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Research Article
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Introduction and Applicability of Nonlinear Principal Components Analysis

Year 2021, Volume: 24 Issue: 2, 442 - 450, 30.04.2021

Yıldırım Demir , Sıddık Keskin , Şeyda Çavuşoğlu

https://doi.org/10.18016/ksutarimdoga.vi.770817
Cited By: 4

Abstract

Nonlinear principal component analysis (NLPCA) is a descriptive dimension reduction method that examines the relationships between variables and displays the results numerically and visually in multivariate datasets that have a linear or nonlinear relationship between them. In this study, it was aimed to present the basic explanatory information about nonlinear principal components analysis (NLPCA) and to emphasize its usability by performing application. In the study, data obtained from 270 samples for 17 continuous variables concerning 3 pepper varieties were evaluated by Principal components analysis (PCA). With the 4 principal components obtained as a result of PCA, being 3 categorical variables Variety, storage time and Application were analyzed by NLPCA. In the analysis made with PCA, approximately 74% of the total variance was explained and in the analysis made with NLPCA, approximately 58% was explained as well. As a result of the analysis; it was observed that there was a strong relationship between PC1 and storage time and variety, and PC3 and PC2 variables, while the relationship between PC4 and application variables and all variables was low. As a result; by examining the linear and nonlinear relationships between the variables in the multivariate datasets, these relationships intended to be presented in an easily interpreted and easily understandable way in two-dimensional space; it was emphasized that NLPCA can be used alone and/or together with other multivariate analysis methods.

Keywords

Dimension reduction Optimal scaling Eigenvalue SOD MDA

References

  • Demir C 2010. Doğrusal Olmayan Temel Bileşenler Analizi ve Sağlık Alanında Uygulaması. Yüzüncü Yıl Üniversitesi Sağlik Bilimleri Enstitüsü Biyoistatistik ve Tıp Bilişimi Anabilim Dalı, Yüksek Lisans Tezi, 55 sy.
  • Demir C 2010. Doğrusal Olmayan Temel Bileşenler Analizi ve Sağlık Alanında Uygulaması. Yüzüncü Yıl Üniversitesi Sağlik Bilimleri Enstitüsü Biyoistatistik ve Tıp Bilişimi Anabilim Dalı, Yüksek Lisans Tezi, 55 sy.
  • Demir Y, Esenbuğa N, Bilgin ÖC 2016. İvesi Koyunlarının Et Kalitesini Değerlendirmede Temel Bileşenler Analizinin (PCA) Kullanılması. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 20(3): 536‐541.
  • Demir Y, Esenbuğa N, Bilgin ÖC 2016. İvesi Koyunlarının Et Kalitesini Değerlendirmede Temel Bileşenler Analizinin (PCA) Kullanılması. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 20(3): 536‐541.
  • Gifi A 1990. Nonlinear Multivariate Analysis. John Wiley & Sons, New York, 579 sy.
  • Gifi A 1990. Nonlinear Multivariate Analysis. John Wiley & Sons, New York, 579 sy.
  • Güç K 2015. Türkiye’de Resmi Kurumlara Duyulan Güvenin Kategorik Regresyon ve Lojistik Regresyon Analizi İle İncelenmesi. Gazi Üniversitesi Fen Bilimleri Enstitüsü İstatistik Anabilim Dalı, Yüksek Lisans Tezi, 75 sy.
  • Güç K 2015. Türkiye’de Resmi Kurumlara Duyulan Güvenin Kategorik Regresyon ve Lojistik Regresyon Analizi İle İncelenmesi. Gazi Üniversitesi Fen Bilimleri Enstitüsü İstatistik Anabilim Dalı, Yüksek Lisans Tezi, 75 sy.
  • IBM SPSS 2011. IBM SPSS Statistics 20 Algorithms. IBM, Inc., New York, 1069 sy.
  • IBM SPSS 2011. IBM SPSS Statistics 20 Algorithms. IBM, Inc., New York, 1069 sy.
  • Jolliffe IT 1986. Principal Component Analysis. Springer-Verlag, New York, 487 sy.
  • Jolliffe IT 1986. Principal Component Analysis. Springer-Verlag, New York, 487 sy.
  • Kapucu T 2016. The Effect of Computer Assisted Instruction On Eight Grade Students’ Permutation-Combination-Probability Achievement And Attitudes Towards Computer Assisted Instruction. Middle East Technical University The Graduate School of Natural And Applied Sciences Statistics Department, Master Thesis, 161 sy.
  • Kapucu T 2016. The Effect of Computer Assisted Instruction On Eight Grade Students’ Permutation-Combination-Probability Achievement And Attitudes Towards Computer Assisted Instruction. Middle East Technical University The Graduate School of Natural And Applied Sciences Statistics Department, Master Thesis, 161 sy.
  • Karaman E 2019. Optimal Ölçekleme Teknikleri ve Bir Uygulama. İstanbul Üniversitesi Sosyal Bilimleri Enstitüsü İşletme Anabilim Dalı, Doktora Tezi, 108 sy.
  • Karaman E 2019. Optimal Ölçekleme Teknikleri ve Bir Uygulama. İstanbul Üniversitesi Sosyal Bilimleri Enstitüsü İşletme Anabilim Dalı, Doktora Tezi, 108 sy.
  • Keskin S 2002. Varyansların Homojenliğini Test Etmede Kullanılan Bazı Yöntemlerin I. Tip Hata ve Testin Gücü Bakımından İrdelenmesi. Ankara Üniversitesi Fen Bilimleri Enstitüsü Zootekni Anabilim Dalı, Doktora Tezi, 210 sy.
  • Keskin S 2002. Varyansların Homojenliğini Test Etmede Kullanılan Bazı Yöntemlerin I. Tip Hata ve Testin Gücü Bakımından İrdelenmesi. Ankara Üniversitesi Fen Bilimleri Enstitüsü Zootekni Anabilim Dalı, Doktora Tezi, 210 sy.
  • Kramer MA 1991. Nonlinear Principal Component Analysis Using Auto-Associative Neural Networks. AIChE Journal 37(2): 233-43.
  • Kramer MA 1991. Nonlinear Principal Component Analysis Using Auto-Associative Neural Networks. AIChE Journal 37(2): 233-43.
  • Linting M, Meulman JJ, Groenen PJF, Van der Kooij AJ 2007. Nonlinear Principal Components Analysis: Introduction and Application. Psychological Methods 12(3): 336-358.
  • Linting M, Meulman JJ, Groenen PJF, Van der Kooij AJ 2007. Nonlinear Principal Components Analysis: Introduction and Application. Psychological Methods 12(3): 336-358.
  • Mair P, De Leeuw J 2010. A General Framework for Multivariate Analysis with Optimal Scaling: The R Package Aspect, Journal of Statistical Software 32(9): 1-23.
  • Mair P, De Leeuw J 2010. A General Framework for Multivariate Analysis with Optimal Scaling: The R Package Aspect, Journal of Statistical Software 32(9): 1-23.
  • Meulman JJ, Heiser WJ 2011. IBM SPSS Categories 20, SPSS Inc., USA, 313 sy.
  • Meulman JJ, Heiser WJ 2011. IBM SPSS Categories 20, SPSS Inc., USA, 313 sy.
  • Meulman JJ, Van der Kooij AJ, Heiser WJ 2004. Principal Components Analysis with Nonlinear Optimal Scaling Transformations for Ordinal And Nominal Data. (The Sage Handbook of Quantitative Methodology for the Social Sciences, UK: Ed. Kaplan D) 49-70.
  • Meulman JJ, Van der Kooij AJ, Heiser WJ 2004. Principal Components Analysis with Nonlinear Optimal Scaling Transformations for Ordinal And Nominal Data. (The Sage Handbook of Quantitative Methodology for the Social Sciences, UK: Ed. Kaplan D) 49-70.
  • Michailidis G, De Leeuw J 1998. The Gifi System of Descriptive Multivariate Analysis. Statistical Science 13(4): 307-336.
  • Michailidis G, De Leeuw J 1998. The Gifi System of Descriptive Multivariate Analysis. Statistical Science 13(4): 307-336.
  • Mori Y, Kuroda M, Makino N 2016. Nonlinear Principal Component Analysis and Its Applications. Springer Nature, Singapore, 80 sy.
  • Mori Y, Kuroda M, Makino N 2016. Nonlinear Principal Component Analysis and Its Applications. Springer Nature, Singapore, 80 sy.
  • Özdamar K 2010. Paket Programlar ile İstatistiksel Veri Analizi-2 (Çok Değişkenli Analizler). Kaan Kitapevi, Eskişehir, 506 sy.
  • Özdamar K 2010. Paket Programlar ile İstatistiksel Veri Analizi-2 (Çok Değişkenli Analizler). Kaan Kitapevi, Eskişehir, 506 sy.

Doğrusal Olmayan Temel Bileşenler Analizinin Tanıtımı ve Uygulanabilirliği

Year 2021, Volume: 24 Issue: 2, 442 - 450, 30.04.2021

Yıldırım Demir , Sıddık Keskin , Şeyda Çavuşoğlu

https://doi.org/10.18016/ksutarimdoga.vi.770817
Cited By: 4

Abstract

Nonlinear principal component analysis (NLPCA) is a descriptive dimension reduction method that examines the relationships between variables and displays the results numerically and visually in multivariate datasets that have a linear or nonlinear relationship between them. In this study, it was aimed to present the basic explanatory information about nonlinear principal components analysis (NLPCA) and to emphasize its usability by performing application. In the study, data obtained from 270 samples for 17 continuous variables concerning 3 pepper varieties were evaluated by Principal components analysis (PCA). With the 4 principal components obtained as a result of PCA, being 3 categorical variables Variety, storage time and Application were analyzed by NLPCA. In the analysis made with PCA, approximately 74% of the total variance was explained and in the analysis made with NLPCA, approximately 58% was explained as well. As a result of the analysis; it was observed that there was a strong relationship between PC1 and storage time and variety, and PC3 and PC2 variables, while the relationship between PC4 and application variables and all variables was low. As a result; by examining the linear and nonlinear relationships between the variables in the multivariate datasets, these relationships intended to be presented in an easily interpreted and easily understandable way in two-dimensional space; it was emphasized that NLPCA can be used alone and/or together with other multivariate analysis methods.

Keywords

Boyut indirgeme MDA Optimal ölçekleme Özdeğer

References

  • Demir C 2010. Doğrusal Olmayan Temel Bileşenler Analizi ve Sağlık Alanında Uygulaması. Yüzüncü Yıl Üniversitesi Sağlik Bilimleri Enstitüsü Biyoistatistik ve Tıp Bilişimi Anabilim Dalı, Yüksek Lisans Tezi, 55 sy.
  • Demir C 2010. Doğrusal Olmayan Temel Bileşenler Analizi ve Sağlık Alanında Uygulaması. Yüzüncü Yıl Üniversitesi Sağlik Bilimleri Enstitüsü Biyoistatistik ve Tıp Bilişimi Anabilim Dalı, Yüksek Lisans Tezi, 55 sy.
  • Demir Y, Esenbuğa N, Bilgin ÖC 2016. İvesi Koyunlarının Et Kalitesini Değerlendirmede Temel Bileşenler Analizinin (PCA) Kullanılması. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 20(3): 536‐541.
  • Demir Y, Esenbuğa N, Bilgin ÖC 2016. İvesi Koyunlarının Et Kalitesini Değerlendirmede Temel Bileşenler Analizinin (PCA) Kullanılması. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 20(3): 536‐541.
  • Gifi A 1990. Nonlinear Multivariate Analysis. John Wiley & Sons, New York, 579 sy.
  • Gifi A 1990. Nonlinear Multivariate Analysis. John Wiley & Sons, New York, 579 sy.
  • Güç K 2015. Türkiye’de Resmi Kurumlara Duyulan Güvenin Kategorik Regresyon ve Lojistik Regresyon Analizi İle İncelenmesi. Gazi Üniversitesi Fen Bilimleri Enstitüsü İstatistik Anabilim Dalı, Yüksek Lisans Tezi, 75 sy.
  • Güç K 2015. Türkiye’de Resmi Kurumlara Duyulan Güvenin Kategorik Regresyon ve Lojistik Regresyon Analizi İle İncelenmesi. Gazi Üniversitesi Fen Bilimleri Enstitüsü İstatistik Anabilim Dalı, Yüksek Lisans Tezi, 75 sy.
  • IBM SPSS 2011. IBM SPSS Statistics 20 Algorithms. IBM, Inc., New York, 1069 sy.
  • IBM SPSS 2011. IBM SPSS Statistics 20 Algorithms. IBM, Inc., New York, 1069 sy.
  • Jolliffe IT 1986. Principal Component Analysis. Springer-Verlag, New York, 487 sy.
  • Jolliffe IT 1986. Principal Component Analysis. Springer-Verlag, New York, 487 sy.
  • Kapucu T 2016. The Effect of Computer Assisted Instruction On Eight Grade Students’ Permutation-Combination-Probability Achievement And Attitudes Towards Computer Assisted Instruction. Middle East Technical University The Graduate School of Natural And Applied Sciences Statistics Department, Master Thesis, 161 sy.
  • Kapucu T 2016. The Effect of Computer Assisted Instruction On Eight Grade Students’ Permutation-Combination-Probability Achievement And Attitudes Towards Computer Assisted Instruction. Middle East Technical University The Graduate School of Natural And Applied Sciences Statistics Department, Master Thesis, 161 sy.
  • Karaman E 2019. Optimal Ölçekleme Teknikleri ve Bir Uygulama. İstanbul Üniversitesi Sosyal Bilimleri Enstitüsü İşletme Anabilim Dalı, Doktora Tezi, 108 sy.
  • Karaman E 2019. Optimal Ölçekleme Teknikleri ve Bir Uygulama. İstanbul Üniversitesi Sosyal Bilimleri Enstitüsü İşletme Anabilim Dalı, Doktora Tezi, 108 sy.
  • Keskin S 2002. Varyansların Homojenliğini Test Etmede Kullanılan Bazı Yöntemlerin I. Tip Hata ve Testin Gücü Bakımından İrdelenmesi. Ankara Üniversitesi Fen Bilimleri Enstitüsü Zootekni Anabilim Dalı, Doktora Tezi, 210 sy.
  • Keskin S 2002. Varyansların Homojenliğini Test Etmede Kullanılan Bazı Yöntemlerin I. Tip Hata ve Testin Gücü Bakımından İrdelenmesi. Ankara Üniversitesi Fen Bilimleri Enstitüsü Zootekni Anabilim Dalı, Doktora Tezi, 210 sy.
  • Kramer MA 1991. Nonlinear Principal Component Analysis Using Auto-Associative Neural Networks. AIChE Journal 37(2): 233-43.
  • Kramer MA 1991. Nonlinear Principal Component Analysis Using Auto-Associative Neural Networks. AIChE Journal 37(2): 233-43.
  • Linting M, Meulman JJ, Groenen PJF, Van der Kooij AJ 2007. Nonlinear Principal Components Analysis: Introduction and Application. Psychological Methods 12(3): 336-358.
  • Linting M, Meulman JJ, Groenen PJF, Van der Kooij AJ 2007. Nonlinear Principal Components Analysis: Introduction and Application. Psychological Methods 12(3): 336-358.
  • Mair P, De Leeuw J 2010. A General Framework for Multivariate Analysis with Optimal Scaling: The R Package Aspect, Journal of Statistical Software 32(9): 1-23.
  • Mair P, De Leeuw J 2010. A General Framework for Multivariate Analysis with Optimal Scaling: The R Package Aspect, Journal of Statistical Software 32(9): 1-23.
  • Meulman JJ, Heiser WJ 2011. IBM SPSS Categories 20, SPSS Inc., USA, 313 sy.
  • Meulman JJ, Heiser WJ 2011. IBM SPSS Categories 20, SPSS Inc., USA, 313 sy.
  • Meulman JJ, Van der Kooij AJ, Heiser WJ 2004. Principal Components Analysis with Nonlinear Optimal Scaling Transformations for Ordinal And Nominal Data. (The Sage Handbook of Quantitative Methodology for the Social Sciences, UK: Ed. Kaplan D) 49-70.
  • Meulman JJ, Van der Kooij AJ, Heiser WJ 2004. Principal Components Analysis with Nonlinear Optimal Scaling Transformations for Ordinal And Nominal Data. (The Sage Handbook of Quantitative Methodology for the Social Sciences, UK: Ed. Kaplan D) 49-70.
  • Michailidis G, De Leeuw J 1998. The Gifi System of Descriptive Multivariate Analysis. Statistical Science 13(4): 307-336.
  • Michailidis G, De Leeuw J 1998. The Gifi System of Descriptive Multivariate Analysis. Statistical Science 13(4): 307-336.
  • Mori Y, Kuroda M, Makino N 2016. Nonlinear Principal Component Analysis and Its Applications. Springer Nature, Singapore, 80 sy.
  • Mori Y, Kuroda M, Makino N 2016. Nonlinear Principal Component Analysis and Its Applications. Springer Nature, Singapore, 80 sy.
  • Özdamar K 2010. Paket Programlar ile İstatistiksel Veri Analizi-2 (Çok Değişkenli Analizler). Kaan Kitapevi, Eskişehir, 506 sy.
  • Özdamar K 2010. Paket Programlar ile İstatistiksel Veri Analizi-2 (Çok Değişkenli Analizler). Kaan Kitapevi, Eskişehir, 506 sy.
There are 34 citations in total.

Details

Primary Language Turkish
Subjects Agricultural, Veterinary and Food Sciences
Journal Section RESEARCH ARTICLE
Authors

Yıldırım Demir 0000-0002-6350-8122

Sıddık Keskin 0000-0001-9355-6558

Şeyda Çavuşoğlu 0000-0001-8797-6687

Publication Date April 30, 2021
Submission Date July 17, 2020
Acceptance Date August 27, 2020
Published in Issue Year 2021 Volume: 24 Issue: 2

Cite

APA Demir, Y., Keskin, S., & Çavuşoğlu, Ş. (2021). Doğrusal Olmayan Temel Bileşenler Analizinin Tanıtımı ve Uygulanabilirliği. Kahramanmaraş Sütçü İmam Üniversitesi Tarım Ve Doğa Dergisi, 24(2), 442-450. https://doi.org/10.18016/ksutarimdoga.vi.770817

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