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Presentation #004 (Google)

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Start Time: 7 p.m. UTC+4.5.

Title: Optimization Algorithms for Hierarchical Clustering

Abstract of the presentation:

Hierarchical Clustering is a popular unsupervised learning method which produces a recursive decomposition of a dataset into clusters of increasingly finer granularity. This problem has been studied for decades in computer science and has applications in a variety of fields. In 2016, Dasgupta proposed a formulation of hierarchical clustering as a minimization problem, and gave an approximation algorithm for this problem. In this talk, we will discuss algorithms for this and similar optimization problems. In particular, we will discuss an algorithm based on a reduction to the sparsest cut problem, a maximization formulation of hierarchical clustering due to Moseley and Wang, and solutions based on semi-definite programming.

 

Persian Title:

الگوریتم‌های بهینه‌سازی برای خوشه‌بندی سلسله‌مراتبی

Abstract in Persian:

خوشه‌بندی یکی از معمول‌ترین روش‌های دسته‌بندی و تحلیل داده‌هاست. خوشه‌بندی سلسله‌مراتبی یکی از مدل‌های خوشه‌بندی است که در آن نقاط داده به صورت بازگشتی به دسته‌های کوچک‌تر و کوچک‌تر دسته‌بندی می‌شوند. این مدل از دهه‌ها پیش موضوع پژوهش و دارای کاربرد در شاخه‌های مختلف علوم کامپیوتر بوده است. در سال ۲۰۱۶، داسگوپتا با تعریف یک تابع هدف مناسب، فرمول‌بندی‌ای از خوشه‌بندی سلسله‌مراتبی به عنوان یک مسئله‌ی کمینه‌سازی ارائه داد و الگوریتم‌های تقریبی‌ای برای حل این مسئله پیشنهاد کرد. در این سخنرانی به الگوریتم‌های تقریبی برای این مسئله و فرمول‌بندی‌های مشابه خوشه‌بندی سلسله‌مراتبی خواهیم پرداخت. به طور خاص، درباره‌ی الگوریتمی مبتنی بر کاهش به مسئله‌ی تنک‌ترین برش در گراف‌ها، فرمول‌بندی بیشینه‌سازی موزلی و وانگ، و الگوریتم‌های مبتنی بر برنامه‌سازی نیمه‌معین برای این فرمول‌بندی صحبت خواهیم کرد.
Categories: Learning, Learning Tags: algorithm, divide-and-conquer, linear transformations, presentation, Walsh-Hadamard Transform, WHT, الگوریتم قطعی, الگوریتمهای کوانتومی, سنجش فشرده, فشرده‌سازی تصویر
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