Determining The Number of Principal Components with Schur's Theorem in Principal Component Analysis

Cihan Karakuzulu; İbrahim Halil Gümüş; Serkan Güldal; Mustafa Yavaş

Makale detayları

Determining The Number of Principal Components with Schur's Theorem in Principal Component Analysis

Yazarlar:

Cihan Karakuzulu | İbrahim Halil Gümüş | Serkan Güldal | Mustafa Yavaş

Yayıncı:

Bitlis Eren University

Ana Başlıklar:

Engineering

Dergi:

Bitlis Eren Üniversitesi Fen Bilimleri Dergisi Vol.12 Issue 2, pp.299-306

Belge Tipi:

Makale

Yayın Tarihi:

6/2023

Belge Dili:

İngilizce

Document ID (Org No.):

2001292716

pISSN:

2147-3129

Anahtar kelimeler:

Özet:

 Principal Component Analysis is a method for reducing the dimensionality of datasets while also limiting information loss. It accomplishes this by producing uncorrelated variables that maximize variance one after the other. The accepted criterion for evaluating a Principal Components PC performance is λ_jtrS where trS denotes the trace of the covariance matrix S. It is standard procedure to determine how many PCs should be maintained using a predetermined percentage of the total variance. In this study, the diagonal elements of the covariance matrix are used instead of the eigenvalues to determine how many PCs need to be considered to obtain the defined threshold of the total variance. For this, an approach which uses one of the important theorems of majorization theory is proposed. Based on the tests, this approach lowers the computational costs.

 Principal Component Analysis is a method for reducing the dimensionality of datasets while also limiting information loss. It accomplishes this by producing uncorrelated variables that maximize variance one after the other. The accepted criterion for evaluating a Principal Components PC performance is λ_jtrS where trS denotes the trace of the covariance matrix S. It is standard procedure to determine how many PCs should be maintained using a predetermined percentage of the total variance. In this study, the diagonal elements of the covariance matrix are used instead of the eigenvalues to determine how many PCs need to be considered to obtain the defined threshold of the total variance. For this, an approach which uses one of the important theorems of majorization theory is proposed. Based on the tests, this approach lowers the computational costs.

 Principal Component Analysis is a method for reducing the dimensionality of datasets while also limiting information loss. It accomplishes this by producing uncorrelated variables that maximize variance one after the other. The accepted criterion for evaluating a Principal Components PC performance is λ_jtrS where trS denotes the trace of the covariance matrix S. It is standard procedure to determine how many PCs should be maintained using a predetermined percentage of the total variance. In this study, the diagonal elements of the covariance matrix are used instead of the eigenvalues to determine how many PCs need to be considered to obtain the defined threshold of the total variance. For this, an approach which uses one of the important theorems of majorization theory is proposed. Based on the tests, this approach lowers the computational costs.

 Principal Component Analysis is a method for reducing the dimensionality of datasets while also limiting information loss. It accomplishes this by producing uncorrelated variables that maximize variance one after the other. The accepted criterion for evaluating a Principal Components PC performance is λ_jtrS where trS denotes the trace of the covariance matrix S. It is standard procedure to determine how many PCs should be maintained using a predetermined percentage of the total variance. In this study, the diagonal elements of the covariance matrix are used instead of the eigenvalues to determine how many PCs need to be considered to obtain the defined threshold of the total variance. For this, an approach which uses one of the important theorems of majorization theory is proposed. Based on the tests, this approach lowers the computational costs.

Makale detayları

Determining The Number of Principal Components with Schur's Theorem in Principal Component Analysis

Yazarlar:

Cihan Karakuzulu | İbrahim Halil Gümüş | Serkan Güldal | Mustafa Yavaş

Yayıncı:

Bitlis Eren University

Ana Başlıklar:

Engineering

Dergi:

Bitlis Eren Üniversitesi Fen Bilimleri Dergisi Vol.12 Issue 2, pp.299-306

Belge Tipi:

Makale

Yayın Tarihi:

6/2023

Belge Dili:

İngilizce

Document ID (Org No.):

2001292716

pISSN:

2147-3129

Principal Component Analysis

Majorization Theory

Schur’s Theorem

Positive Semidefinite Matrices

Eigenvalues

Machine Learning.

Sayı

Makale detayları

Determining The Number of Principal Components with Schur's Theorem in Principal Component Analysis

Yazarlar: Cihan Karakuzulu | İbrahim Halil Gümüş | Serkan Güldal | Mustafa Yavaş

Yayıncı: Bitlis Eren University

Ana Başlıklar: Engineering

Dergi: Bitlis Eren Üniversitesi Fen Bilimleri Dergisi Vol.12 Issue 2, pp.299-306

Belge Tipi: Makale

Yayın Tarihi: 6/2023

Belge Dili: İngilizce

Document ID (Org No.): 2001292716

pISSN: 2147-3129

Principal Component Analysis

Majorization Theory

Schur’s Theorem

Positive Semidefinite Matrices

Eigenvalues

Machine Learning.

Sayı

Yazarlar:

Cihan Karakuzulu | İbrahim Halil Gümüş | Serkan Güldal | Mustafa Yavaş

Yayıncı:

Bitlis Eren University

Ana Başlıklar:

Engineering

Dergi:

Bitlis Eren Üniversitesi Fen Bilimleri Dergisi Vol.12 Issue 2, pp.299-306

Belge Tipi:

Makale

Yayın Tarihi:

6/2023

Belge Dili:

İngilizce

Document ID (Org No.):

2001292716

pISSN:

2147-3129