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Sains Malaysiana 54(11)(2025): 2773-2783
http://doi.org/10.17576/jsm-2025-5411-16
Determination of the Optimal Number of PLS Components Based on the Combination of Cross-Validation and RMD-MRCD-PCA
Weighting Function
(Penentuan Bilangan Komponen PLS yang Optimum berasaskan Gabungan
Pengesahan Silang dan Fungsi Pemberat RMD-MRCD-PCA)
HABSHAH MIDI1, SITI ZAHARIAH ABDUL WAHAB2,* & AZREE SHAHREL AHMAD NAZRI1
1Institute for Mathematical Research, Universiti Putra Malaysia, 43400 UPM Serdang,
Selangor, Malaysia
2Malaysian Institute of Information Technology, Universiti Kuala Lumpur, 50250 Kuala Lumpur, Malaysia
Received: 19 November 2024/Accepted: 24 October 2025
ABSTRACT
Partial least squares (PLS) regression is a very
useful tool for the analysis of high dimensional data (HDD). Choosing the ideal
number of PLS components is a vital step in developing the best model. The
accuracy of the model will be affected if there are too many or too few PLS
components being selected. Numerous classical methods, such as the
leave-one-out cross-validation (LOOCV) and K-fold cross-validation (K-FoldCV) are developed to determine the optimal number of
PLS components. Nonetheless, they are easily affected by high leverage points
(HLPs). Thus, robust cross validation techniques, denoted as RMD- MRCD-PCA-LOOCV
and RMD-MRCD-PCA-K-FoldCV are proposed to remedy this problem. The results of
the simulation study and real data set indicate that the proposed methods
successfully select the appropriate number of PLS components.
Keywords: High leverage points;
leave-one-out cross validation; minimum regularized covariance determinant; partial
least squares; principal component analysis
Abstrak
Regresi kuasadua kecil separa (PLS) adalah kaedah yang sangat berguna bagi menganalisis data berdimensi tinggi (HDD). Pemilihan bilangan komponen PLS yang ideal adalah langkah penting bagi membangunkan model terbaik. Ketepatan model akan dipengaruhi sekiranya terlalu banyak atau terlalu sedikit komponen PLS yang dipilih. Pelbagai kaedah klasik seperti pengesahan silang leave-one-out (LOOCV) dan pengesahan silang lipatan K (K-FoldCV) dibangunkan untuk menentukan bilangan komponen PLS yang optimum. Namun begitu, mereka mudah dipengaruhi oleh titik tuasan tinggi (HLPs). Oleh itu teknik pengesahan silang teguh yang ditandakan dengan RMD- MRCD-PCA-LOOCV
dan RMD-MRCD-PCA-K-FoldCV dicadangkan bagi menyelesaikan masalah ini. Keputusan kajian simulasi dan set data sebenar menunjukkan kaedah yang dicadangkan berjaya memilih bilangan komponen PLS yang sesuai.
Kata kunci: Analisis komponen utama; kuasadua terkecil separa; penentu kovarian teratur minimum; pengesahan silang leave-one out; titik tuasan tinggi
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*Corresponding author; email:
sitizahariah@unikl.edu.my
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