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Journals / Bitlis Eren Üniversitesi Fen Bilimleri Dergisi / 2023 / Cilt: 12 Sayı: 2

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

Cihan KARAKUZULU
İbrahim Halil GÜMÜŞ
Serkan GÜLDAL
Mustafa YAVAŞ
Pages
299–306
Publication Date
2023-06-27
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Based on the tests, this approach lowers the computational costs.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Principal Component Analysis is a method for reducing the dimensionality of datasets while also limiting information loss.
📊
Key Findings & Data:The accepted criterion for evaluating a Principal Component’s (PC) performance is λ_j/tr(S) where tr(S) denotes the trace of the covariance matrix S.
💡
Conclusion & Impact:Based on the tests, this approach lowers the computational costs.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Principal Component Analysis · Majorization Theory · Schur’s Theorem

Abstract

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 Component’s (PC) performance is λ_j/tr(S) where tr(S) 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.

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Cite This Article

KARAKUZULU, C., GÜMÜŞ, İ. H., GÜLDAL, S., YAVAŞ, M. (2023). Determining The Number of Principal Components with Schur's Theorem in Principal Component Analysis. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, Cilt: 12 Sayı: 2, 299–306. https://ajindex.com/articles/948735

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