy ISODATA Algorithm for Credit Risk

Assessment of the EIT Enterprises*

Jike Yu, Zongfang Zhou#, Hua Zhong, Huizhong Huang

School of Management and Economics, University of Electronic Science and Technology of China, Chengdu, China

Email: #zhouzf@uestc.edu.cn

Received July 5, 2012; revised August 6, 2012; accepted August 17, 2012

ABSTRACT

We proposed an improved fuzzy ISODATA algorithm for credit risk assessment of the emerging information technol-

ogy enterprise in this paper. Firstly, as the uncertainty of th e EIT en terprise is relativ ely la rge, we set a reference sample

and an initial clustering center matrix so that we overcame the shortcomings of traditional ISODATA algorithm and

improved the reliability of fuzzy clus tering analysis. Secondly, we proposed the step s of evaluating the EIT enterprises’

credit risk with improved fu zzy ISODATA algorithm. Last but not least, we assessed 10 EIT enterprises’ credit risk of a

certain city, which proved the effectiveness and op erability.

Keywords: EIT Enterprise; Credit Risk; Reference Sample; ISODATA Algorithm; Fuzzy Clustering

1. Introduction

Emerging Information Technology (EIT) is defined as a

technology that can innovate or upgrade the function, pr o d-

uct, or service of information technology by using the ba-

sic principles and methods of information science, as well

as with the technical characte ristics of emerging technolo -

gies [1]. As there are uncertain elements like the EIT it-

self, product market of the EIT enterprise and so on, the

EIT enterprises are facing large credit risk [2,3].

Credit is the inevitable product of social economic de-

velopment, and is also an essential part of modern social

economy. Credit risk is the possibility that a bond issuer

or borrower will default b y failing to repay princip al and

interest in a timely manner, lead ing to a lo ss to a bank , or

investors. EIT enterprises are the typical venture business.

To make objective and comprehensive assessment of thei r

credit risk is not only necessary foundation for a smooth

financing, but also the essential part for the EIT enter-

prises’ risk management.

The current credit risk assessment models are Credit

Metrics, Credit Risk+, KMV, multi-objective decision mak-

ing, non-parametric statistical methods, neural network a nd

so on. Using fuzzy clustering analysis for corporate c redit

risk assessment is non-parametric statistical methods [4,

5]. It’s especially in kinds of methods are unsure of the

overall distribution function, with good results. The cur-

rent literatures usually no longer evalu ate the merits after

classify the target objectives with fuzzy clustering me-

thod, or they consider all indicators as efficiency indica-

tors in the ratings analysis, and the classification is ac-

cording to the properties of specific target range set. Ac-

cording to this current way, it is possible that the credit

rating results are different, if we cluster and rate the same

EIT enterprise separately with two (or more than two)

groups of the EIT enterpri ses with different qualification s

as one target set. Especially in the case that there is very

small number of objects in one group, the possibility

tha t this situation happens is huge, which reduce the ob-

jectivity of the EIT enterprise credit risk assessment. On

the other hand, as an EIT enterprise is usually in initial

period of foundation, there is large uncertainty of its grow-

ing and development, and the index data used to assess

its credit risk is usually incomplete which need to set up

a corresponding reference sample system firstly. Refer-

ence sample system is an objective standard for the spe-

cific requirement of the EIT enterprise credit risk assess-

ment, which is set as ide al value of every characteristic of

every grade, used to stu dy t he targe t clu s t e ring. Curr e ntly ,

there are few literatures about the EIT enterprise credit

risk assessment.

In view of this, we’ve improved the traditional fuzzy

clustering method through setting the reference sample s y s-

tem of the EIT enterprises, and hav e proposed an imp r o v e d

fuzzy clustering algorith m to cluster the credit risk of the

EIT enterprises. Example shows that the improved algo-

rithm solves the problem of insufficient ob jectivity of th e

traditional fuzzy clustering method applied in the credit

risk assessment in a certain extent.

*This research has been supported by National Natural Science Foundation

of China (No.70971015), The Special Research Foundation of PhD

Program of Chin a (2011 0185110021).

#Corresponding author.

J. K. YU ET AL. 687

2. Fuzzy Cluster Analysis

Fuzzy ISODATA (I terative Self-Organizing Data Analy-

sis Techniques Algorithm) is an interactive sel f- org ani zin g

data analysis technique for fuzzy cluster [6,7]. Cluster using

standard Fuzzy ISODATA works as follow, suppose

classes’ number has been decided, and choose an original

fuzzy cluster matrix, calculate optimal fuzzy cluster ma-

tr ix a nd optimal cluster center matrix using iterative opera-

tion, then classify the inspected object. The algorithm re-

quires more stringent selection of original fuzzy cluster

matrix. Inappropriate selection would cause distortion in

iterative process. There are limitations when standard

fuzzy ISODATA was used in the scene of rating of target

object. The algorithm can only cluster object into specific

classes, but can’t discriminate whether classes meet the

“meaningful distance”. Based on this, reference sample

system and investigation sample will be collected to be

cluster. Improved fuzzy ISODATA algorithm steps are

as follows:

1) Establish the original characteristic indicators ma-

trix U* that descript each attribute value of all inspected

object and r eference samples. ij is on behalf of the cha r-

acteristic indicators j of object i.



** *

, ,

2) Standardize the data of original characteristic indi-

cators matrix U* by range method to get U, define

12 12



** *

max ,, ;min

jjnj jjjnj

uuu muu u for

column j of U*, calculate uij using formula (1)

ij j







V0, 1,2,l



(1)

3) Start iterative operation based on original cluster center

matrix of reference sample sy stem, .

4) Calculate fuzzy classified matrix using formula

(2), where c is on behalf of classes number. And based on

Euclid distance,



kjij

u v















,





























 



,, T









 (2)

5) Modify cluster center matrix for ,

 



, where



()

ij k







R





V (3)

6) Repeat step 2), compare and , for given

 

1ll

precision ε > 0, if max ik









R



V

1ll



,,,T

VVV V

 

k

, iterative opera-

tion should be stopped and should be out-

putted. In opposite condition, , repeat step 3).

7) Get fuzzy cluster based on optimal cluster center

matrix discrimination principle--suppose the optimal

cluster center matrix ,, if





min

kik j

uV uV





 



,,,

Ppp p

, object

should be classified

to class i.

3. Assessment Steps of Integration of Rough

Set and Improved Fuzzy Clustering

The evaluation indicators should be screened at first w he n

we assess the EIT enterprises’ credit risk. Based on indi-

cators screening, the application of improved fuzzy ISO-

DATA algorithm for classification of the EIT enterprises

credit risk would have a better result. The following are

specific steps of assessing and classifying the EIT enter-

prises credit r isk with attribute reduction method from i n te -

gration of rough set theory and improved fuzzy ISODATA

algorithm:

1) Establish an initial set of assessment indicators and

sample set to be inspected. Suppose 12

is the initial set of assessment indicators, and





,,,

12 n

xx x



is the sample set. aij is the value of

assessment indicator j of sample I;

2) Discretization of data aij;

3) Attribute reduction to the indicator set with applica-

tion of rough set theory [8,9];

4) Establish a proper reference sample set, and con-

struct an initial clustering center matrix ;

5) Add the reference sample set into sample set to be

inspected, and cluster all the samples with above-mentio-

ned improved fuzzy ISODATA algorithm in order to a ch-

ieve risk rating of the EIT enterprises.

4. Case Analysis

We assessed credit risk of 10 EIT enterprises (denoted by

A, B, C, D, E, F, G, H, I and J) in certain city. Firstly,

choose 4 primary-level indicators and 15 secondary indic-

ators, according to systematic, scientific, operational, obje-

ctive principle as well as a combination of quantitative and

qualitative principle, and referring the evaluation indexes

system of emerging technology enterprise credit risk [1].

They are financial benefits status indicator (P1): ROE (P11),

ROA (P12), asset maintenance and appreciation indicator

(P13), OPE (P14); assets operating state indicator (P2):

total asset turnover (P21), current assets turnover (P22),

inventory turnover (P23), receivable accounts turnover

(P24); debtpaying ability indicator (P3): asset-liability ratio

(P31), acidtest ratio (P32), cash flow debt ratio (P33);

development state indicator (P4): sales growth rate (P41),

capital accumulation rate (P42), the average growth rate of

capital (P43) and the ability of technological innovation

and application (P44). The data is from the financial

statements of 10 EIT enterprises, except (P44) is through

experts grading.

J. K. YU ET AL.

688



3341 44

,,,PPPP

00.0220.073 0.20700.5310

0.004 0.138 0.219 0.322 0.039 0.595 0.500

0.014 0.294 0.366 0.4370.1010.675 0.500

0.050 0.392 0.439 0.632 0.200 0.7301.000

0.117 0.487 0.51210.3010.8061.000











Set the accuracy ε = 0.001, and according to the above

classification results could be got according

Table 1. Indicators of credit riskharacteristics of eit enterprises.

development state

Then the initial clustering centers matrix is got after

normalization of the data in Table 2:

Secondly, make the index data of the EIT enterprise

discrete. Use the software, Rosetta, and choose the Entr o-

py Scalar tool in it, which can measure entropy, to accom-

pany this step.

The next step is attribute reduction. With help of Ge-

netic Algorithm tool in Rosetta, we get the indicators of

credit risk characteristics of these 10 EIT enterprises as

Table 1, denoted by ,

while 8 indicators such as ROA are redundant attributes.

12 1421 24

,,,PPPP



Last but not least, establish the 5-level reference sam-

ple system, denoted as K、L、M、N and O, referring to the

current 5-level credit risk standard of commercial bank

[5] and credit rating standard of the IT corporate in the

EIT corporate [10 ], as Ta ble 2 shows (V indicates the high-

est credit rating and correspond to the lowest credit risk).

entioned improved fuzzy ISODATA algorithm specific

steps, through computer multiple iterative operation, get

such as shown in Table 3 the clus tering cente r of the c r edi t

rating.

Now the

Table 3 and the principle of optimal clustering center

financial benefits status assets operating state debt-paying ability

ROA P12 OPE P14 total asset

turnover P21 receivable accounts cash flow debt ratio P33 sales g r owth rate P41

chnological

turnover P24 innovation and

application P44

ability of te

A 0.085 0.234 0.562 2.455 0.085 0.077 1

B 0.134 0.199 0.243 0.142 0.563 0.001 1

C 0.572 0.345 1.365 2.458 0.428 0.052 0

D 0.102 0.313 0.341 2.336 0.225 0.002 1

E 0.878 0.255 0.785 0.183 0.372 0.001 2

F 0.172 0.444 0.759 2.225 0.278 0.089 2

G 0.074 0.755 0.378 3.376 2.064 0.002 1

H 0.254 0.001 0.566 0.904 0.010 0.001 0

I 0.052 0.58 0.567 2.761 0.899 0.001 0

J 0.029 – 0.2260.001 0005 0.039 –0.87 1

Table 2. Credit risk reference sle system for eit enterprises.

P12 14 21243341P44 Credit grade

amp

PP P P P

K – – 0 1 – – 0.0840.204.100.8000.0820.1160 I

L –0.005 –0.091 0.300 2.800 0.001 –0.025 1 II

M 0.004 0.062 0.500 3.800 0.135 0.088 1 III

N 0.036 0.159 0.600 5.500 0.347 0.167 2 IV

O 0.095 0.252 0.700 8.700 0.564 0.275 2 V

Table 3. The clustering cers of every credit grade.

Credit Grade P12 P14 P21 P24 P33 P41 P44

nte

I –0–0.0.1.–0.–0.1..075 202 092 685 004 134 055

II –0.002 –0.080 0.308 2.753 0.011 –0.002 1.317

III 0.005 0.080 0.522 3.529 0.209 0.067 2.004

IV 0.040 0.187 0.707 5.133 0.396 0.113 2.358

V 0.105 0.358 0.803 7.121 0.661 0.298 2.887

J. K. YU ET AL. 689

le 4. The fications.

Crses

Tabclassi result

edit Grade EIT Enterpri

I B G J K

II A D L

III C E I M H

IV F N

V O

matrix discrimion, shown in Table 4zzy I SOD

sample system in this paper overc ome s

center matrix, talculati initial classifica-

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Setting a reference

Chi

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