In the study of hierarchical clustering, Dasgupta's objective is a measure of the quality of a clustering, defined from a similarity measure on the elements to be clustered. It is named after Sanjoy Dasgupta, who formulated it in 2016. Its key property is that, when the similarity comes from an ultrametric space, the optimal clustering for this quality measure follows the underlying structure of the ultrametric space. In this sense, clustering methods that produce good clusterings for this objective can be expected to approximate the ground truth underlying the given similarity measure. In Dasgupta's formulation, the input to a clustering problem consists of similarity scores between certain pairs of elements, represented as an undirected graph , with the elements as its vertices and with non-negative real weights on its edges. Large weights indicate elements that should be considered more similar to each other, while small weights or missing edges indicate pairs of elements that are not similar. A hierarchical clustering can be described as a tree (not necessarily a binary tree) whose leaves are the elements to be clustered; the clusters are then the subsets of elements descending from each tree node, and the size of any cluster is its number of elements. For each edge of the input graph, let denote the weight of edge and let denote the smallest cluster of a given clustering that contains both and . Then Dasgupta defines the cost of a clustering to be The optimal clustering for this objective is NP-hard to find. However, it is possible to find a clustering that approximates the minimum value of the objective in polynomial time by a divisive (top-down) clustering algorithm that repeatedly subdivides the elements using an approximation algorithm for the sparsest cut problem, the problem of finding a partition that minimizes the ratio of the total weight of cut edges to the total number of cut pairs.Equivalently, for purposes of approximation, one may minimize the ratio of the total weight of cut edges to the number of elements on the smaller side of the cut. Using the best known approximation for the sparsest cut problem, the approximation ratio of this approach is . (Wikipedia).
Ban Ki-Moon: United Nations Secretary General
Ban Ki-Moon, United Nations Secretary General, explains the important role women can play in the effort to address global challenges. This video is part of the Yale Global Perspectives series. To learn more about this series, visit http://world.yale.edu.
From playlist Global Perspectives
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Join my wife and me on the 1st day of our Diwali
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Kesang Tseten on Documentary Film
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'This Circle is Mine' is a short documentation of a day in the life of Krishnadas, a man who stands everyday for hours on end at Juhu Circle in Mumbai with a sign that says 'Apne dharm par chalo, sabse prem karo (Follow your religion, love everybody)'. The film documents various aspects of
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David Attenborough and Venki Ramakrishnan on the Dasgupta Review | The Royal Society
Sir David Attenborough joins economist Professor Sir Partha Dasgupta and Nobel-prize winning biologist Sir Venki Ramakrishnan to mark the publication of The Economics of Biodiversity: The Dasgupta Review. #Dasgupta #DavidAttenborough #health #Ecosystems #Biodiversity #Nature #economics #N
From playlist Popular talks and lectures
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Mod-03 Lec-05 The Samkhya Philosophy - I
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The Impossible Dream of Neutrino Astronomy by Basu Dasgupta
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Ashani Dasgupta: Local Connectedness of Boundaries for Relatively Hyperbolic Groups
Ashani Dasgupta, University of Wisconsin-Milwaukee Title: Local Connectedness of Boundaries for Relatively Hyperbolic Groups Let $(\Gamma,\mathbb{P})$ be a relatively hyperbolic group pair that is relatively one ended. Then the Bowditch boundary of $(\Gamma,\mathbb{P})$ is locally connect
From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022
David Rolnick & Ishita Dasgupta: Modeling Dynamic Memory with Hopfield Networks
MIT RES.9-003 Brains, Minds and Machines Summer Course, Summer 2015 View the complete course: https://ocw.mit.edu/RES-9-003SU15 Instructor: David Rolnick, Ishita Dasgupta David Rolnick and Ishita Dasgupta explore how Hopfield networks, commonly used to model static memories, can be extend
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Modern Trends in Electron Transfer Chemistry: From Molecular Electronics to Devices URL: https://www.icts.res.in/discussion-meeting/MTETC2016 DATES: Thursday 28 Jan, 2016 - Friday 29 Jan, 2016 VENUE : Madhava Lecture Hall, ICTS Bangalore DESCRIPTION: The meeting aims to introduce stud
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Mod-04 Lec-11 The Yoga Philosophy - I
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Spin Glasses and Related Systems (Lecture 2) by Chandan Dasgupta
PROGRAM: BANGALORE SCHOOL ON STATISTICAL PHYSICS - XIII (HYBRID) ORGANIZERS: Abhishek Dhar (ICTS-TIFR, India) and Sanjib Sabhapandit (RRI, India) DATE & TIME: 11 July 2022 to 22 July 2022 VENUE: Madhava Lecture Hall and Online This school is the thirteenth in the series. The schoo
From playlist Bangalore School on Statistical Physics - XIII - 2022 (Live Streamed)
Spin Glasses and Related Systems (Lecture 4) by Chandan Dasgupta
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From playlist Bangalore School on Statistical Physics - XIII - 2022 (Live Streamed)
Dipole Alignment of Water Molecules Flowing Through a Carbon... by Chandan Dasgupta
DISCUSSION MEETING STATISTICAL PHYSICS: RECENT ADVANCES AND FUTURE DIRECTIONS (ONLINE) ORGANIZERS: Sakuntala Chatterjee (SNBNCBS, Kolkata), Kavita Jain (JNCASR, Bangalore) and Tridib Sadhu (TIFR, Mumbai) DATE: 14 February 2022 to 15 February 2022 VENUE: Online In the past few dec
From playlist Statistical Physics: Recent advances and Future directions (ONLINE) 2022
Here’s How That Annoying Fly Dodges Your Swatter | Deep Look
A fly has a pair of tiny, dumbbell-shaped limbs called halteres that were once a second pair of wings. They wield them to make razor-sharp turns and land out of reach on your ceiling. But don't despair – there *is* a trick to smacking these infuriating insects. SUBSCRIBE to Deep Look! ht
From playlist Deep Look | Series | KQED
Understanding DevOps | What is DevOps?
DevOps is a widely used term, but people interpret it differently. What does it mean and what does it really take to implement DevOps and Continuous Delivery? Ideas like DevOps Pipelines (Deployment Pipelines) implementing the core technical practices of Continuous Delivery, Continuous Dep
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Generative Models for Networks (Lecture 3) by Anirban Dasgupta
Program Summer Research Program on Dynamics of Complex Systems ORGANIZERS: Amit Apte, Soumitro Banerjee, Pranay Goel, Partha Guha, Neelima Gupte, Govindan Rangarajan and Somdatta Sinha DATE : 15 May 2019 to 12 July 2019 VENUE : Madhava hall for Summer School & Ramanujan hall f
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