Proximity Visualization via Common Fate Luminance Changes

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Proximity Visualization via Common Fate Luminance
Changes

• Lior Wolf, Chen Goldberg,
• Hezy Yeshurun
• School of computer science,
• Tel-Aviv University, 2009

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Proximity information
The Simpsons (9 items)
Movie Stars (50 items)
NASDAQ (100 items)
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Common Solutions

• Embedding in lower dimensional space
• Representing data in a lower dimensionality while
  maximizing original distance properties
• Techniques MDS, Isomap, CCA.
• Usually lowered to 2 or 3 dimensions
• 2D graphs
• 3D visualizations

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Points of Weakness

• Space limitations
• All icons cant fit in display at once
• Occlusions occur
• Capacity of low-dimensionality
• Reduction to 2,3 dimensions cant maintain
  sufficient accuracy
• Few more dimensions can be added (e.g. Color
  coding)
• However these are taxing on the user

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Motivation

• Looking for a better visualization techniques
  that
• Escapes the inherent problems of low
  dimensionality
• Utilizes display space more efficiently
• Targeted at non-professional audience
• Should require no training
• Intuitive
• Visually attractive

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Proposed design

• Embed in space and time
• Icons placed on a 2D grid
• Icons luminance change over time conveys
  proximity
• Icons appearing in the same moment in time are
  related
• User internalizes connections in the data while
  passively watching visualization unfolds over
  time
• Interaction is optional

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Proposed design concept
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Advantage

• Dimensionality capacity determined only by
  animation length and smoothness
• User selects a duration of time
• Generated animation makes optimal use of that
  time
• Space limitation less problematic
• Grid layout makes optimal use of display
• Occlusions free

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More

• Cognitively natural
• Based on the Gestalt principle of Common Fate
• Icons are perceived as a unit if they move
  together
• Psychophysical evidence suggest that
  luminance-based common fate is also prominent
  SEKULER 2001
• Runs fully automatic once parameters are set
• Visually aesthetic

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Design challenges

• Embedding in time
• Related icons should appear at the same time
• Luminance changes should occur smoothly
• Embedding in space
• Items lit together should be placed closely
  together on the grid
• View control
• Grid larger than display requires a camera
  control to show only the most lit
• Each problem is optimized separately

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Embedding in time

• Requirement
• Related icons should appear lit at the same time
• Lets define
• Anxn to be the affinity matrix (input)
• fi(t), 0ltiltn, to be a non-negative function that
  captures an item luminance over time (output)
• Then formally what we want is to minimize the
  following discrepancy score

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Smooth Embedding in time

• In addition we want a gradual change in luminance
• Therefore we should also minimize

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Time embedding optimization
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Solving the optimization problem

• Discretize the loss function
• Functions fi replaced by vectors vi?Rm
• Where m the number of animation frames
• Continuous derivative operator replaced with
  matrix operator H

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Solving the optimization problem

• Optimize using the gradient projection method
• initialize a random matrix V0
• Update

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Example solutions
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Embedding in Space

• Wed like to place the items on the grid such
  that
• Positioning conveys proximity
• Temporarily lit items grouped together
• Thus we look for an optimal grid arrangement that
  preserves the new proximity matrix VTV
• However finding an optimal positioning on a grid
  is NP-complete
• Instead we employ a heuristic method

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Embedding in Space (cont.)

• Given desired grid proportions assign each item
  to a cell
• Spare cells stacked at the bottom of grid
• First use MDS to embed the data on a 2D plane
• Then perform a recursive quadtree-like
  partitioning of the data
• Separate grid evenly along an axis (excluding
  spare cells)
• Divide Items between sub-grids accordingly
• Recursively repeat for each of the two sub-grids
  with alternating axes

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Quadtree Partitioning Example
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View control

• The challenge is to try and fit all lit items in
  the display at a given time
• To make orientation easier we want Items to stay
  fixed at global location
• So instead a camera must move across the grid to
  capture temporarily lit items

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Camera control

• We employ a naïve solution
• In a given time calculate a weighted average of
  icon position by their luminance
• The resulting expectancy is the temporary center
  of density
• The camera then moves to this center

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Camera movement

• Center of density usually shifts gradually over
  time
• luminance changes gradually so expectancy changes
  smoothly as well
• Embedding in space groups together
  temporarily/consequentially lit items
• But sometimes camera moves a long distance
• So play rate is always kept inversely
  proportional to distance of camera to target

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Interactivity

• User can control animation play rate and can seek
  in time
• Mouse-clicking icons constraints the animation to
  show only frames where selected icons appear lit
  together

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Results

• Demo (Adobe Flash)
• http//www.cs.tau.ac.il/research/chen.goldberg/vis
  ualization/final/
• We demonstrate four datasets
• NASDAQ (100 items)
• Move Stars (50 items)
• Netflix (500 items)
• Facebook (160 items)

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Facebook user study

• To test the effectiveness of our method we
  created Cliqster, a Facebook application which
  utilized the proposed visualization method
• Cliqster allows Facebook users to visualize
  friendship information between their friends

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Feedback

• Overall about 100 users installed Cliqster
• Mostly CS student
• Reception was largely positive
• All users confirmed that the visualization
  accurately depicts the clique structures
• Initially many users didnt understand what was
  going on
• We added a toy example visualizing social
  affinity in The Simpsons television series
• Accompanied with a caption Cliques (groups of
  friends) appear lit together

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More feedback

• Common complaints
• Some friends never appear lit
• Sometimes non-friends do appear lit together
• Animation is too slow/fast, and other control
  issues
• Only later we enables users with finer control
  management
• Why is this information interesting

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Variations

• Alternatives to embedding in time
• NMF Sort
• K-means
• Fuzzy K-means
• Alternative to embedding in space
• Luminance and depth
• Animating a graph
• Animating parallel coordinates

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Conclusion

• Presented an intuitive new technique for
  visualizing proximity information
• Free from the problems of low-dimensionality by
  expanding into the time domain
• Spatial limitations still impose a problem and
  the addition of camera movement may hinder
  perception.
• Embedding in time can be easily and effectively
  incorporated in many existing static
  visualizations

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Thank you for your attention