یک روش جدید تجزیه ماتریسی نامنفی استوار توزیعی مبتنی بر منظم‌ساز گراف دوتصادفی برای خوشه‌بندی داده

مقالات آماده انتشار

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشجوی دکتری هوش مصنوعی و رباتیکز، دانشکده مهندسی، دانشگاه کردستان، سنندج، ایران

2 دانشیار گروه کامپیوتر، دانشکده مهندسی، دانشگاه کردستان، سنندج، ایران

10.22034/abmir.2026.24826.1262

چکیده

تجزیه ماتریسی نامنفی (NMF) یکی از روش‌های پرکاربرد برای یادگیری بازنمایی داده و خوشه‌بندی داده‌های نامنفی است. با این حال، اکثر روش‌های موجود مبتنی بر فرض یک توزیع نوفه مشخص هستند و در مواجهه با داده‌های واقعی که معمولاً دارای نوفه­های ناشناخته، ناهمگن یا ترکیبی هستند، با افت عملکرد مواجه می‌شوند. به‌منظور رفع این محدودیت، در این مقاله چارچوبی جدید با عنوان تجزیه ماتریسی نامنفی استوار توزیعی با منظم‌ساز گراف دو‌تصادفی  (DRNMF-bS) ارائه می‌شود. هسته اصلی روش پیشنهادی بر پایه یک مدل تجزیه ماتریسی نامنفی استوار توزیعی نمونه‌محور است که در آن تابع هدف به‌صورت ترکیبی تطبیقی از چندین تابع زیان متناظر با توزیع‌های مختلف نوفه تعریف شده و مسئله در قالب یک بهینه‌سازی حداقل–حداکثر بر روی مجموعه ابهام احتمالاتی فرمول‌بندی می‌شود. این چارچوب امکان یادگیری خودکار وزن توابع زیان و در نتیجه سازگاری پویا با شرایط نوفه­ای مختلف را فراهم کرده و موجب افزایش پایداری مدل در برابر طیف گسترده‌ای از توزیع‌های نوفه و ترکیب آن‌ها می‌شود. علاوه بر این، به‌منظور بهره‌برداری مؤثر از ساختار هندسی داده‌ها، یک منظم‌ساز گراف دو‌تصادفی به مدل افزوده شده است که از طریق یادگیری ماتریس شباهت، اطلاعات محلی داده را به‌صورت درون‌زا در فرآیند تجزیه ادغام می‌کند. برای حل مسئله بهینه‌سازی حاصل، یک الگوریتم تکراری با تضمین کاهش تابع هدف ارائه شده است. نتایج آزمایش‌ها بر روی ۱۲ مجموعه‌داده و در مقایسه با ۱۰ روش مبتنی بر NMF نشان می‌دهد که روش پیشنهادی از نظر دقت خوشه‌بندی، مقاومت در برابر نوفه و قابلیت تعمیم، عملکردی برتر و پایدارتر نسبت به روش‌های رقیب ارائه می‌دهد.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Distributionally robust nonnegative matrix factorization for data clustering

نویسندگان [English]

  • Wafa Barkhoda 1
  • Fardin Akhlaghian Tab 2
1 Ph.D. student, Department of Computer, University of Kurdistan, Sanandaj, Iran
2 Associate Professor, Department of Computer, University of Kurdistan, Sanandaj, Iran
چکیده [English]

Nonnegative Matrix Factorization (NMF) is a widely used technique for nonnegative data representation learning and clustering. However, most existing NMF methods assume a predefined noise distribution, leading to degraded performance on real-world data contaminated by unknown, heterogeneous, or mixed noise. To address this limitation, we propose a novel framework, termed Distributionally Robust Nonnegative Matrix Factorization with a bi-Stochastic Graph Regularizer (DRNMF-bS). The proposed method is built upon an instance-wise distributionally robust NMF model, where the objective function is formulated as an adaptive combination of multiple loss functions associated with different noise distributions and optimized through a min–max problem over a probabilistic ambiguity set. This formulation enables adaptive learning of loss weights, allowing dynamic adaptation to diverse noise conditions while improving robustness against a broad range of noise distributions and their mixtures. Furthermore, a bi-stochastic graph regularizer is incorporated to exploit the intrinsic geometric structure of the data by jointly learning an adaptive similarity matrix. An efficient iterative optimization algorithm with guaranteed objective descent is developed. Extensive experiments on 12 benchmark datasets against 10 representative NMF-based methods demonstrate superior clustering accuracy, robustness to noise, and generalization performance.

کلیدواژه‌ها [English]

  • Data clustering
  • Distributionally robust learning
  • Robust matrix factorization
  • Nonnegative matrix factorization
  • bi-stochastic graph regularization

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