Using Space Effectively

Transcription

1 CS448B :: 8 Nov 2012 Using Space Effectively Space is the most important encoding. Use it to support spatial reasoning. Jeffrey Heer Stanford University Topics Displaying data in graphs Aspect ratio selection Zoomable displays Focus + context and spatial distortion Graphical calculation Displaying Data in Graphs 1

2 Effective use of space Which graph is better? Axis bounds Yearly CO2 concentrations [Cleveland 85] Government payrolls in 1937 [How To Lie With Statistics. Huff] Clearly mark scale breaks Scale break vs. Log scale Poor scale break [Cleveland 85] Well marked scale break [Cleveland 85] [Cleveland 85] 2

3 Scale break vs. Log scale Linear scale vs. Log scale MSFT Both increase visual resolution Log scale - easy comparisons of all data Scale break more difficult to compare across break MSFT Linear scale vs. Log scale Linear scale Absolute change Semilog graph: Exponential growth Exponential functions (y = ka mx ) transform into lines log(y) = log(k) + log(a)mx Intercept: log(k) Slope: log(a)m 10 0 MSFT Log scale Small fluctuations Percent change d(10,20) = d(30,60) MSFT y = 6 0.5x, slope in semilog space: log(6)*0.5 =

4 Semilog graph: Exponential decay Exponential functions (y = ka mx ) transform into lines log(y) = log(k) + log(a)mx Intercept: log(k) Slope: log(a)m Log-Log graph Power functions (y = kx a ) transform into lines Example - Steven s power laws: S = ki p log S = log k + p log I Intensity log(sensation) 1 Sensation 10 y = 0.5 2x, slope in semilog space: log(0.7)*2 = log(intensity) [The Elements of Graphing Data. Cleveland 94] [The Elements of Graphing Data. Cleveland 94] 4

5 [The Elements of Graphing Data. Cleveland 94] [The Elements of Graphing Data. Cleveland 94] Transforming data How well does curve fit data? Residual graph Plot vertical distance from best fit curve Residual graph shows accuracy of fit [Cleveland 85] [Cleveland 85] 5

6 Design Parameters Given a visual encoding (e.g., line chart), what aspects might affect graphical perception? Physical Size Aspect Ratio Ticks, Labels, Gridlines Line Width Data Points (e.g., dots) How might we determine optimal choices? William S. Cleveland The Elements of Graphing Data Banking to 45 [Cleveland] Aspect Ratio Selection To facilitate perception of trends, maximize the discriminability of line segment orientations Two line segments are maximally discriminable when their average absolute angle is 45 Optimize the aspect ratio to bank to 45 6

7 Aspect-Ratio Banking Techniques Median-Absolute-Slope α = median si Rx / Ry Has Closed Form Solution Average-Absolute-Slope α = mean si Rx / Ry An alternate approach: Minimize arc length (hold area constant) Average-Absolute-Orientation Unweighted i( ) θ α = 45 i n Weighted i θi( α) li( α) = 45 l ( α) i i Max-Orientation-Resolution Global (over all i, j s.t. i j) 2 θi( α) θj( α) i j Local (over adjacent segments) i θ ( α) θ ( α) i i+ 1 Requires Iterative Optimization 2 Straight line -> 45 deg Ellipse -> Circle [Talbot et al, 2011] Parameterization invariance Robustness: banking y = 1 / x Weighted by length Not weighted by length [Talbot et al, 2011] [Talbot et al, 2011] 7

8 Compromise Arc-length banking produces aspect ratios in-between those produced by other methods. Discussion Arc-length banking preferable to prior methods - Parameterization invariant - Robust (handles corner cases, gives compromise results) - Applicable to both plotted curves and contour lines - Fast to compute (fast-converging iterative optimization) But what about perceptual effectiveness? We lack theory to deeply motivate aspect ratio selection [Talbot et al, 2011] Perceptual experiments needed to assess? Multi-Scale Banking Goal Optimized aspect ratios for varying data scales Aspect Ratio = 1.17 Aspect Ratio = 7.87 CO 2 Measurements William S. Cleveland Visualizing Data Approach Identify Scales of Interest Generate Scale-Specific Trend Lines Bank Trend Lines to Optimized Aspect Ratios Filter Redundant Aspect Ratios 8

9 Multi-Scale Banking Idea: Use Spectral Analysis to identify trends Find strong frequency components Lowpass filter to create trend lines Other trend-identification methods? Regression methods Wavelet analysis Compute Power Spectrum Original Data Power Spectrum Take Discrete Fourier Transform Compute squared magnitudes Smooth the Spectrum Threshold the Spectrum Convolve with Gaussian filter window size = 3, σ = 1 Threshold at µ + kσ (k=0 by default) Retain last values of contiguous runs Smoothed Power Spectrum Power Spectrum Smoothed Thresholded Power Spectrum 9

10 Generate Trend Lines Bank Trend Lines to 45 Trend Lines Thresholded Power Spectrum Generate trend lines with lowpass filter Trend Lines Aspect Ratios Bank each trend line to 45 Filter Aspect Ratios Sunspot Cycles Yearly values Filter similar aspect ratios Keep if α i+1 > cα i (c=1.25 by default) Aspect Ratio = 4.23 Aspect Ratio = Filtered Aspect Ratios Aspect Ratios Power Spectrum Aspect Ratios 10

11 CO 2 Monthly concentrations from the Mauna Loa Observatory, Aspect Ratio = 1.17 Administrivia Aspect Ratio = 7.87 Power Spectrum Aspect Ratios Final Project Design a new visualization system or technique Many options: new system, interaction technique, design study 6-8 page paper in conference paper format 2 Presentations: in-class report & final poster session Schedule Project Proposal: Thursday, Nov 8 (end of day) In-Class Presentation: Tuesday, Nov 27 Poster Presentation: Tuesday, Dec 11 (5-7pm) Final Papers: Wednesday, Dec 12 (end of day) Logistics Groups of 2 to 4 people, graded individually Clearly report responsibilities of each member Final Project Ideas Read the Final Project Wiki Page! Also follow the links for suggested projects. A number of domain experts have provided project ideas and are excited to collaborate with you. We strongly encourage you to consider working in a partnership with a domain expert, especially if you have difficulty formulating a problem-focused project idea. Unsure? Come to office hours or schedule an appointment to discuss project ideas. 11

12 Final Project Proposal Deliverables Form project group (2-4 people) Create project wiki page Post project abstract (1-2 paragraphs) Should clearly state the problem, relevance & planned solution Start your related work search now to inform your proposal Zooming Due Thur Nov 8 (by end of day) Zooming Overview + Detail Eames Powers of Ten [ [Hornbaek et al. 2002] 12

13 Interactive Zooming Pad++ Play video Pad++ [Bederson and Hollan 94] Semantic Zooming Change representations as zoom level changes Speed-Dependent Zooming Integrate Pan and Zoom into single interation Automatically zoom to maintain optical flow Semantic zooming can simplify zoomed-out view PAD [Perlin and Fox 93] [Igarashi 00] 13

14 Halo [Baudisch 03] Focus + Context 14

15 Degree-of-Interest [Furnas 81, 06] TableLens [Rao & Card 94] Estimate the saliency of information to display Can affect what is shown and/or how to show it DOI ~ f(current Focus, A Priori Importance) Example: Google Search Current Focus = Query Hits (e.g., TF.IDF score) A Priori Importance = PageRank What: Top N results, How: List DateLens Single view focus + context Focus area local details De-magnified area surrounding context Like a rubber sheet with borders tacked down Nonlinear Magnification Infocenter [ [Bederson et al. 04] 15

16 Bifocal display [Leung and Apperley 94] Multifocal display [Leung and Apperley 94] 2D distortion Fisheye [Leung and Apperley 94] States as nodes in a graph 1D 2D Polar Graphical fisheye views of graphs [Sarkar & Brown 92] 16

17 Nonlinear magnification [Leung and Apperley 94] Perspective wall 1D 2D Multifocal Perspective allows more context Uses (and abuses) of distortion Often more harm than help, unless Builds on experience (e.g., perspective wall) and enables a particular task Intended to elicit response, capture attention In which case it should draw attention directly to the phenomenon of interest. Pan and zoom more familiar and visually stable than rubber sheet Consider F+C of data rather than view Perspective Wall [Mackinlay et al. 91] 17

18 Graphical Calculation Lambert s graphical construction Nomograms Johannes Lambert used graphs to study the rate of water evaporation as function of temperature [from Tufte 83] Sailing: The Rule of Three 18

19 Nomograms Slide rule 1. Compute in any direction; fix n-1 params and read nth param 2. Illustrate sensitivity to perturbation of inputs 3. Clearly show domain of validity of computation Model Electrotechnica 18 Scales Tehnolemn Timisoara Slide Rule Archive Chi-square test (Obs Exp) 2 / Exp Blue line: (9-5) 2 / 5 = 3.2 Red line: (81-70) 2 / 70 =

20 Summary Spatial layout is the most important encoding but you need to be in the right space. Geometric properties of spatial transforms support geometric reasoning Emphasize important information Consider what to show, not just how 20