Regularized K-Means Clustering via Fully Corrective Frank-Wolfe Optimization

محتوى المقالة الرئيسي

Ahmed Yacoub Yousif
Basad Al-Sarray

الملخص

يُستخدم التعلم غير المُراقب لتحليل هياكل البيانات في عمليات التجميع، إلا أن خوارزمية k-means التقليدية تعاني من الحساسية للضوضاء والقيم الشاذة والبيانات عالية الأبعاد، مما يؤدي إلى أداء غير مستقر. وللتغلب على هذه القيود، تُقدَّم في هذه الدراسة إطار مُحسَّن للتجميع باستخدام k-means المُنظَّم، حيث يتم تحسينه باستخدام خوارزمية فرانك-وولف المصححة بالكامل (FCFW). يساهم التنظيم باستخدام معيار فروبينياس (Frobenius norm) في زيادة استقرار المجموعات، والحد من فرط التكيّف، وتحقيق توزيع أكثر تماسكًا للعناقيد. بالإضافة إلى ذلك، يتيح تعيين المجموعات الاحتمالي مرونة أكبر، حيث يمكن لكل نقطة بيانات الانتماء إلى عدة مجموعات بمستويات عضوية مختلفة. كما يتم تنفيذ اختيار الميزات باستخدام اختبار كروسكال-واليس (Kruskal-Wallis)، وهو اختبار إحصائي غير معلمي يُستخدم لتحديد الميزات المهمة في البيانات عالية الأبعاد، خصوصًا في تحليل التعبير الجيني.


تم تقييم كفاءة الطريقة المقترحة من خلال التجارب على مجموعات بيانات تركيبية وبيانات تعبير جيني لسرطان الثدي عالية الأبعاد، حيث أثبتت التجارب قدرة النموذج على التعامل مع العناقيد غير الخطية والمتداخلة بفعالية. أظهرت النتائج أن خوارزمية k-means المُنظَّمة باستخدام FCFW تتفوق على k-means التقليدية والخوارزميات الأخرى من حيث الدقة وسرعة التقارب. وبالتالي، تؤكد هذه الدراسة أن النهج المقترح يتمتع بالقوة والفعالية، مما يجعله مناسبًا لتطبيقات تحليل البيانات عالية الأبعاد.

تفاصيل المقالة

القسم

Articles

كيفية الاقتباس

"Regularized K-Means Clustering via Fully Corrective Frank-Wolfe Optimization" (2025) مجلة الهندسة, 31(8), ص 178–199. doi:10.31026/j.eng.2025.08.11.

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