Improving Hybrid MDS Application to Antarctic Data

1
Improving Hybrid MDS Application to Antarctic
Data

• Matthew Chalmers, Alistair Morrison, Greg Ross
• University of Glasgow

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Introduction

• Visualising multidimensional (gt3D) data
• Standard MDS fast, but just a linear combination
  of input dimensions
• Non-linear MDS more detail/structure, but simple
  spring model is O(N3)
• Tinkering with spring models for non-linear MDS
• 1992 k-d tree spatial subdivision for an
  O(N2logN) algorithm
• 1996 stochastic sampling for an O(N2) algorithm
• 2002 hybrid multistage algorithm, O(N?N)
• 2003 hybrid multistage algorithm, O(N5/4 ) using
  pivots
• Antarctic data test set for non-Equator work
• Possible integration into CAVE? Coupling infovis
  and urban vis?

3
HIVE a Toolkit and Workspace for InfoVis
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Spring Model An Iterative Non-Linear MDS
Algorithm
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O(N?N) MDS algorithm

• Select ?N subset of objects O(?N)
• Create 2D layout of subset using 96 algorithm
  O(N)
• Interpolate remaining objects
  O(N?N)
• Fine-tune layout with k 96 algorithm iterations
  O(N)

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O(N?N) MDS algorithm

• Select ?N subset of objects O(?N)
• Create 2D layout of subset using 96 algorithm
  O(N)
• Interpolate remaining objects
  O(N?N)
• Fine-tune layout with k 96 algorithm iterations
  O(N)

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O(N?N) MDS algorithm

• Select ?N subset of objects O(?N)
• Create 2D layout of subset using 96 algorithm
  O(N)
• Interpolate remaining objects
  O(N?N)
• Fine-tune layout with k 96 algorithm iterations
  O(N)

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O(N?N) MDS algorithm

• Select ?N subset of objects O(?N)
• Create 2D layout of subset using 96 algorithm
  O(N)
• Interpolate remaining objects
  O(N?N)
• Fine-tune layout with k 96 algorithm iterations
  O(N)

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O(N?N) MDS algorithm

• Select ?N subset of objects O(?N)
• Create 2D layout of subset using 96 algorithm
  O(N)
• Interpolate remaining objects
  O(N?N)
• Fine-tune layout with k 96 algorithm iterations
  O(N)

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O(N?N) MDS algorithm

• Select ?N subset of objects O(?N)
• Create 2D layout of subset using 96 algorithm
  O(N)
• Interpolate remaining objects
  O(N?N)
• Fine-tune layout with k 96 algorithm iterations
  O(N)

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O(N?N) MDS algorithm

• Select ?N subset of objects O(?N)
• Create 2D layout of subset using 96 algorithm
  O(N)
• Interpolate remaining objects
  O(N?N)
• Fine-tune layout with k 96 algorithm iterations
  O(N)

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O(N?N) MDS algorithm

• Select ?N subset of objects O(?N)
• Create 2D layout of subset using 96 algorithm
  O(N)
• Interpolate remaining objects
  O(N?N)
• Fine-tune layout with k 96 algorithm iterations
  O(N)

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O(N?N) MDS algorithm

• Select ?N subset of objects O(?N)
• Create 2D layout of subset using 96 algorithm
  O(N)
• Interpolate remaining objects
  O(N?N)
• Fine-tune layout with k 96 algorithm iterations
  O(N)

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O(N?N) MDS algorithm
Interpolation is the most complex
phase Specifically, the parent-finding stage of
interpolation We used the Antarctic data as a
test set when working to improve this algorithm

• Select ?N subset of objects O(?N)
• Create 2D layout of subset using 96 algorithm
  O(N)
• Interpolate remaining objects
  O(N?N)
• Fine-tune layout with k 96 algorithm iterations
  O(N)

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Pivots Improving Parent Search
Use pivots to discretise inter-object
distances An array of distances from k pivots
Later searches will use this k-dimensional space
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Pivots Improving Parent Search
Use pivots to discretise inter-object
distances an array of distances from k pivots
Later searches will use this k-dimensional space
A
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Pivots Improving Parent Search
Use pivots to discretise inter-object
distances an array of distances from k pivots
Later searches will use this k-dimensional space
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Pivots Improving Parent Search
Use pivots to discretise inter-object
distances an array of distances from k pivots
Later searches will use this k-dimensional space
3
2
1
B
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Performance Stress
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Performance Time

• 108000 elements in 360 seconds

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Pivots in 14D Antarctic Data
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Springs v. PCA on 17D Antarctic Data
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Springs v. PCA on 17D Antarctic Data
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Sensor Failure in the Antarctic Data
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Conclusion

• Antarctic data set real data for our algorithms
  and HIVE toolkit
• Quick good layouts of large-ish data sets on your
  mothers PC
• O(N5/4) time, 100000 objects, 4 papers
• Layouts made sense but no take-up by env
  scientists
• Exploratory data analysis v. simple standard
  questions in practice?
• A few HIVE components passed to Nottm grid folks
• Fisheye tables not the hardcore spring stuff or
  the overall toolkit
• Greg case study of HIVE in social science, then
  writing up PhD
• Alistair recent PhD, now RA looking at MIAS data
  and PinPlay

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matthew_at_dcs.gla.ac.uk www.dcs.gla.ac.uk/matthew
www.equator.ac.uk