Metrik Spektral Terpadu untuk Stabilitas dan Komputasi Eigen Paper

Desi Vinsensia; Yulia Utami; Joya Rahmawida; Chessie Paquita Senjaya

doi:10.55338/jumin.v6i4.6559

Authors

Desi Vinsensia, STMIK Pelita Nusantara, Indonesia
Yulia Utami, STMIK Pelita Nusantara, Indonesia
Joya Rahmawida, STMIK Pelita Nusantara, Indonesia
Chessie Paquita Senjaya, STMIK Pelita Nusantara, Indonesia

DOI:

https://doi.org/10.55338/jumin.v6i4.6559

Keywords:

Clustering, Eigenvalue, Grassmannian, Metric, Perturbation, Spectral, Stability

Abstract

Penelitian ini mengusulkan kerangka terpadu untuk analisis stabilitas berbasis metrik spectral yang menggabungkan jarak spectral matriks, jarak spectral graf dan evaluasi stabilitas komunitas melalui clustering, serta jarak antar subruang eigen guna menilai sensitivitas terhadap perturbasi. Tujuan penelitian adalah menurunkan metrik terpadu yang konsisten secara teori (kelengkapan, kompak) dan empiris untuk membandingkan struktur spektral di bawah noise. Metode diuji pada (a) matriks sintetis dengan noise Gaussian aditif multi-level dan (b) graf jaringan jalan realistik (serta rencana penambahan satu dataset graf publik kecil untuk validasi eksternal). Hasil menunjukkan peningkatan kualitas clustering (Adjusted Rand Index/ARI naik dibanding baseline adjacency) dan penurunan rata-rata error estimasi sensitivitas subruang sebesar ketika menggunakan bound geodesik Grassmannian dibanding bound klasik; overhead waktu komputasi hanya marginal (sekitar . Kerangka ini menyediakan dasar untuk analitik spektral lintas domain dan berpotensi memperbaiki desain bound perturbasi yang lebih presisi di masa depan.

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