Financial Distress Prediction of K-means Clustering Based on Genetic Algorithm and Rough Set Theory

Transcription

1 505 A publcaton of CHEMICAL ENGINEERING TRANSACTIONS VOL. 51, 2016 Guest Edtors: Tchun Wang, Hongyang Zhang, Le Tan Copyrght 2016, AIDIC Servz S.r.l., ISBN ; ISSN The Italan Assocaton of Chemcal Engneerng Onlne at DOI: /CET Fnancal Dstress Predcton of K-means Clusterng Based on Genetc Algorthm and Rough Set Theory Baozhen Hou X'an Internatonal Unversty, 18 Yudou Lu, Yanta Dstrct, X'an Shaanx, PRC @qq.com To the enterprse, the fnancal rsks are mpersonal. If there s no scentfc method to predct and prevent fnancal rsks, t s lkely to cause the enterprse to fall nto a dffcult stuaton, even go bankrupt. In realty, the fnancal crss of enterprses s expressed as a gradual deteroraton of the fnancal ndcators. Therefore, the fnancal crss s symptomatc, and can be predcted. The man research drecton of the current fnancal crss early warnng s to lookng for a better model to help enterprses to fnd the fnancal crss earler. In vew of the early warnng of lsted company s fnancal crss, ths paper ntroduces the K clusterng algorthm based on genetc algorthm; overcomes some problems of tradtonal K-means clusterng, such as senstve to the ntal cluster center, easy to fall nto the local optmal value; puts forward a new model whch s K-means clusterng model based on genetc algorthm. Then, we combne Rough set theory to evaluate fnancal poston of the company comprehensvely, and test the ratonalty of the model classfcaton. Studes have shown that K- means clusterng based on genetc algorthm can dvde the company effcently. The goodness of ft to evaluaton results of rough set s up to 87.5%. 1. Introducton For enterprses, f there s no scentfc method to predct and prevent fnancal rsks, t wll make the enterprse fall nto trouble, and even cause bankruptcy. Therefore, t s very necessary to fnd a senstve and accurate fnancal early-warnng method. Snce 1930s, methods already have more than a dozen through many years development. Over the years, scholars have made the mult-level researches about how to predct the fnancal crss of enterprses more accurately. These studes are focused on the followng four aspects: 1) The defnton of enterprse fnancal crss. Altman(1994) defned "enterng legal bankruptcy" as the man mark of fnancal crss. Deakn(1972) regarded the fnancal crss as an enterprse that had been bankrupt or had sold out for nsolvency. Foster(1986) treated the fnancal crss as a busness that must be massve restructured. In our country, Chen Jng(1999) used serous sustaned loss as the symbol of fnancal crss. Zhao Alng (2000) took busnesses unable to pay due debts or expenses as the symbol of fnancal crss. Lu Lang(2006) beleved that the fnancal crss s defned as the company contnued losses. He defned companes sufferng losses for two years as a fnancal crss company. At present, for company stock n abnormal condton, the Shangha and Shenzhen Stock Exchange takes specal treatments for t. The specal treatments nclude two methods that are delstng rsk warnng (st*) and other specal treatment. 2) Fnancal crss early warnng model constructon. Nu Xaochen(2014) combned neural network model and rough set theory to predct the fnancal stuaton of enterprses. Bao Xnzhong(2013) appled two theores that were K-means algorthm based on partcle swarm optmzaton and rough set theory to predct the fnancal stuaton of enterprses. Yang Shue et al. (2005) mposed Back Propagaton (BP) neural network model on predct enterprses fnancal condton. Lang fan(2008) used mproved support vector machne model based on genetc algorthm to predct enterprses fnancal condton. Thus, searchng for a better algorthm s one of the trends of the current fnancal dstress predcton n varous countres. La Yuxa(2008) proposed a genetc algorthm based K-means clusterng analyss, and mproved the orgnal K-means clusterng algorthm to construct a better clusterng model. 3) Selecton of synthetcally evaluatng ndexes. Altman (1968) selected Workng Captal / Total Assets, Retaned Earnngs / Total Assets and other fnancal ndcators n hs study. Then, he found that EBIT/ Total Please cte ths artcle as: Hou B.Z., 2016, Fnancal dstress predcton of k-means clusterng based on genetc algorthm and rough set theory, Chemcal Engneerng Transactons, 51, DOI: /CET

2 506 Assets, Sales Revenue / Total Assets, Market Value of Shareholder Equty /Book Value of Total Labltes showed good predctve ablty. In 2006, on the bass of actual stuaton, Berrada T (2006) selected dfferent methods to fnd the senstve ndcators by usng net operatng proft rate and return on equty rato to construct the early warnng model whch were obtaned good effect. In our country, n the research of fnancal early warnng, song Bao et al. (2015) selected the Lqudty Rato, Quck Rato and other 32 fnancal ndcators as the alternatve varables. Fnally, there are only 5 ndcators by usng the normal dstrbuton test, such as the Rato of Fxed Assets, Intangble Assets, etc. 4) Sample selecton. Altman et al. (1968) used the data of ndustral enterprses Italy between 1982 and 1992 as samples n the study of fnancal early-warnng. In the study, Nu Xaochen (2014) based on companes lsted n the Shangha and Shenzhen Stock Exchange, and selected the companes whch were specally treated from 2010 to Accordng to the conclusons above, we defne those companes suffered specal treatment as the fnancal dstress companes. In addton, we use the K-mean clusterng algorthm based on genetc algorthm, whch s commonly use n the feld of fnancal early warnng. In ths paper, we select 28 fnancal ndcators as examne varables, and preserve 7 ndcators accordng to the sgnfcant test. We select 24 A shares of lstng Corporaton as the objects of study. Half of them get specal treatment and the others of them are normal fnancal companes. 2. Algorthm Descrpton 2.1 Archtecture of Wreless Sensor Networks K-means algorthm s one of the most wdely used clusterng algorthm. The algorthm takes K as parameter, and dvdes the n objects nto K clusters, whch makes hgher smlarty between the ntra-cluster, and lower smlarty between the nter-clusters. Frst, the algorthm randomly chooses K objects, each object represents an average or center of a cluster. For the remander of each object, the algorthm assgns t to the nearest cluster accordng to the dstance from the center of each cluster, then the algorthm recalculates the average value of each cluster. We repeat ths progress untl the crteron functon converges. The crteron functon s as follows: K E X X (1) 1XC 2 Among them, X s the average value of C cluster. K-mean algorthm s descrbed as follows: (1) K-records are randomly selected as the ntal cluster centers. (2) Calculatng the dstance between each record and the K cluster center, and regards ths pont assgned to the clusterng whch s nearest to t. (3) Calculatng the centrod (mean value) of each aggregaton and the dstance between each object and the center object, and re-dvdng the correspondng object accordng to the mnmum dstance. Repeat ths step untl the formula (1) no longer changes sgnfcantly. Generally, the smaller the value of the formula (1) s, the better the clusterng effect s. 2.2 K-mean Clusterng Algorthm Based on Genetc Algorthm The genetc algorthm s appled to cluster analyss. The combnaton of the global optmal searchng ablty of genetc algorthm and the local optmzaton ablty of cluster analyss can overcome localty of clusterng algorthm. In the process of populaton evoluton, the K-means operaton s ntroduced. Because of the strong local search ablty of K, the convergence speed of genetc algorthm can be greatly mproved after the ntroducton of K-means. At the same tme, n order to avod prematurty, the adaptve method s used to adjust the crossover probablty and mutaton probablty dynamcally n the populaton, so that t can be changed automatcally wth the degree of adaptve functon. The specfc steps of the algorthm are summarzed as follows: Step 1: Chromosome codng. We code floatng pont number based on cluster center, and code the center of each category as the chromosome. Step 2: Generatng ntal populaton. In order to obtan the global optmal soluton, the ntal populaton s randomly generated. The algorthm randomly assgns each sample to a class as the ntal clusterng. Then t uses the cluster centers of each cluster as the ntal ndvdual chromosome encoded strng. Fnally, the algorthm generates M ntal ndvduals, so as to generate the frst generaton of populaton.

3 Step 3: Selectng the ftness functon. The ftness functon s used to measure the ndvdual groups n the optmal soluton, n the meantme ndvduals may reach or close to the optmal soluton of the excellent degree. In ths paper, we use the formula (1) to construct the ftness functon: f=b/(1+e) (2) Among them, b s constant. Step 4: Selectng crossover operator, mutaton operator, genetc operator. We calculate the probablty of ndvdual be selected on the bass of the ftness. Then we replace the worst ndvdual wth the current optmal ndvdual n the new populaton. Ths artcle mplements the crossover accordng to the followng formula: X ax a X, t 1 t 1- t A A B X a X ax, 0,1 t 1 ( 1- ) t t B A B a (3) For each aberrance pont, algorthm uses a random number n the value of the correspondng gene to replace the orgnal gene and makes the mutaton. Algorthm uses the non-fxed probablty value for the adaptve genetc operator n the process of genetc algorthm. For the bgger ftness ndvduals, algorthm gves t correspondng crossover and mutaton probablty. For example, algorthm sets the correspondng crossover and mutaton probablty to the ndvduals whch have a bgger ftness. In ths way, the adaptve genetc algorthm can keep the dversty of the populaton whle ensurng the convergence of the algorthm. Step 5: K-means operaton. Frstly, we defne the values of the new populaton after the mutaton as centered, and assgn each data pont to the nearest class, so as to form a new cluster. Secondly, we calculate the new cluster center accordng to the new cluster partton, and replace the orgnal encodng value. Step 6: Loop termnaton. Cyclc teraton starts at 0, plus 1 for each cycle. If the current cyclc teraton s less than the pre-specfed maxmum cycle, then the cycle s contnued; otherwse, the end of the cycle. If the current cyclc teraton s less than the predetermned maxmum cyclc teraton, the loop contnues; otherwse, ths loop ends. 2.3 Rough Set In ths paper, rough set s used to attrbute reducton of the fnancal data of the lstng Corporaton. In the rough set, an nformaton system s defned as S=(U, C, D, V, f). Among them, U s a collecton of objects; C and D s collectons of attrbutes; V s a collecton of attrbute values; and F s an nformaton functon, whch gves an nformaton value to each attrbute of each object n the U. Decson table s a specal knd of knowledge expresson system. It s a four tuples T=U, CD, V, f. It means that when certan condtons are met, how decsons should be performed. Defntons are as follows: Defnton 1: The lower approxmaton of the set X on the R s defned as R_(X)={xU:[x] RX}. R_(X) also known as the R postve doman of X, marked as POS R(X). Defnton 2: In decson table S=(U, C, D, V, f), the dependency of decson attrbute D on condtonal attrbute set BC s defned as D POS D U. B B 507 Defnton 3: In decson table S=(U, C, D, V, f), cc, the mportance of the condton attrbute (ndex) C s defned as S g c D - D. c C- c Defnton 4: The weght of the condton attrbute (ndex) C s defned as W o c Sg c. Sg C In the tradtonal rough set theory, the attrbute s regarded as redundant when the attrbute mportance s 0. At ths pont, attrbute reducton should be carred out before the calculaton of attrbute weghts. 2.4 Introducton to Fnancal Early Warnng Model The man body of ths paper s based on the genetc algorthm K-means. We use ths model to categorze. Besdes, we use descrptve statstcs and rough set to test results. Step as shown n fgure 1:

4 508 Update the center of K-means clusterng No Code chromosome Generate ntal populaton Select the ftness functon Select crossover, genetc, mutaton operator K-means clusterng Iteratve number =100? Yes End Start Select data Data preprocess Comparson Identfy the degree of concdence Descrptve statstcs Rough set test Fgure 1: The Prncple of Fnancal Early Warnng Model 3 Smulaton Experment and Result Analyss 3.1 Data Selecton If we want predct the monthly sales and get the better results, we need to fnd out the smlar hstorcal month (1) Selecton of sample frms. Most of the specally treated company have fnancal crss and encounter serous dffculty n ts busness management. Based on the prevous study experence, we defne those companes suffered specal treatment as the fnancal dstress companes. Ths paper selects 24 A-share companes lsted n Shangha Stock Exchange and Shenzhen Stock Exchange as the research object. Among them, there are 12 specal treatment companes. At the same tme, based on selecton crtera of smlar ndustry and smlar asset sze, ths paper selects 12 normal fnancal companes as pared samples. In ths paper, the emprcal data are derved from (Table 1) Table 1: Sample Companes Number(ST*) Stock symbol Number Stock symbol (2) Selecton of fnancal ndex. The fnancal crss s symptomatc, and can be predcted by a seres of observable fnancal ndcators. Whether the fnancal early-warnng ndexes are reasonable, t wll determne the accuracy of the fnancal early-warnng model. Ths paper makes full use of prevous research n fnancal warnng ndex selecton, ntally selects 28 ndcators as an alternatve to evaluate varables. They are Current Rato (X1), Quck Rato (X2), Asset-lablty Rato(X3), Interest Coverage Rato(X4), Proft Rate to Net Worth(X5), Gross Margns on Sales(X6), Net Proft Margn on Sales(X7), Earnng Per Share(EPS) (X8), Recevables Turnover Rato(X9), Inventory Turnover(X10), Current Assets Turnover(X11), Total Assets Turnover(X12), Net Asset Growth Rato(X13), Net Proft Growth Rato(X14), Man Busness Income Growth Rate(X15), operatng proft growth rate(x16), total proft growth rate(x17), total asset growth(x18), man proft growth rate(x19), cash flow growth rate per share(x20), growth rate of net assets per share(x21), growth rate of earnngs per share(x22), rato of asset nflaton proof and ncremental value(x23), Rato of retaned earnngs to total assets(x24), cash-flow rate(x25), Operatng net cash flow per share(x26), fxed assets rato(x27), and ntangble assets rato(x28). 3.2 Data Classfcaton We need to classfy 24 companes. However, due to the bg sample data and the lmted space, we only put four companes fnancal data n our paper. These are two st* companes and two normal companes, as shown n the followng Table 2 whch had pre-processed the defect data.

5 509 Table 2: Fnancal data of companes Type Symbol (st*) (st*) Debt-payng Ablty X X X X , , , Proftablty X X X Operatonal capacty X , X X X Development ablty X X X X Cash flow X Captal structure X X Emprcal Study and Analyss 4.1 Indcators Screenng Although the prmary ndcators of fnancal early warnng are very comprehensve, t may not be able to senstvely forecast the Ltd fnancal stuatons. Too much of the early warnng ndexes not only become the heavy workload, but ncrease the runnng tme of model and affect the accuracy. Therefore, t s necessary for us to further screenng of ndexes before the constructon of early warnng model. And there may be a strong correlaton between the ndcators, whch also affect the predcton result. We use sgnfcant tests to screen. Effectve early warnng ndcators should be at least show sgnfcant dfferences between ST* companes and normal companes, so as to correctly judge the fnancal stuaton of enterprses. In ths paper, the ndexes are sgnfcant analyzed to complete the screenng by the Evews software. Besdes, we remove the ndexes whch do not contrbute to dstngush normal companes from those companes n fnancal crss. The results show that only ndcators X1, X4, X8, X9, X11, X18, X25 pass the sgnfcant test, the rest of ndcators are excluded because they don t pass the test of sgnfcance. 4.2 Test of Rough Step 1: Weght calculaton. We use the formula of rough set theory to calculate the weght of the 7 fnancal ndexes. o W c C S g c S g Step 2: Comprehensve score for each company. We get comprehensve evaluaton scores by C W C. Step 3: Test. In order to further test the correctness of clusterng results, we use descrptve statstcs and varance analyss to analyze the comprehensve score of the companes n each category. The results are shown n table 3. Table 3: Descrptve statstcs stuaton of the companes Data Mean N Std. devaton Class Ⅰ Class Ⅱ Class Ⅲ Total (4)

6 Result analyss Accordng to the above test, we fnd that the average s on the upward trend from the frst to the thrd category. It shows that the average score s sgnfcant dfference between the dfferent categores. The mean errors of the frst class, the second class and the thrd class are small. It shows that dfferent s small wthn the groups and the companes wthn each group are smlar. There are three companes whch are not consstent wth the expermental results. We obtan the concluson that the accuracy of the model s 87.5%. 5. Concluson At present, there are a lot of models n the feld of fnancal early warnng research, how to choose the approprate early warnng methods play a key role n the valdty and accuracy of the warnng. In ths paper, we fnd that the K-means clusterng algorthm based on genetc algorthm s more accurate than the tradtonal clusterng algorthm. The results of ths study provde a new dea for the company classfcaton and a good way of fnancal warnng. It provdes an effectve bass for the relevant personnel to forecast the fnancal crss of enterprses. For protectng the nterests of nvestors and credtors, helpng the management departments to montor lstng Corporaton qualty and avodng the rsk of the securtes market, t also has mportant practcal sgnfcance. References Altman E.I., 1994, Corporate dstress dagnoss comparsons usng lnear dscrmnate analyss and neural networks (the Italan experence) [J].Journal of Bankng and Fnance, Altman E.I., 1968, Dscrmnate Analyss and the Predcton of Corporate Bankruptcy. Journal of Fnance 23, [J]. Fnance, 23(4): Bao X.Z., Yang Y., 2013, The Early Warnng of Enterprse Fnancal Crss Based on Clusterng, Rough Set and Neural Network [J]. Journal of Systems & Management, 22(3): Berrada T., 2006, Incomplete Informaton, Heterogenety, and Asset Prcng [J]. Journal of Fnancal Econometrcs, 4(4): Chen J., 1999, The Emprcal Analyss on the Predcton of Lstng Corporaton s Fnancal Deteroraton [J]. Accountng Research, 4: Deakn E.B, 1972, A Dscrmnate Analyss of Predcton of Busness Falure [J]. Journal of Accountng Research, 3: Foster G., 1986, Fnancal Statement Analyss [M]. New Jersey: Prentce-Hall. La Y.X., Lu J.P., Yang G.X., 2008, K-Means Clusterng Based on Genetc Algorthm [J]. Computer Engneerng, 34(20): Lang F., 2008, Research on Fnancal Early Warnng of Improved Support Vector Machne Based on Genetc Algorthm [D]. Journal of Bejng Jaotong Unversty. Lu L., 2006, The Emprcal Research of Fnancal Crss Predcton n Lsted Company [D]. Journal of Soochow Unversty. Nu X.C., 2014, Research on the Fnancal Early Warnng of Lstng Corporaton whch Based on Neural Network Model [J]. Scence Technology and Industry, 14(11): , DOI: / _49 Song B., Zhu J.M., L X., 2015, Research on Enterprse Fnancal Early Warnng Based on Bg Data [J]. Journal of Central Unversty of Fnance & Economcs, 6: Yang S.E., Huang L., 2005, Fnancal Crss Warnng Model based on BP Neural Network [J]. System Engneerng Theory and Practce, 25(1): Zhao A.L., 2000, Recognton and Analyss of Enterprse s Fnancal Crss [J]. The Theory and Practce of Fnance and Economcs, 21(108):