Sains Malaysiana 54(8)(2025): 2087-2097

http://doi.org/10.17576/jsm-2025-5408-17

 

Improved Robust Principal Component Analysis based on Minimum Regularized Covariance Determinant for the Detection of High Leverage Points in High Dimensional Data

(Penambahbaikan Analisis Komponen Utama berdasarkan Penentu Kovarian Teratur Minimum bagi Mengecam Titik Tuasan Tinggi untuk Data Dimensi Tinggi)

 

HABSHAH MIDI^1,2,*, JAAZ SUHAIZA^1,3, MOHD ASLAM^1,2, HANI SYAHIDA² & EMI AMIELDA³

 

¹Institute for Mathematical Research, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia

²Department of Mathematics & Statistics, Universiti Putra Malaysia, 43400 UPM Serdang,

Selangor, Malaysia

³Faculty of Computing & Multimedia, Universiti Poly-Tech Malaysia, 56100 Cheras, Kuala Lumpur, Malaysia

 

Diserahkan: 22 April 2024/Diterima: 13 Mac 2025

 

Abstract

This paper presents an extension work of robust principal component analysis (ROBPCA) denoted as IRPCA, to improve the accuracy of the detection of high leverage points (HLPs) in high dimensional data (HDD). The IRPCA employs the Principal Component Analysis (PCA) to reduce the dimension of the data set and subsequently a robust location and scatter estimates of the PC scores are obtained based on the Minimum Regularized Covariance Determinant (MRCD). Instead of using robust score distance to detect HLPs as in ROBPCA; in the proposed IRPCA, we have considered using Robust Mahalanobis distance (RMD).  The performance of the IRPCA is compared to the ROBPCA and the Minimum Regularized Covariance Determinant and PCA-based method (MRCD-PCA) for the identification of HLPs in HDD. The results signify that all the three methods are very successful in the detection of HLPs with no masking effect. Nonetheless, the ROBPCA suffers from serious swamping problems for less than 30% of HLPs. The proposed IRPCA and the MRCD-PCA have similar performance, having very small swamping effect. However, the MRCD-PCA algorithm is quite cumbersome and required longer computational running time. The attractive feature of the IRPCA is that it provides a simpler algorithm and it is very fast.

Keywords: High Leverage Point; minimum regularized covariance determinant; principal component analysis; robust mahalanobis distance

 

Abstrak

Kertas ini membentangkan kerja lanjutan bagi Analisis Komponen Utama Teguh (ROBPCA) ditandakan dengan IRPCA, untuk meningkatkan ketepatan pengecaman titik tuasan tinggi (HLPs) dalam data dimensi tinggi (HDD). IRPCA menggunakan Analisis Komponen Utama (PCA) bagi menurunkan dimensi set data dan seterusnya penganggar lokasi dan skala skor PC dikira berdasarkan Penentu Kovarian Teratur Minimum (MRCD).  Dengan tidak menggunakan jarak skor teguh untuk pengecaman HLPs seperti ROBPCA; dalam kaedah IRPCA yang dicadangkan, kami telah mempertimbangkan penggunaan Jarak Mahalanobis Teguh (RMD). Prestasi IRPCA yang dicadang dibandingkan dengan kaedah ROBPCA dan kaedah Penentu Kovarian Teratur Minimum dan PCA (MRCD-PCA) bagi mengecam HLPs dalam HDD. Keputusan menunjukkan ketiga-tiga kaedah sangat berjaya dalam pengesanan HLPs tanpa kesan penyorokan. Walau bagaimanapun, ROBPCA mengalami masalah kesan limpahan yang serius apabila terdapat HLPs kurang daripada 30%. Prestasi IRPCA yang dicadangkan dan ROBPCA ada lah sama; mempunyai kesan limpahan yang sangat kecil. Namun begitu, algoritma MRCD-PCA agak rumit dan memerlukan masa yang panjang. Sifat menarik bagi IRPCA ialah ia memberi algoritma yang mudah dan masa pengiraan yang singkat.

Kata kunci: Analisis komponen utama; jarak Mahalanobis teguh; penentu kovarian teratur minimum; titik tuasan baik

 

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*Pengarang untuk surat-menyurat; email: habshah@upm.edu.my