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Visualization of Clusters with a Density- Based Similarity Measure Rebecca Nugent Department of Statistics, Carnegie Mellon University June 9, 2007 Joint with: Werner Stuetzle (U. of Washington Statistics) Xiaoyi Fei (CMU Computer Science)

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Page 1: Visualization of Clusters with a Density-Based Similarity Measure Rebecca Nugent Department of Statistics, Carnegie Mellon University June 9, 2007 Joint

Visualization of Clusters with a Density-Based Similarity Measure

Rebecca NugentDepartment of Statistics,

Carnegie Mellon UniversityJune 9, 2007

Joint with: Werner Stuetzle (U. of Washington Statistics) Xiaoyi Fei (CMU Computer Science)

Page 2: Visualization of Clusters with a Density-Based Similarity Measure Rebecca Nugent Department of Statistics, Carnegie Mellon University June 9, 2007 Joint

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Outline

Page 3: Visualization of Clusters with a Density-Based Similarity Measure Rebecca Nugent Department of Statistics, Carnegie Mellon University June 9, 2007 Joint

Introduction & Motivation

Page 4: Visualization of Clusters with a Density-Based Similarity Measure Rebecca Nugent Department of Statistics, Carnegie Mellon University June 9, 2007 Joint

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Introduction & Motivation

Page 5: Visualization of Clusters with a Density-Based Similarity Measure Rebecca Nugent Department of Statistics, Carnegie Mellon University June 9, 2007 Joint

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Introduction & Motivation: Applications

Page 6: Visualization of Clusters with a Density-Based Similarity Measure Rebecca Nugent Department of Statistics, Carnegie Mellon University June 9, 2007 Joint

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Page 7: Visualization of Clusters with a Density-Based Similarity Measure Rebecca Nugent Department of Statistics, Carnegie Mellon University June 9, 2007 Joint

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Page 8: Visualization of Clusters with a Density-Based Similarity Measure Rebecca Nugent Department of Statistics, Carnegie Mellon University June 9, 2007 Joint

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Introduction & Motivation: Applications

Page 9: Visualization of Clusters with a Density-Based Similarity Measure Rebecca Nugent Department of Statistics, Carnegie Mellon University June 9, 2007 Joint
Page 10: Visualization of Clusters with a Density-Based Similarity Measure Rebecca Nugent Department of Statistics, Carnegie Mellon University June 9, 2007 Joint

Clustering Approaches

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Clustering Approaches: Algorithmic

Page 12: Visualization of Clusters with a Density-Based Similarity Measure Rebecca Nugent Department of Statistics, Carnegie Mellon University June 9, 2007 Joint

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Clustering Approaches: Statistical/Parametric

Page 13: Visualization of Clusters with a Density-Based Similarity Measure Rebecca Nugent Department of Statistics, Carnegie Mellon University June 9, 2007 Joint

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Page 14: Visualization of Clusters with a Density-Based Similarity Measure Rebecca Nugent Department of Statistics, Carnegie Mellon University June 9, 2007 Joint

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

QuickTime™ and aTIFF (LZW) decompressor

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Page 15: Visualization of Clusters with a Density-Based Similarity Measure Rebecca Nugent Department of Statistics, Carnegie Mellon University June 9, 2007 Joint

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QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

Page 16: Visualization of Clusters with a Density-Based Similarity Measure Rebecca Nugent Department of Statistics, Carnegie Mellon University June 9, 2007 Joint

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Clustering Approaches: Statistical/Nonparametric

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Clustering Approaches: Statistical/Nonparametric

Page 18: Visualization of Clusters with a Density-Based Similarity Measure Rebecca Nugent Department of Statistics, Carnegie Mellon University June 9, 2007 Joint
Page 19: Visualization of Clusters with a Density-Based Similarity Measure Rebecca Nugent Department of Statistics, Carnegie Mellon University June 9, 2007 Joint

Closer Look at Single Linkage

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Single Linkage Clustering

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Single Linkage Clustering

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Single Linkage Clustering

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Single Linkage Clustering: Minimum Density Distance

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Single Linkage Clustering: 1-nn Density Estimate

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Single Linkage Clustering: Graph Cluster Tree

Page 26: Visualization of Clusters with a Density-Based Similarity Measure Rebecca Nugent Department of Statistics, Carnegie Mellon University June 9, 2007 Joint

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QuickTime™ and aTIFF (LZW) decompressor

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QuickTime™ and aTIFF (LZW) decompressor

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Page 27: Visualization of Clusters with a Density-Based Similarity Measure Rebecca Nugent Department of Statistics, Carnegie Mellon University June 9, 2007 Joint

Generalized Single Linkage

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Generalized Single Linkage

Page 29: Visualization of Clusters with a Density-Based Similarity Measure Rebecca Nugent Department of Statistics, Carnegie Mellon University June 9, 2007 Joint

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Olive Oil

Page 30: Visualization of Clusters with a Density-Based Similarity Measure Rebecca Nugent Department of Statistics, Carnegie Mellon University June 9, 2007 Joint
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In practice

Page 32: Visualization of Clusters with a Density-Based Similarity Measure Rebecca Nugent Department of Statistics, Carnegie Mellon University June 9, 2007 Joint

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Page 33: Visualization of Clusters with a Density-Based Similarity Measure Rebecca Nugent Department of Statistics, Carnegie Mellon University June 9, 2007 Joint

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

Page 34: Visualization of Clusters with a Density-Based Similarity Measure Rebecca Nugent Department of Statistics, Carnegie Mellon University June 9, 2007 Joint

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

QuickTime™ and aTIFF (LZW) decompressor

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Page 35: Visualization of Clusters with a Density-Based Similarity Measure Rebecca Nugent Department of Statistics, Carnegie Mellon University June 9, 2007 Joint
Page 36: Visualization of Clusters with a Density-Based Similarity Measure Rebecca Nugent Department of Statistics, Carnegie Mellon University June 9, 2007 Joint
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Comments/Future Work

Page 38: Visualization of Clusters with a Density-Based Similarity Measure Rebecca Nugent Department of Statistics, Carnegie Mellon University June 9, 2007 Joint

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Acknowledgments

Page 39: Visualization of Clusters with a Density-Based Similarity Measure Rebecca Nugent Department of Statistics, Carnegie Mellon University June 9, 2007 Joint

Thank you

Page 40: Visualization of Clusters with a Density-Based Similarity Measure Rebecca Nugent Department of Statistics, Carnegie Mellon University June 9, 2007 Joint
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Bounding the Minimum

Page 42: Visualization of Clusters with a Density-Based Similarity Measure Rebecca Nugent Department of Statistics, Carnegie Mellon University June 9, 2007 Joint

-1.0

-0.5

0.0

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Pt.1 Pt.2

Density

g.u.0

g.l.0

g.u.L

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p((1-t)xi + txj))

Uncertainty

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Bounding the Minimum

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0.00

0.05

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Density

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Density

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Density

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Bounding the Minimum