Visual Abstraction and Exploration of Multi-class Scatterplots Haidong Chen, Wei Chen, Honghui Mei, Zhiqi Liu, Kun Zhou, Weifeng Chen, Wentao Gu, Kwan-Liu Ma

Motivations Multi-class scatterplots Aid comparison Make relative judgments

Motivations Multi-class scatterplots Aid comparison Make relative judgments Challenges Severe point overdraw

Motivations Multi-class scatterplots Aid comparison Make relative judgments Challenges Severe point overdraw Drawn order dependent

1. Existing Techniques Density Estimation Changing the Visual Channels Spatial Distortion Interactions

1. Existing Techniques a) Woodruff et al., 1998 d) Choo et al., 2013 c) Dan et al., 2010 b) Chen et al., 2009 a) Constant density visualizations of non-uniform distributions of data b) A novel interface for interactive exploration of DTI fibers c) Stacking graphic elements to avoid over-plotting d) Utopian: User-driven topic modeling based on interactive nonnegative matrix factorization Density Estimation Changing the Visual Channels Spatial Distortion Interactions

1. Existing Techniques b) Feng et al., 2010 a) Bachthaler et al., 2008 c) Mayorga et al., 2013 a) Continuous Scatterplot b) Matching Visual Saliency to Confidence in Plots of Uncertain Data c) Splatterplots: Overcoming Overdraw in Scatter Plots Density Estimation Changing the Visual Channels Spatial Distortion Interactions

1. Existing Techniques a) Keim et al., 1998 b) Keim et al., 2009 c) Janetzko et al., 2013 a) The Gridfit Algorithm: An Efficient and Effective Approach to Visualizing Large Amounts of Spatial Data b) Generalized scatter plot c) Enhancing scatter plots using ellipsoid pixel placement and shading Density Estimation Changing the Visual Channels Spatial Distortion Interactions

1. Existing Techniques a) Buring, et al., 2006 b) Yuan, et al Zooming Focus + Context Brushing Fisheye Dragging a) User interaction with scatterplots on small screens-a comparative evaluation of geometric-semantic zoom and fisheye distortion b) Dimension projection matrix/tree: Interactive subspace visual exploration and analysis of high dimensional data Density Estimation Changing the Visual Channels Spatial Distortion Interactions

2. Our Solution – Overview Point Density EstimationPoint Resampling Interactive ExplorationColor OptimizationShape Design

2. Our Solution – Visual Abstraction Point Density EstimationPoint Resampling Interactive ExplorationColor OptimizationShape Design

Point Resampling Background for multi-class blue noise sampling r Single-Class sampling r : minimum distance away from each other Multi-Class sampling r 00 Rx =Rx = r 01 r 02 Class 0 Class 1 Class 2 r 10 r 11 r 12 r 20 r 21 r 22 [Wei et al., 2010] r 01 r 10

Point Resampling Sampling spaces The input scatterplotContinuous sampling

Point Resampling Sampling spaces The input data pointsContinuous samplingDiscrete sampling

Point Resampling Zooming inconsistency Resampling once the view zoomed Zoom in Coarse zooming level Fine zooming level

Point Resampling Hierarchical sampling Coarse zooming level Zoom in: New points are added Fine zooming level Zoom out: New points are removed Coarse zooming level Samples generated at coarse zooming levels Samples generated at fine zooming levels The Core Idea: Using samples generated in previous coarse levels as anchor points to constrain sampling at a fine level The Core Idea: Using samples generated in previous coarse levels as anchor points to constrain sampling at a fine level

2. Our Solution – Abstractive Visualization Point Density EstimationPoint Resampling Interactive ExplorationColor OptimizationShape Design

Abstractive Visualization Point color optimization Color set in the CIELAB color space: Objective function: : the account of the divided blocks : the inter-class weight for the m-th block : the intra-class weight for the m-th block Color distance constraint:

Abstractive Visualization Point shape design Orientation of the shape:: the local linear regression coefficients Ellipse Dot-Line

2. Our Solution – Interactive Exploration Point Density EstimationPoint Resampling Interactive ExplorationColor OptimizationShape Design

The Exploration System Interaction tools: Highlighting Selection Painting Brushing Annotations Snapshot

3. Comparison Conventional multi-class scatterplot Splatterplots [ Mayorga et al., 2013 ] Splatterplots enhanced with additional noise Ours Point count in the selected region before abstraction: #(■) = 464 #(■) = 1796 #(■) = 2756 Point count in the selected region after abstraction: #(■) = 4 #(■) = 27 #(■) = 41 Density order before abstraction: #(■) < #(■) < #(■) Density order after abstraction: #(■) < #(■) < #(■) Relative density orders are preserved by our method

4. Evaluations Case studies The NBA Teams’ Shooting Positions Dataset in the Season 382,779 Mobile User Profile Dataset in a Month User study 32 synthetic and real datasets

4. Evaluations – Case Study I Conventional Multi-class Scatterplot Ours

4. Evaluations – Case Study II Conventional Multi-class ScatterplotOurs Dot-line Representation total-call-charge total-talk-time

4. Evaluations – User Study Profiles of the 32 datasets tested in our user study Compared schemes the conventional scatterplots (C) the color blending method (CB) the color weaving method (CW) our method (OURS) Participants 26 (19 males, 7 females) Tasks T1 Data classes identification T2 Relative densities recognition Datasets

4. Evaluations – User Study Results of scores for each task Tasks: T1 Data classes identification T2 Relative densities recognition

5. Conclusions and Future Work Conclusions A new visual abstraction approach for multi-class scatterplot

5. Conclusions and Future Work Conclusions A new visual abstraction approach for multi-class scatterplot A visual exploration system

5. Conclusions and Future Work Conclusions A new visual abstraction approach for multi-class scatterplot A visual exploration system Future Work A sophisticated point color optimization model

5. Conclusions and Future Work Conclusions A new visual abstraction approach for multi-class scatterplot A visual exploration system Future Work A sophisticated point color optimization model A non-uniform sampling scheme Conventional multi-class scatterplot Ours

Visual Abstraction and Exploration of Multi-class Scatterplots Different multi-class scatterplot schemes for the Person Activity dataset. (a) The conventional scatterplot. (b) The Splatterplots. (c) The Splatterplots with additional noise. (d) Our method.