2 Search Results for "Dasgupta, Sanjoy"

Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2021.18
Upper and Lower Bounds for Complete Linkage in General Metric Spaces

Authors: Anna Arutyunova, Anna Großwendt, Heiko Röglin, Melanie Schmidt, and Julian Wargalla

Published in: LIPIcs, Volume 207, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)

Abstract
In a hierarchical clustering problem the task is to compute a series of mutually compatible clusterings of a finite metric space (P,dist). Starting with the clustering where every point forms its own cluster, one iteratively merges two clusters until only one cluster remains. Complete linkage is a well-known and popular algorithm to compute such clusterings: in every step it merges the two clusters whose union has the smallest radius (or diameter) among all currently possible merges. We prove that the radius (or diameter) of every k-clustering computed by complete linkage is at most by factor O(k) (or O(k²)) worse than an optimal k-clustering minimizing the radius (or diameter). Furthermore we give a negative answer to the question proposed by Dasgupta and Long [Sanjoy Dasgupta and Philip M. Long, 2005], who show a lower bound of Ω(log(k)) and ask if the approximation guarantee is in fact Θ(log(k)). We present instances where complete linkage performs poorly in the sense that the k-clustering computed by complete linkage is off by a factor of Ω(k) from an optimal solution for radius and diameter. We conclude that in general metric spaces complete linkage does not perform asymptotically better than single linkage, merging the two clusters with smallest inter-cluster distance, for which we prove an approximation guarantee of O(k).
Cite as

Anna Arutyunova, Anna Großwendt, Heiko Röglin, Melanie Schmidt, and Julian Wargalla. Upper and Lower Bounds for Complete Linkage in General Metric Spaces. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 207, pp. 18:1-18:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{arutyunova_et_al:LIPIcs.APPROX/RANDOM.2021.18,
  author =	{Arutyunova, Anna and Gro{\ss}wendt, Anna and R\"{o}glin, Heiko and Schmidt, Melanie and Wargalla, Julian},
  title =	{{Upper and Lower Bounds for Complete Linkage in General Metric Spaces}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)},
  pages =	{18:1--18:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-207-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{207},
  editor =	{Wootters, Mary and Sanit\`{a}, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2021.18},
  URN =		{urn:nbn:de:0030-drops-147115},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2021.18},
  annote =	{Keywords: Hierarchical Clustering, Complete Linkage, agglomerative Clustering, k-Center}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.SoCG.2019.1
A Geometric Data Structure from Neuroscience (Invited Talk)

Authors: Sanjoy Dasgupta

Published in: LIPIcs, Volume 129, 35th International Symposium on Computational Geometry (SoCG 2019)

Abstract
An intriguing geometric primitive, "expand-and-sparsify", has been found in the olfactory system of the fly and several other organisms. It maps an input vector to a much higher-dimensional sparse representation, using a random linear transformation followed by winner-take-all thresholding. I will show that this representation has a variety of formal properties, such as locality preservation, that make it an attractive data structure for algorithms and machine learning. In particular, mimicking the fly’s circuitry yields algorithms for similarity search and for novelty detection that have provable guarantees as well as having practical performance that is competitive with state-of-the-art methods. This talk is based on work with Saket Navlakha (Salk Institute), Chuck Stevens (Salk Institute), and Chris Tosh (Columbia).
Cite as

Sanjoy Dasgupta. A Geometric Data Structure from Neuroscience (Invited Talk). In 35th International Symposium on Computational Geometry (SoCG 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 129, p. 1:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

Copy BibTex To Clipboard

@InProceedings{dasgupta:LIPIcs.SoCG.2019.1,
  author =	{Dasgupta, Sanjoy},
  title =	{{A Geometric Data Structure from Neuroscience}},
  booktitle =	{35th International Symposium on Computational Geometry (SoCG 2019)},
  pages =	{1:1--1:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-104-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{129},
  editor =	{Barequet, Gill and Wang, Yusu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2019.1},
  URN =		{urn:nbn:de:0030-drops-104055},
  doi =		{10.4230/LIPIcs.SoCG.2019.1},
  annote =	{Keywords: Geometric data structure, algorithm design, neuroscience}
}
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