Cluster Type Methodologies for Grouping Data - Science Direct

Available online at www.sciencedirect.com

ScienceDirect Procedia Economics and Finance 15 (2014) 357 – 362

(PHUJLQJ0DUNHWV4XHULHVLQ)LQDQFHDQG%XVLQHVV

&OXVWHU7\SH0HWKRGRORJLHVIRU*URXSLQJ'DWD 5DOXFD0DULDQD‫܇‬WHIDQD  a

Academy of Economic Studies, Bucharest, 6 Piata Romana, Romania

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

 © 2014 The‹3XEOLVKHGE\(OVHYLHU/WG6HOHFWLRQDQGSHHUUHYLHZXQGHUUHVSRQVLELOLW\RI(PHUJLQJ Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/). 0DUNHWV4XHULHVLQ)LQDQFHDQG%XVLQHVVORFDORUJDQL]DWLRQ Selection and peer-review under responsibility of the Emerging Markets Queries in Finance and Business local organization



Keywords: GDWDFODVVLILFDWLRQXQVXSHUYLVHGFODVVLILFDWLRQFOXVWHUW\SHPHWKRGRORJ\FOXVWHULQJDOJRULWKP

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



&RUUHVSRQGLQJDXWKRU7HO E-mail address: UVWHIDQ#\DKRRFRP

2212-5671 © 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/). Selection and peer-review under responsibility of the Emerging Markets Queries in Finance and Business local organization doi:10.1016/S2212-5671(14)00438-9

358

Raluca-Mariana Ştefan / Procedia Economics and Finance 15 (2014) 357 – 362

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¶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

Raluca-Mariana Ştefan / Procedia Economics and Finance 15 (2014) 357 – 362

359

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± OHYHO FOXVWHULQJ 0/&  DOJRULWKP WKDW XVHV WKH WHFKQLTXH RI DOWHUQDWLYH GHFLVLRQ WUHH $'7  PHWKRGSURYHGLWVHIILFLHQF\E\UHGXFLQJFRPSXWDWLRQDOFRPSOH[LW\DQGWKDWOHDGVWRDFRQVLGHUDEOHUHGXFWLRQ RIWLPH7KHPHWKRGLVPRUHUREXVWDQGHDV\WRJHWWKHDFFXUDWHVROXWLRQIRUDSUREOHPIURPWKHUHDOFRPSOH[ HFRQRPLFZRUOGWKLVPHWKRGRIIHUVPRUHDFFXUDF\RIFOXVWHUGDWDZLWKRXWPDQXDOLQWHUYHQWLRQDWWKHWLPHRI FOXVWHUIRUPDWLRQ*RWKDL%DODVXEUDPDQLH   0RVW)UHTXHQWO\8VHG$OJRULWKPVIRU&OXVWHU7\SH0HWKRGRORJLHV 7KHUHLVDYHU\ODUJHFOXVWHURIJURXSVWKDWDUHIRUPHGE\FOXVWHULQJDOJRULWKPVDQGLWZLOONHHSRQJHWWLQJ ODUJHU DV ORQJ DV WKHUH ZLOO FRQWLQXH WR EH DQ LQFUHDVLQJO\ TXDQWLW\ RI GDWD ZDLWLQJ WR EHFRPH UHOHYDQW LQIRUPDWLRQDQGNQRZOHGJH7KHPRVWIUHTXHQWO\XVHGPHWKRGVZHUHVHOHFWHGDQGWKHLUSKDVHVDUHGHVFULEHG 3.1. K-means Algorithm 6WHS&KRRVHLQLWLDOYDOXHIRUNDQGREMHFWSRLQWVUHSUHVHQWLQJWKHLQLWLDOFHQWURLGVRIWKRVHNFOXVWHUV 6WHS. (DFKREMHFWSRLQWLVDVVLJQHGWRWKHFOXVWHUWKDWKDVWKHFHQWURLGWKHFORVHVWWRWKDWREMHFW 6WHS&RPSXWHDJDLQWKHSRVLWLRQVRIWKHFHQWURLGVDQGFRQWLQXHWRGRWKDWXQWLODOOREMHFWSRLQWVKDYHEHHQ DVVLJQHGWRDJURXS 6WHS5HSHDWVWHSDQGVWHSXQWLOWKHFHQWURLGVGRQRWFKDQJHDQ\PRUHVRWKDWWKHPLQLPL]HGGLVWDQFH EHWZHHQWKHPFDQEHFRPSXWHG 3.2. SOM Algorithm 6WHS$VVLJQUDQGRPYDOXHVWRWKHZHLJKWYHFWRUVRIDQHXURQ 6WHS3URYLGHDQLQSXWYHFWRUWRWKHQHWZRUN 6WHS7UDYHUVHHDFKQRGHLQWKHQHWZRUNILQGVLPLODULW\EHWZHHQWKHLQSXWYHFWRUDQGWKHQHWZRUN¶VQRGH¶V ZHLJKWYHFWRUXVLQJ(XFOLGHDQGLVWDQFHDQGILQGWKHQRGHWKDWSURGXFHVWKHVPDOOHVWGLVWDQFHZKLFKLVDVVLJQHG DVWKH%HVW0DWFKLQJ8QLW%08  6WHS8SGDWHWKHQRGHVLQWKHQHLJKERUKRRGRIWKH%08E\FKDQJLQJWKHZHLJKWV%KDWLD'L[LW 

360

Raluca-Mariana Ştefan / Procedia Economics and Finance 15 (2014) 357 – 362

3.3. Hierarchical clustering 6WHS&DOFXODWHWKHGLVWDQFHEHWZHHQWKHVHWREMHFWVDQGSXWWKHUHVXOWVLQDPDWUL[ 6WHS)LQGLQWKHPDWUL[WKHHOHPHQWWKDWKDVWKHVPDOOHVWYDOXHLHWKHPLQLPXPGLVWDQFHEHWZHHQWZR REMHFWV 6WHS&RPELQHWKHWZRREMHFWVDQGIRUPDFOXVWHU 6WHS  7KH QHZ HOHPHQWV RI WKH PDWUL[ DUH YDOXHV RI WKH GLVWDQFHV FDOFXODWHG EHWZHHQ WKH QHZ IRUPHG FOXVWHUDQGWKHUHVWRIWKHFOXVWHUV 6WHS5HSHDWVWHSXQWLODOOREMHFWVEHORQJWRDFOXVWHU  $SSO\LQJ+LHUDUFKLFDO&OXVWHULQJ0HWKRGRORJ\WR*URXS&RXQWULHV 0DQ\ DSSOLFDWLRQV LQ GLIIHUHQW GRPDLQV UHTXLUH DQ LQVWUXPHQW OLNH FOXVWHU DQDO\VLV WHFKQLTXH DQG WKH HFRQRPLFILHOGPDNHVQRH[FHSWLRQ &RQVLGHULQJWKDWFOXVWHULQJDOJRULWKPVDUHFODVVLILHGDFFRUGLQJWRWKHLUPHWKRGWRJURXSGDWDWKH\DUH x 3DUWLWLRQDODOJRULWKPVWKHZHOONQRZQNPHDQVDOJRULWKP  x +LHUDUFKLFDODOJRULWKPVDJJORPHUDWLYHDQGGLYLVLYH  x 'HQVLW\EDVHGDOJRULWKPV x *ULGEDVHGDOJRULWKPV 7KHUH DUH PDQ\ FRPSDULVRQV DQG DVSHFLILF RQH LV PDGHEDVHGRQ WKHIROORZLQJIHDWXUHVRI WKH FOXVWHULQJ DOJRULWKPV x 7KHW\SHRIWKHGDWDWKDWWKHDOJRULWKPVXSSRUWVQXPHULFDOFDWHJRULFDO  x 7KHVKDSHRIFOXVWHUV x $ELOLW\WRKDQGOHQRLVHRURXWOLHUV x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

Raluca-Mariana Ştefan / Procedia Economics and Finance 15 (2014) 357 – 362

361

         

                         

Fig. 1. Dendrogram of the 26 countries clustered by development economic indicators data - Ward’s method (source: author’s Matlab output)

:DUG¶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¶V PHWKRG DQGWKHGHIDXOWGLVWDQFH (XFOLGHDQGLVWDQFH PHDQLQJ WKDWLQWKLVFDVHWKHGHQGURJUDPDFFXUDF\LVORZHUEXWLWLVVWLOOYHU\FORVHWR 7DEOH&RPSDULQJ+LHUDUFKLFDO&OXVWHULQJ$OJRULWKPV3HUIRUPDQFHVLQ7HUPVRI&RUUHODWLRQ&RSKHQHWLF&RHIILFLHQWVRXUFHDXWKRU¶V 0DWODEFDOFXODWLRQV  /LQNDJH

'LVWDQFH

&RUUHODWLRQ&RSKHQHWLF&RHIILFLHQWF 

:DUG

(XFOLGHDQ



6LQJOH

&LW\EORFN



&RPSOHWH

0LQNRZVNL



Raluca-Mariana Ştefan / Procedia Economics and Finance 15 (2014) 357 – 362

362 $YHUDJH

&KHE\VKHY



:HLJKWHG

0LQNRZVNL



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± &KHQJ ' .DQQDQ 5 9HPSDOD 6 :DQJ * $ 'LYLGH DQG 0HUJH 0HWKRGRORJ\ IRU &OXVWHULQJ  DYDLODEOH DW KWWSSHRSOHFVDLOPLWHGXJMZSDSHUVGLYPHUJHSGI *RWKDL(%DODVXEUDPDQLH3$Q(IILFLHQW:D\IRU&OXVWHULQJ8VLQJ$OWHUQDWLYH'HFLVLRQ7UHH$PHULFDQ-RXUQDORI$SSOLHG6FLHQFHV 9RO SS *UDEXVWV 3 %RULVRY $ &OXVWHULQJ PHWKRGRORJ\ IRU WLPH VHULHV PLQLQJ 6FLHQWLILF -RXUQDO RI 5LJD 7HFKQLFDO 8QLYHUVLW\ Computer Science Information Technology and Management Science,SS± +HQQLJ&/LDR7+RZWRILQGDQDSSURSULDWHFOXVWHULQJIRUPL[HGW\SHYDULDEOHVZLWKDSSOLFDWLRQWRVRFLRHFRQRPLFVWUDWLILFDWLRQ$SSO 6WDWLVW9RO3DUWSS± .DXU16DKLZDO-..DXU1(IILFLHQW.0HDQV&OXVWHULQJ$OJRULWKP8VLQJ5DQNLQJ0HWKRGLQ'DWD0LQLQJ9ROXPH,VVXH 0D\SS± .LUFKJDVVQHU*:ROWHU-,QWURGXFWLRQWRPRGHUQWLPHVHULHVDQDO\VLV%HUOLQ6SULQJHUS 0LOOLJDQ *: &RRSHU 0& 0HWKRGRORJ\ UHYLHZ &OXVWHULQJ PHWKRGV 9ROXPH  QR  'HF  $SSOLHG 3V\FKRORJLFDO 0HDVXUHPHQW 6HOYDNXPDU$$Q$GDSWLYH3DUWLWLRQDO&OXVWHULQJ0HWKRGIRU&DWHJRULFDO$WWULEXWH8VLQJ.PHGRLG,QWHUQDWLRQDO-RXUQDORI&RPSXWHU 6FLHQFHDQG0RELOH&RPSXWLQJ,-&60&9RO,VVXH$SULOSJ± 6RX]D -5 /XGHUPLU 7% $OPHLGD /0 $ 7ZR 6WDJH &OXVWHULQJ 0HWKRG &RPELQLQJ 6HOI2UJDQL]LQJ 0DSV DQG $QW .PHDQV :RUNVKRS)UDQFH%UHVLOVXUODIRXLOOHGHGRQQHHV'DWD0LQLQJ  ‫܇‬WHIDQ50‫܇‬HUEDQ03UHGD%+LHUDUFKLFDO&OXVWHULQJ$OJRULWKPV DQG'DWD6HFXULW\LQ)LQDQFLDO0DQDJHPHQWWK,QWHUQDWLRQDO (FRQRPLF&RQIHUHQFH±,(&6±0D\ ùWHIDQ50$Q2YHUYLHZRI)UHTXHQWO\8VHG$OJRULWKPVWR%XLOG&OXVWHUV-RXUQDORI,QWHUQDWLRQDO6FLHQWLILF3XEOLFDWLRQV0DWHULDOV 0HWKRGV 7HFKQRORJLHV9ROXPH6XQQ\%HDFK%XOJDULD 7VD\56$QDO\VLVRIILQDQFLDOWLPHVHULHV-RKQ:LOH\ 6RQVS ;X5:XQFK'&&OXVWHULQJ-RKQ:LOH\ 6RQVS