University of Lampung | LPPM-UNILA Institutional Repository (LPPM-UNILA-IR)

  International Conference on Mathematics and Natural Sciences (ICMNS) November 29-30, 2006, Bandung-Indonesia

  Preface

  ICMNS was held in ITB Campus, Bandung, 29 – 30 November 2006, under the joint auspices of Faculty of Mathematics and Natural Sciences, School of Pharmacy, and School of Life Sciences and Technology, Institut Teknologi Bandung. We have been, almost, overwhelmed by the level of interest and participation in the conference. Overall, 13 invited lectures were delivered and 526 papers were presented (212 oral presentations and 314 poster presentations). The proceedings published in a CD-ROM form.

  Space is unfortunately too short to thank individually all those people whose dedicated efforts, often over a period of many months, were responsible for the success of the conference - especially the members of the Steering and Organizing Committees.

  Ismunandar Conference Chairman

  

Committee

  ™ Organizing Committee

  1. Dr. Ismunandar

  2. Dr. Johan Matheus Tuwankotta

  3. Dr. Mikrajuddin

  4. Dr. Taufiq Hidayat

  5. Dr. Heni Rachmawati 6. Dr. Rina Ratnasih, M.SC.

  7. Dr. I Ketut Adnyana

  8. Dr. Khairurrijal

  9. Dr. Veinardi Suendo ™ Advisory Committee

  1. Prof. Hideaki Kasai (Osaka Univ., Japan)

  2. Prof. Karel van der Hucht (Space Research Organizing, Netherlands)

  3. Dr. Terry Mart (UI)

  4. Prof. Dr. Sri Wahyuni (UGM)

  5. Dr. Akhmaloka (ITB)

  6. Dr. Tutus Gusnidar K. (ITB)

  7. Dr. Intan Ahmad (ITB)

  8. Dr. Ing. Cynthia L. Radiman (ITB)

  9. Dr. Edy Tri Baskoro (ITB)

  10. Dr. Dody Sutarno (ITB)

  11. Dr. Suhardja D. Wiramihardja (ITB)

  12. Dr. Asep Gana Suganda (ITB)

  13. Dr. I Nyoman P. Aryanta (ITB) ™ Editor Committee

  1. Dr. Mikrajuddin

  2. Dr. Taufiq Hidayat

  3. Dr. Akhmaloka

  4. Dr. Asep Gana Suganda

  5. Dr. Dody Sutarno

  6. Dr. Edy Tri Baskoro

  7. Dr. Heni Rachmawati

  8. Dr. I Ketut Adnyana

  9. Dr. I Nyoman P. Aryanta

  10. Dr. Idam Arif

  11. Dr. Ing. Cynthia L. Radiman

  12. Dr. Ismunandar

  13. Dr. Johan Matheus Tuwankotta

  14. Dr. Khairurrijal

  15. Dr. Pudji Astuti 16. Dr. Rina Ratnasih, M.SC.

  17. Dr. Suhardja D. Wiramihardja

  18. Dr. Veinardi Suendo ™ Technical Editor

  1. G. Gumilar

  2. Arif Surachman

  3. Tiin Sinatra

  4. Rini Latifah ™ Technical Committee

  1. Sulaeman 2. Ella Nurlaela Jamilah, S.Sos.

  3. Lani Marlina, A.Md.

  4. Ahmad Rosad Mahmud, S.Sos 5. Binarti Dyah Pertiwi. Dra.

  

6. Yun Yun Hendra Gunawan, ST.

  7. Untung Slamet MR.

  8. Dede Enan

  9. Kliwon

  10. Nani Mursiani 11. Cece Saefuddin, A.Md.

  12. Rachman

  13. Sri Rahmawati

  14. Rusmala Dewi Sjarif 15. Harsenawati, S.Sos.

  16. Dede Ruslan, SE.

  17. Wawan Setiawan

  18. Adityawarman

  19. Jajat 20. Didi Sudiana, S.Pd.

  21. Kurdi

  22. Yuyun Yunior 23. A. Nur Izzatul M.

  24. Nur Asiah Aprianti

  25. Rena Denya

  26. Yanuar Syapaat

  27. Johan Ardian

  28. Heri Permadi 29. Bebeh Wahid N.

  30. Widya Febrina

  31. Mia Ledyastuti

  32. Puti Syahrani

  33. Jessica Trisina

  34. Dedy Hamdani

  35. Angga

  36. Haery Yasdi 37. Kapriosi N.R.

  38. Ninuk

  39. Elly Mulyani

  40. Rosy Rofianti 41. Hadiana A.R.

  42. Alexander Sobri

  43. Melisa Asrianti

  44. Tendy Rusdiana

  45. Iman Nurchaedi

  46. Arie Wibowo

  47. Dian Karamita

  48. Edi Pramono

  49. Lenggana

  50. Nizar Happyana 51. Anton Restu P.

  52. Alfarius Eko N.

  53. Randi R.

  54. Suryadi

  November 29-30, 2006, Bandung-Indonesia

  

  40 I13 Gunawan Ibrahim, Nanang T

  Puspito, and Sri Widiyantoro

  49 ¾ Participants OA01 Sonita

  Syarifah, Mamot Bin Said and Abdullah Al-Hajjaji

  52 OA02

  Bambang Kuswandi1, Nuriman1, Henk Dam2, Willem Verboom2, David N. Reinhoudt2

  55 OA04

  

  29 I09 H.-D. Ließ 33 I10 by Kazuhiro Kogure 34 I11 by Z. Jamal, P. Poopalan and S. S.

  

  

  

  Arief Movadhy Rakhman

  59 OA05

   Yeyet C. Sumirtapura, Sudana Atmawidjaja, Ida Parwati and Apip Hadi

  63 OA06

  67 International Conference on Mathematics and Natural Sciences (ICMNS)

  Mat Isa

  Herbert O. Moser

  Contents

  2 I03 Zainal

  ii v

CONTENTS vi

   xxi

   li PAPERS

  Code Title Page

  ¾ Invited I01 Hideaki

  Kasai, Rifki Muhida and Wilson A. Dino

  1 I02

   Josiane Cillard and Pierre Cillard

  Abdul Aziz

  26 I08 by

  5 I04

   by Pikul Wanichapichart, Jutiporn Sudsiri, Kanokkarn maswiwat, Tanawat Wongluksanapun and Sorawuth Bunthawin

  14 I05 by

  Jin Akiyama and Chie Nara

  17 I06

  Dr. Stephan Wirth

  23 I07

   Sri Wahyuni1, Ari Suparwanto1, Widodo1, Ikrar Pramudya2, Ema Carnia3

• by Yahdiana Harahap, Hayun,

  

by Utamy Sri Rahayu, Suwendar,

Joseph I. Sigit

  Yohana Chaerunisaa, Boesro Soebagio and Marline Abdassah

  120 PA26

   Leni Herliani Afrianti Priyatno , Elin Yulinah Sukandar , Slamet Ibrahim and I Ketut Adnyana

  122 PA27 by Yahdiana Harahap, Umar Mansur

  and Fitria Handayani R

  127 PA28

   Wiwiek Indriyati, Jutti Levita and Titta Hartyana

  131 PA29

   Marline Abdassah, Anis Yohana Chaerunisaa and Mutakin

  135 PA30 Anis

  139 PA31 Emma Surachman,

  116 PA20 by

  Anis Yohana Chaerunisaa

  143 OB07 Endang Semiara, Nilo

  Suseno, Muhtadi Raharjo, V. Esti Windiastri, Sulastri Isminingsih, Chiyoko Machida and Yasunori Machida

  147 OB08

   Nur Aini, Lulu Lusianti Fitri, and Ahmad Ridwan

  151 OB09

   by Annisa Rahmah Furqaani, Lulu Lusianti Fitri, and Mariana Rahmasari

  156 OB10 Totik Sri Mariani and Erlangga B.P.

  160

  Moelyono MW., Eli Halimah, and Safdestha Pratiwi

  113 PA17 by Herman Suryadi, Maksum Radji, Juwita Dianingtyas, Arni Hidayah AP

  OA07

  86 PA03

   by Lia Amalia , Rully M.A Roesli , Joseph I.Sigit and Elin Yulinah Sukandar

  72 OA09

  

by Slamet Ibrahim

Surantaatmadja, Daryono Hadi Tjahjono, Musyarofah

  76 OA10 by Jessie Sofia

  Pamudji, Fauzi Sjuib, Yeyet C. Sumirtapura and Slamet Ibrahim S

  79 OA12

   Sukmadjaja Asyarie, Maria Immaculata I, As’ari Nawawi

  83 PA01

   Kharmeina Hervitanty

   Lita Vidianty Sunardi, Yeyet Cahyati Sumirtapura, Sukrasno, and Heni Rachmawati

  J. I. Sigit, L. Meliani, H. Rachmawati

  91 PA06

   by Muhctaridi, Jutti Levita, Holida Rahmi L

  97 PA07

   by Meta Santika Sari 1, Yeyet Cahyati 1, Heni Rachmawati 1

  101 PA11

   Daryono Hadi Tjahjono, Slamet Ibrahim and Sakinah Juliani Utami

  105 PA12

  Sukrasno, Irda Fidrianny and Komar Ruslan Wirasutisna

  109 PA13 by

  International Conference on Mathematics and Natural Sciences (ICMNS) November 29-30, 2006, Bandung-Indonesia OB11

   Siti Sumarmi, Brian Dancer and J.H. Slate

  236 OB36 by R.

  218 OB30

   A.L.N. Aminin, F. Madayanti, P. Aditiawati, and Akhmaloka

  222 OB31

   Intan Ahmad, Sita Astari, Bayu Rahardjo, Marselina Tan and Amrul Munif

  226 OB32

   by Agus D. Permana and Rostaman

  230 OB34

   by Anggraini Barlian and Benny Atmanegara

  Hertadi , S. Nurbaiti and Akhmaloka

  214 OB29

  240 OB37

   by Arlyna B. Pustika and Erna Winarti

  244 OB38

   by Rizkita Rachmi Esyanti, Dingse Pandiangan and Veny Usviani

  248 OB41

   by Anggraini Barlian and Nandana

  252 OB42

   by Iis Nur Asyiah, Elin Yulinah, Mumu Sutisna and Buchari

  256

   Aisah Jamili, Tjandra Anggraeni

  R. Moeis, B.A. Wahjoedi and A.S. Noer

  165 OB12 by Asmoro Lelono 169 OB13 by Amirul A. A, Ahmad R. M. Yahya, Kumar Sudesh, M. N.

   by Arina Novilla, I Nyoman Pugeg Aryantha and Dea Indriani Astuti

  M. Azizan and M. I. A. Majid

  174 OB14

   by Hera Noviana, Maelita Ramdani, Zeily Nurachman, Tintin Gartinah, Isak Solikin2 and AS Noer

  179 OB15 by Dyah Ratna

  Wulan, Dessy Natalia and Zeily Nurachman

  181 OB16

   Gede Suantika, Cecilia Rochmalita Triwardhani

  184 OB17

  189 OB19

  210 OB28 by Yoni F. Syukriani, Maelita

   by Fenny M. Dwivany, Sony Suhandono, Listya Utami Karmawan, Arif R. Sadjuri, Britanto Dani W. and Dio Ramondrana

  193 OB21

   by B.S. Daryono, R. Susandarini and K.T. Natsuaki

  197 OB22 P.E. Susilowati, P. Aditiawati, F.

  Madayanti and Akhmaloka

  202 OB23 by Marselina I. Tan, Dewi S.

  Rachmawati

  206 OB24

   Maelita Ramdani Moeis, Dwi Arisandi Wijaya

  International Conference on Mathematics and Natural Sciences (ICMNS) November 29-30, 2006, Bandung-Indonesia OB43

   by Siti Khodijah Chaerun

  

by Misni Bin Surif, Mohd Noor Ahmad , Mahmad Nor Jaafar, Adibi

Rahiman Md. Nor, Ibrahim Jaafar and Rashidah Mat Resat

  310 PB07 by

  Nurkhasanah and Azimahtol Hawariah LP

  314 PB08

   by Ronny Rianto, Arya Widyawan, Nining Betawati Prihantini, Wisnu Wardhana and Dian Hendrayanti

  318 PB10

   Gede Suantika and Yuliana

  322 PB11

   Gede Suantika, R Ria Antarini

  326 PB12

  330 PB15

  306 PB06

   R. Susandarini1, Purnomo, and I.Y.B. Safitri

  334 PB16

   Noer,L.F and Taufikurahman

  337 PB17

   Heni Yohandini, F. Madayanti, P. Aditiawati, and Akhmaloka

  341 PB18 by Subandi, P.E.

  Susilowati, Muntholib, E. Susanti, H. Sutedjo, P. Aditiawati, F. Madayanti and Akhmaloka

  345 PB19

   S. Nurbaiti, F.M. Warganegara and Akhmaloka

  349 PB20 353

  

Hartinio N Nahampun, Wiwit

Widyasari , Sony Suhandono and I Nyoman P Aryantha

   by Misni Bin Surif, Ahmad Zahuri Dahalan, Siti Amirah Jusoh and Siti Syazwina Shahar

  261 OB45 by Y.

  by Firman Alamsyah, Wiwit

  Satitiningrum, N.Juli and D.I. Astuti

  265 OB46 Akhmaloka , S. Nurbaiti, R. Hertadi, H. Yohandini, A.L. Aminin, H. Helwati and F.

  Madayanti

  269 OB47 Indri Garnasih, Ayda

  T.Yusuf

  273 OB48 by Ernawati A. Giri-

  Rachman, Thomas Robertus and Sarwono Hadi

  277 OB49

  

  Widyasari and Sony Suhandono

  302 PB05

  280 OB51 Marieska

  Verawaty, Adam J. Bogdanove and Volker Brendel

  285 OB52

  Fatchiyah, Mohamad Zubair and Ken-Ichirou Morohashi

  290 OB53

  

by Sasanti Tarini D., Marlia

Singgih W., Irda Fidrianny and Shinta Caroline

  294 PB02

   by Annisa Rahmah Furqaani, Lulu Lusianti Fitri, and Mariana Rahmasari

  298 PB04

   Topik Hidayat and Adi Pancoro

  International Conference on Mathematics and Natural Sciences (ICMNS) November 29-30, 2006, Bandung-Indonesia

   by Agung Purnamam and Adi Pancoro

  420 OC03 by Zulhadjri, Naoki

  400 PB39 Diah Inayati and

  Ayda T. Yusuf

  404 PB43 by E. Nugraheni and S. Nurmawati

  408 PB46 Nisa Rachmania Mubarik

  and Sri Listiyowati

  412 OC01

  416 OC02

  

by Afisah Osman, Abd Mutalib Jani and Ibrahim Abu

Talib

  Kamegashira, Touetsu Shishido

  396 PB38

  425 OC05

  

Deana Wahyuningrum, Sadijah Achmad, Yana

Maolana Syah, Buchari, and Bambang Ariwahjoedi

  428 OC07 Orasa

  Patarapaiboolchai and Jatuporn Jaiboon

  436 OC08 by Juliana Jumal , Jalifah

  Latip and Bohari M Yamin

  439

  International Conference on Mathematics and Natural Sciences (ICMNS) November 29-30, 2006, Bandung-Indonesia

   by Endah P. Handayani and Ayda T. Yusuf

   Fitria Yulyanti and Ayda T. Yusuf

  PB21 Marselina I. Tan, Dewi S.

   by Deasy Sartika

  Rachmawati

  357 PB23

   Fenny Martha Dwivany and Karlia Meitha

  361 PB25

  

Didot Budi Prasetyo and Tjandra Anggraeni

  365 PB26 Fenny M.

  Dwivany, Sony Suhandono, Listya Utami Karmawan and Arif R. Sadjuri

  369 PB28

  273 PB29 by Dian Rosleine, Devi N.

  393 PB37

  Choesin and Endah Sulistyawati

  378 PB30

  

by Y. Satitiningrum, D.I. Astuti and

N.Juli

  381 PB33 by Arlyna B. Pustika and Niniek K.

  Wardhani

  385 PB35

  

Tati S. S. Subahar, Avni

Khairunnisa, Tami Idiyanti, and Pingkan Aditiawati

  389 PB36

   Yadi Haryadi and I Nyoman Pugeg Aryantha

B. Prijamboedi

  OC09

  Rosyidah, Djulia Onggoa, Khairurrijal and Ismunandar

  

  

  

  

  

  

  

  

  

  by Atiek Rostika Noviyanti and Ismunandar 506

  PC04 Afifah

  511 PC05 Galuh

  501 PC03

  Yuliani and Cynthia L. Radiman

  515 PC10 Sundari Wirasmi and

  Ismunandar

  519 PC11 Amilia Linggawati, Abdul Wahab

  Mohammad and Zulkafli Gazali

  523 PC12

  

Deana Wahyuningrum, Sadijah

Achmad, Wiwin Widaningsih, Bambang Ariwahjoedi and Anna Permanasari

  527 PC14

   by Randi

  Rohandi and I Made Arcana

  532

  

  

by Sahidin, Euis H. Hakim, Lia D. Juliawaty, Yana M. Syah,

Jalifah Latip, Laily B. Din, Emilio L. Ghisalberti and Sjamsul A. Achmad

   Noor Azilah Mohd Kasim and Bohari M Yamin

  471 OC22

  444 OC11

  

Karimah Kassim, Hadariah Bahrona, Sharifah Rohaiza Syed Omara and

Bohari M.Yaminb

  447 OC12

   Damris muhammad

  452 OC14

   Yossi Kemal, Enny Ratnaningsih and Sadijah Achmad

  456 OC15 S. Soepriyanto

  and T. Hidayat

  460 OC16 Hadariah Bahron, Karimah Kassim, S. Rohaiza S. Omar and Yong S.K.

  465 OC17

  

by Yonan Nurgaman , Rukman Hertadi, and

Muhamad A. Martoprawiro

   Indra Noviandri and Wahono

  498 OC34

  475 OC23

  Rahmat Gunawan , Muhamad A. Martoprawiro, and Cynthia L. Radiman

  478 OC24

  

by Ira Handayani, M. Abdulkadir Martoprawiro, Akhmaloka and

Fida M. Warganegara

  482 OC25

   by Anne Carolina, Akhmaloka and Fida M. Warganegara

  487 OC26

  y Anna Roosdiana, Diah Mardiana, Tutik Setianingsih and Suratmo

  491 OC30

  Irani Ruth Julita, Akhmaloka and Fida M. Warganegara

  494 OC33 by Iqbal Musthapa,

  

Euis H. Hakim, Yana M. Syah, Lia D. Juliawaty, Sjamsul A. Achmad, Lukman Makmur,

and Jalifah Latip

  International Conference on Mathematics and Natural Sciences (ICMNS) November 29-30, 2006, Bandung-Indonesia PC15

   Lenggana and I Made Arcana

   by Dessy Natalia, Akhlis Nursetiadi, Anisa Ur Rahmah, Rizky Darmawan, Bambang Ariwahjoedi and Muliawati Sindumarta

  Martoprawiro and Dieter Ziessow

  584 PC32 Arie Srihardyastutie, Anna

  Roosdiana and Suratmo

  588 PC33

   Jaslin Ikhsan, Endang Widjajanti LFX and Sunarto

  593 PC34

   Haryoto Saroyobudiyono, Euis H. Hakim1, Yana M. Syah, Sjamsul A. Achmad, Lia D. Juliawaty and Jalifah Latip

  597 PC35 by Muhtadi, Euis H. Hakim, Yana M. Syah, Lia D.

  Juliawaty, Sjamsul A. Achmad, Ikram M. Said, Laily bin Din dan Jalifah Latip

  604 PC36

  609 PC37 by Ferlinahayati, Euis

  579 PC31

  H. Hakim, Yana M. Syah, Lia D. Juliawaty, Sjamsul A. Achmad, Lukman Makmur, Jalifah Latif

  612 PC38 by

  Fanni Mayasari and Cynthia Linaya Radiman

  616 PC39 by

  Mohammad Masykuri, Cynthia L. Radiman, I Made Arcana and Sadijah Achmad

  620 PC41 by Y. Sunarya, C. L. Radiman, S.

  Achmad, B. Bundjali and B. Ariewahyoedi

  623 PC42

   Muhammad Iqbal and Muhammad Bachri Amran

  627

   Parsaoran Siahaan, Cynthia L. Radiman, Susanto Imam Rahayu, Muhamad A.

   Sadijah Achmad, Cynthia L. Radiman, Bambang Ariwahjoedi and Noerati PC43

  535 PC16

   by Ahmed Almehdi and Nadeya Hosani

   Widya Febrina and Cynthia Linaya Radiman

  539 PC17

   by Rachmawati and Cynthia Linaya Radiman

  543 PC18 Edi

  Pramono and Cynthia L. Radiman

  547 PC19

   Fahimah Martak, Djulia Onggo, Ismunandar, Agung Nugroho, Bohari M. Yamin, Mustaffa Abdullah and Abd Rahim Yacob

  551 PC21 Noerati, C. L.

  Radiman, S. Achmad and B. Ariwahjoedi

  560 PC23

  564 PC24

  575 PC30

   by Waluyo, Parouli M. Pakpahan, Suwarno and Bambang Anggoro

  567 PC25

  

  

  

  

  

  

  

Iis Siti Jahro, Djulia Onggo, Ismunandar, Susanto Imam Rahayu and J. Antonio Real

  571 PC28 by Lia Amelia

  and I Made Arcana

  International Conference on Mathematics and Natural Sciences (ICMNS) November 29-30, 2006, Bandung-Indonesia

  Alfarius Eko Nugroho, Lia Dewi Juliawaty, Euis Holisotan Hakim, Yana Maolana Syah, Sjamsul Arifin Achmad, Lukman Makmur and Jalifah Latip

  695 OD15 by Maman A. Djauhari and Rian F. Umbara 700 OD17

  668 OD01 Eko Nugroho 672 OD06

  Novriana Sumarti

  676 OD09 Mohd.Najib Md.Salleh,

  Patrice Boursier and Christophe Demko

  681 OD10 by Nur Azman Abu, Shahrin Sahib and Nanna Suryana 686 OD11

   Roselina Sallehuddin, Siti Mariyam Shamsuddin and Mohd Shukor Talib

  691 OD14 by Mohd

  Salleh Sahimi Bin Mohamed, Amna Abdurrahman, Ahmad Kamal Bin Zulkifle and Ishak Hashim

   A.K. Supriatna and Edy Soewono

  665 PC58

  704 OD20 by N.

  Nuraini, E. Soewono and KA. Sidarto

  709 OD21

  Arief Hariyant and Gerhard Regner

  714 OD24 Lucyantie

  Mazalan, Jamilin Jais, NoorSalizaMohd Salleh, Roslan Ismail, Salman Yussof, Azhana Ahmad, Adzly Anuar and Dzulkifli Mohamad

  718 OD25

  Sutawanir Darwis (sdarwis@math.itb.ac.id), Ali Ashat, Sri Wahyuni, Nurtiti Sunusi and

  723

   by Edi Priyo Utomo, Warsito, Wahyu Widoretno and Yeny Diah Rahmawati

   by Warsito, M. Farid Rahman. Edi Priyo Utomo and Firda Amalia Maslakah.

  630 PC44 by Arba’at Hassan and

  La Kilo and Ismunandar

  Maimunah Sokro

  632 PC45

   by Eli Rohaeti, Suharto, Susila Kristianingrum and Crys Fajar Partana

  639 PC46

  

   Emiliana Arni Ardiyanti and

  Ismunandar

  643 PC47 Akram

  646 PC48 Johnson Siallagan, Euis H. Hakim, Yana M. Syah, Lia D.

  662 PC57

  Juliawaty, Sjamsul A. Achmad, Lukman Makmur, Ikram M. Said, Laily bin Din and Jalifah Latip

  648 PC50

  Yonan Nurgaman , Rukman Hertadi, and Muhamad A. Martoprawiro

  651 PC51 by Heni Imaniarti,

  Dina Livia and Erfin Yundra Febrianto

  655 PC54

  Abdul Haris Watoni , Suryo Gandasasmita, Indra Noviandri, and Buchari

  659 PC55

   by Fariati, Nugrahaningsih, Evi Susanti and Yudi Utomo

  International Conference on Mathematics and Natural Sciences (ICMNS) November 29-30, 2006, Bandung-Indonesia

  Jonathan W

  and Dani Gustaman Syarif

  789 PD11 by Sri Wahyuningsih, Sutawanir Darwis, Udjianna

  S. Pasaribu, A.Y Gunawan and M.A. Ashat

  793 PD12

   Wirawan and Rahmat Hidayat

  797 PD14

   by John Maspupu

  801 OE01

   by Marzuki, Wizri Yasir, Toshiaki Kozu and Toyoshi Shimomai

  804 OE05 by Wiendartun

  809 OE07

  781 PD06 Sangadji and Ngarap Im. Manik 785 PD09

  

  

Dwi Asmi, Fitri Rahmawati, Sunyono and Muhammad Badaruddin

  814 OE08

   Estevanus Kristian Huliselan and Satria Bijaksana

  819 OE09 by S. W. Harun and H. Ahmad

  823 OE10 by Frank Freykamp and Jessica

  Rubart

  826 OE11

   by Uda Hashim, Sutikno and Z.A.Z. Jamal

  830

   Khoirin Nisa, Netti Herawati, Eri Setiawan and Nusyirwan

   by Nurdin, A. N. M. Salman and E. T. Baskoro

  OD26 by Edi

  748 OD37 S.R.

  Cahyono, Arman, David Taniar and J. Wenny Rahayu

  726 OD28 F. Adi-

  Kusumoa and J.M. Tuwankotta

  731 OD30 by Agus Maman Abadi, Subanar, Widodo and

  Samsubar Saleh

  736 OD31 Miswanto, Iwan

  Pranoto and Hari Muhammad

  740 OD35 by Anati Ali, Norsarahaida Amin and Ioan Pop

  743 OD36 by Dwi Astuti Aprijani

  Pudjaprasetya

  778 PD05

  752 OD38 by Sugih S. Tjandra

  and S.R. Pudjaprasetya

  756 OD42 Nunung and Udjianna S

  Pasaribu

  760 OD44 by Erna Tri Herdiani 765 PD01

  Mohamad Shukor Talib, Haswadi Hassan and Nor Shahida Binti Abi Khallad

  769 PD03

  Karyati and Sri Wahyuni

  774 PD04 R. Heru Tjahjana, I. Pranoto, H. Muhammad and J.

  Naiborhu

  International Conference on Mathematics and Natural Sciences (ICMNS) November 29-30, 2006, Bandung-Indonesia

  International Conference on Mathematics and Natural Sciences (ICMNS) November 29-30, 2006, Bandung-Indonesia

  907 OE38 by Endang W.

   M. Hamzah Fauzi, Juli Cha Tarido, Rizal Kurniadi and Yudi Darma

  885 OE32

  Akhmad Yulianto, M. Ginanjar Azie, Khairurrijal, Rizal Kurniadi and Yudi Darma

  889 OE33 Bambang Heru

  Iswanto and Klaus Obermayer

  893 OE34

   by Tulus Ikhsan Nasution, Zaliman Bin

  Sauli and Ramli Omar

  898 OE35

  

by Alexander A. Iskandar, Muldarisnur, Agoes Soehianie

and M.O. Tjia

  902 OE36 H. Hardhienata, T. P. Negara, B.

  Sulistiyo, H. Mayditia and H. Alatas

  Laksono, AK. Prodjosantoso and Jaslin Ikhsan

  by Khairul Basar, Takashi Sakuma and Evvy Kartini 881

  912 OE39

   Triyanta, A. Y. Wardaya, F. P. Zen and J. S. Kosasih

  916 OE40

  

  

  

  by

  Mohammad Ihsan, Evvy Kartini, Supandi Suminta and Mardiyanto

  920 OE44

  

   E.Kartini, M.Nakamura, M.Arai, Y.Inamuar and J.W.Taylor

  925

  OE31

  

  OE12

  855 OE22

   by Husin Alatas

  835 OE16

  

by Asep Suhendi, Muhammad M. Munir, Hernawan Mahfudz,

Mikrajuddin Abdullah and Khairurrijal

  839 OE17

   by Rusminto

  Tjatur Widodo And Norio Terada

  842 OE18

   by Wahyu Tri Cahyanto, Kamsul Abraha and Pekik Nurwantoro

  847 OE19 by Muhammad

  Irvan and Satria Bijaksana

  851 OE20 by Bobby E.

  Gunara, Freddy P. Zen and Arianto

  

by Pekik Nurwantoro,Agung Bambang Setio Utomo and

Ahmad Ashari

  

  859 OE23 by I. Fathrio

  and D. Sutarno

  862 OE24

   by Harry Mahardika, Alamta Singarimbun, Adhitya Sumardi Sunarya and Wahyu Srigutomo

  866 OE26

  

Mahardika Prasetya Aji, Agus Yulianto and Satria

Bijaksana

  870 OE28

   S. Riyadi, Muafif, A. A. Nugroho, N. Mufti and M. O. Tjia

  873 OE29 by

  Arianto, Freddy P. Zen and Bobby E. Gunara

  877 OE30

  

  

OE45

   Topan Setiadipura and Utaja

  991 PE09

  977 PE01 by Asep Suhendi,

  Muhammad M. Munir, Mikrajuddin Abdullah and Khairurrijal

  981 PE02 A.Soehianie,

  A.R.J. Silalahi and A.A. Iskandar

  984 PE04

   Iis Nurhasanah, Khairurrijal, Mikrajuddin Abdullah, Maman Budiman and Sukirno

  988 PE06

   by Tri Fatirahman, Ahmad Ridwan, Khairurrijal, Rizal Kurniadi and Yudi Darma

   Karyono, Utomo Y.R. , Guntur Maruto, Agung BSU and Ikhsan Setiawan

  969 OE59 Jorga Ibrahim 973 OE60

  995 PE11

   by Rena Widita

  1000 PE12

   by Afnidar, Amril Latif, Musa Ahmad and Lee Yook Heng

  1004 PE13

   Mike Susmikanti

  1009 PE14

   Mike Susmikanti and Arya Adhiyaksa

  1014

   Agus Purwanto, Maxim Dvornikov and Takuya Morozumi

   Rahmat Hidayat, Waode Sukmawati, Wilzuard Yonan, Okihiro Sugihara and Toshikuni Kaino PE15

  929 OE46

  945 OE51

   Heri Sutanto, Agus Subagio, Horasdia Saragih, Edy Supriyanto, Pepen Arifin, Maman Budiman, Sukirno and Moehamad Barmawi

  1

  932 OE47 by

  Muldarisnur, A.A. Iskandar, A. Soehianie and M.O Tjia

  936 OE48

   Adi Bagus Suryamas, Mikrajuddin Abdullah and Khairurrijal

  941 OE49

   T. Winata, I. Usman, Mursal, Sukirno and M.

  Barmawi

   Lilik Hasanah, Khairurrijal,

  965 OE58

  Mikrajuddin Abdullah, Toto Winata and Sukirno

  949 OE52 Agus Yulianto, Satria Bijaksana, Waloejo

  Loeksmanto and Daniel Kurnia

  954 OE53

   by Idam Arif and Ratnawulan

  957 OE54 by

  Akhmad A. Korda, Y. Mutoh, Y. Miyashita and T. Sadasue

  961 OE55 Wahyu Srigutomo,

  Imran Hilman Mohammad, Enjang Jaenal Mustopa and Doddy Sutarno

  International Conference on Mathematics and Natural Sciences (ICMNS) November 29-30, 2006, Bandung-Indonesia

   Alfi Rachman and Freddy Haryanto

  1091 PE52

  1075 PE44

   by Mitra Djamal, Wulan Anggraeni, Akfiny Hasdi Aimon, Habibullah Akbar and Yulkifli

  1078 PE45

   Mitra Djamal, Akfiny Hasdi Aimon, Wulan Anggraeni, Habibullah Akbar dan Yulkifli

  1082 PE46

   Purwati, Roto and Kuwat Triyana

  1086 PE50

   Edy Supriyanto, Iis Nurhasanah, Agus Subagio, Horasdia Saragih, Heri Sutanto,Pepen Arifin,Maman Budiman, Sukirno and Moehammad Barmawi

  Waode Sukmawati, Wilzuard Yonan, Herman, Rahmat Hidayat and Tjia May On

  Widhya Budiawan, Mikrajuddin Abdullah, Khairurrijal, Leni Marlina and Aunuddin S. Vioktalamo

  1095 PE54 by Mitra

  Djamal and Rahmondia Nanda Setiadi

  1099 PE55 by Mitra

  Djamal and Rahmondia Nanda Setiadi

  1103 PE59

   by Supandi Suminta, Evvy Kartini, Mardiyanto and Wisnu Ari Adi

  1107

  International Conference on Mathematics and Natural Sciences (ICMNS) November 29-30, 2006, Bandung-Indonesia

  1069 PE40 by A. Mostavan and Afghany M 1073 PE43 by Y.E. Gunanto,

  1060 PE35 Lily Suparlina 1065 PE37

  1019 PE16 by S.

  Triyana, Ari Dwi Nugraheni, Ahmad Kusumaatmaja, Chotimah and Harsojo

  Feranie, Y. R. Tayubi, S. Karim, A. Suhandi, D. Rusdiana and P. Arifin

  1022 PE17

  Arif Surachman, Asep Suhendi, Muhammad M. Munir and Khairurrijal

  1026 PE23 by B.

  Setiawan

  1029 PE26

   Prasandhya Astagiri Yusuf, Siti Nurul Khotimah and Ratna Anggraeni Agustian

  1033 PE28 by Kuwat

  1037 PE29

  Hamzah

   Gunawan Handayani

  1041 PE30 by A.

  Subagio, H. Sutanto, E. Supriyanto, M. Budiman, P. Arifin, Sukirno and M. Barmawi

  1045 PE31

   Endiah Puji Hastuti

  1048 PE32 by Tukiran S. and Surian P.

  1052 PE33

  Surian Pinem and Tagor Malem Sembiring

  1056 PE34 Amir

A. Purwanto, B. Kurniawan, A.Fajar and H.Mugirahardjo

  PE60

  Denny Mandey and Putra Mahasena

  1156 PF02 by Sri Wahyu Cahya Ningsih,

  S.Si, Hakim Luthfi Malasan and Taufiq Hidayat

  1160 PF03 A. Yamani, R. Satyaningsih, T.

  Hidayat, I. Radiman, B. Dermawan and S. Siregar

  1164 PF04 by R.

  Satyaningsih, B. Dermawan, T. Hidayat, S. Siregar, I. Radiman and A. Yamani

  1168 PF05

   Hendro Setyanto and Taufiq Hidayat

  1172 PF06

  

Clara Y. Yatini, Mamat Ruhimat and

Jiyo

  1176 PF07

  1180 PF08

  1151 PF01

  Nur Hasanah and Putra Mahasena

  1184 PF09

   by Puji Irawati and Putra Mahasena

  1188 PF10 by M. L. A. Ginanjar and P. Mahasena

  1192 PF11 by F. Maulana, P. Mahasena, B. Dermawan, H. L. Malasan, T.

  Hidayat, E. Senawardhana, P. I. Siregar and J. Qithri

  1196 PF12

  

by Dading H. Nugroho,

Hakim L. Malasan, Desima Kristyowati and Evan I. Akbar

  1200 PF13

   by Deasy Tresnoningrum and Dhani Herdiwijaya

  1204

   Bambang Setiahadi

  and Moedji Raharto

  M. Diantoro and A. Purwanto

  

  1111 OF01

   Desima Kristyowati, Hakim L. Malasan and Hanindyo Kuncarayakti

  1114 OF02

  

  

Fathonah D. Rahayu and Hakim L. Malasan

  1118 OF03 D.N. Dawanas, A.

  Wardana and H.L. Malasan

  1122 OF04

  

  

  

  by S.Siregar and D. Hadi Nugroho 1126

  1148 OF12 Hepi Irfianni Sofian

  OF05

   by Bambang Setiahadi

  1130 OF06 by Iratius Radiman, Suhardja D. Wiramihardja and Mochamad Irfan

  1135 OF07 Anwar, R., Andarto, F.T., Malasan, H.L., Hidayat, T. and Putra, M.

  1

  1138 OF08

  Dhani Herdiwijaya

  1141 OF09 by B. Dermawan, K.

  Kinugasa, H. Taguchi and O. Hashimoto

  1144 OF10

   G. I. Prasetyono, H. L. Malasan and C. Kunjaya

  International Conference on Mathematics and Natural Sciences (ICMNS) November 29-30, 2006, Bandung-Indonesia PF14

   Emanuel Sungging Mumpuni, Dhani Herdiwidjaja and Rasdewita Kesumaningrum

  1277 OG08

  1255 OG02

  U. Fauzi and T. Ariwibowo

  1260 OG04 by Khumaedi

  Sastrawiharja, Satria Bijaksana, Umar Fauzi and Linus Ampang Pasasa

  1264 OG05

   Muhammad Syukri, Faisal and Md Noordin Abu Bakar

  1268 OG06

  Armi Susandi, Budi Setio Prasanto, Safwan Hadi, Totok Suprijo and Genia Atma Nagara

  1273 OG07

   by Sarmoko Saroso

  Asep Harja, Wahyu Srigutomo and Doddy Sutarno

  1252 OG01

  1281 OG09 by Enjang Jaenal Mustopa

  1284 OG10

   Suaydhi

  1289 PG01 by

  Juniarti Visa

  1293 PG02

  Jalu Tejo Nugroho and Clara Yono Yatini

  1298 PG03 by

  Habirun

  1301

   Sismanto

  Raharto and Oki Neswan

  1207 PF15 J. Aria Utama , Dading H. Nugroho, M.

  1221 PF20 by H. Kuncarayakti, D. Kristyowati, D.

  Irfan and D. Mandey

  1210 PF17 Mochamad Ikbal Arifyanto 1213 PF18 by

  Endang Soegiartini, Iratius Radiman and Emanuel Sungging Mumpuni

  1217 PF19

  

  

  

  

  

   Rukman Nugraha and S. Siregar

  Mandey and M. L. A. Ginanjar

  1245 PF29 by Bachtiar Anwar 1248 PF30 Zainal Abidin, Moedji

  1225 PF21 by Retno Pujijayanti, Chatief Kunjaya, Hakim Luthfi Malasan, Stephen Dawni Nugraha

  and Desima Kristyowati

  1228 PF22 Dhani Herdiwijaya, Zadrach L. Dupe, Endang Soegiartini and E. Sungging M.

  1231 PF24 by S. D. Wiramihardja, M. Raharto, T.

  Laksmana, S. Prianto, S. W. C. Ningsih, M. Irfan, A. S. Maryam and M. I. Arifyanto

  1234 PF26

  

   Riser Fahdiran and Hakim L.

  Malasan

  1237 PF27 Moedji Raharto 1240 PF28 by Mochamad

  Irfan, Denny Mandey and Hanindyo Kuncarayakti

  International Conference on Mathematics and Natural Sciences (ICMNS) November 29-30, 2006, Bandung-Indonesia

  

International Conference on Mathematics and Natural Sciences (ICMNS)

November 29-30, 2006, Bandung-Indonesia

  PG05 Mumen Tarigan 1305 PG06 1309 by Nurtiti Sunusi, Sutawanir Darwis and Udjianna S. P PG07 1313

   Laras Tursilowati

  PG08 by Laras Tursilowati and 1318

  Mulyana Wirasasmita

  PG09 1324

   Suaydhi

  PG10 Sarmoko Saroso 1328 PG11 Armi 1332

  Susandi

  PG12 1336

   by Rahmat Gernowo, Bayong Tj. H.K., The H.L., Tri Wahyu Hadi and Ina Juaeni

  PG13 Bangun 1340 Baramantyono and Bayong Tjasyono H.K. PG14 1343 by Supeno MT PG15 1347

   by Eddy Hermawan

  PG17 1350

   Eddy Hermawan

  PG18 1354

  

  by U. Fauzi and I. Hamzah OH03 1358

   by Zulkardi and Sutarto Hadi

  OH04 Siti M. Amin 1362 OH06 Rita Desfitri 1365 OH07 Max Stephens 1370 PH06 A Mostavan and Afghany M 1375 PA04 by 1378

  Faizatun, Heni Rachmawati, Sukmadjaja Asyarie

  PA05 by 1383

  Hestiary Ratih, Heni Rachmawati, Sundani Nurono

  Robust Principal Component Analysis Using Minimum Covariance Determinant Estimator Khoirin Nisa

  1 , Netti Herawati

  1 , Eri Setiawan

  1 , Nusyirwan

  1

1 Department of Mathematics, Faculty Of Mathematics and Natural Sciences, Lampung University

  Jl. Prof. Dr. Soemantri Brojonegoro No.1 Bandar Lampung 35145 Abstract

  Principal component analysis (PCA) is one of the most widely used statistical techniques for data dimension reduction. And a robust technique on PCA when data contains outlier is an important problem. In this paper, we consider the problem of robust PCA based on Minimum Covariance Determinant (MCD) mean and covariance matrix estimator. We aimed to look at the behavior of the principal component scores of robust PCA using MCD through their graphical plot of the first and the second PCS. The effect of outliers on PCA is studied by comparing the mean square error (MSE) resulted by MCD and by classical method in presence of outliers.

  Keywords

  : Robust, principal component analysis, minimum covariance determinant

  International Conference on Mathematics and Natural Sciences (ICMNS) November 29-30, 2006, Bandung-Indonesia

I. Introduction

  Cov(x) = Σ. The covariance matrix can be decomposed as Σ = ΓΛΓ

  as well as S are highly sensitive with respect to outlying observations. Therefore, data reduction based on classical PCA becomes unreliable if outliers are present in the data. A robust version of principal component analysis is needed.

  Principal component analysis (PCA) is a popular statistical method which tries to explain the covariance structure of data by means of a small number of components. The main use of PCA is to reduce the dimensionality of a data set while retaining as much information as is possible. In essence, PCA seeks to reduce the dimension of the data by finding a few orthogonal linear combinations (the PCs) of the original variables with the largest variance. The first PC is the linear combination with the largest variance, the second PC is the linear combination with the second largest variance and orthogonal to the first PC, and so on. There can be as many possible PCs as there are variables.

  789

  Computation of PCs is based on a decomposition of covariance matrices. Let x be a

  is the number of variables. Since in general we cannot consider all h-subsets, we must rely on approximate algorithms. Rousseeuw and Van Driessen (1999) proposed a hybrid algorithm which they called the FAST-MCD. The algorithm can be described as follows:

  h = (n + p + 1)/2, where n is the sample size and p