CS171 Visualization Alexander Lex alex@seas.harvard.edu Tables - - PowerPoint PPT Presentation

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CS171 Visualization Alexander Lex alex@seas.harvard.edu Tables - - PowerPoint PPT Presentation

Oct 17, 2022 266 likes •999 views

CS171 Visualization Alexander Lex alex@seas.harvard.edu Tables Part II [xkcd] Next Week Reading: VAD, Chapters 9 Lecture 11: Text & Documents Lecture 12: Homework 3 Design Studio Sections: view coordination, linking & brushing

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CS171 Visualization

Alexander Lex alex@seas.harvard.edu

[xkcd]

Tables Part II

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Next Week

Reading: VAD, Chapters 9 Lecture 11: Text & Documents Lecture 12: Homework 3 Design Studio Sections: view coordination, linking & brushing Updates

Design Studio moved to Thursday Project Proposal moved to HW 4

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Tables & Multi- Dimensional Data

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Comparisons

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Direction

Nicolas Rapp

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Plot Change Instead

https://eagereyes.org/basics/baselines

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Trends Over Time

http://xkcd.com/605/

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Bars vs. Lines

Lines imply connections & 
 sampling from continuous data. Do not use for categorical 
 data.

Zacks 1999

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SLIDE 9

Baseline Problem (again)

https://eagereyes.org/basics/baselines

True Baseline Clipped Baseline Plotting Change

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Linear vs. Logarithmic Scale

Linear Scale Log Scale

http://finance.yahoo.com/echarts?s=AAPL

Apple Stock Price

http://xkcd.com/1162/

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Aspect Ratios

Rule of Thumb: Banking to 45º (average line 
 slope: 45º)

eagereyes.org

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Correlations

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Scatterplots

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Overplotting

alpha = 1/100

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Compositions

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Stacked Bar Chart

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Comparison of bar chart types

Small 
 Multiples Stacked bar chart Pie Chart Layered
 Bar
 Chart Grouped
 Bar 
 Chart

Streit & Gehlenborg, PoV, Nature Methods, 2014

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Stacked Area Chart

http://stackoverflow.com/questions/2225995/how-can-i-create-stacked-line-graph-with-matplotlib

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100% Stacked Area Chart

http://stackoverflow.com/questions/16875546/create-a-100-stacked-area-chart-with-matplotlib

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Stacked Area vs. Line Graphs

leancrew.com & Practically Efficient

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Distributions

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Histogram

#bins hard to predict make interactive! rule of thumb: #bins = sqrt(n)

10 Bins 20 Bins age age # passengers # passengers

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Box Plots

aka Box-and-Whisker Plot Wikipedia

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Comparison

Streit & Gehlenborg, PoV, Nature Methods, 2014

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Showing Expected Values & Uncertainty

Error Bars Considered Harmful: Exploring Alternate Encodings for Mean and Error Michael Correll, and Michael Gleicher

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Highdimensional Data

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What is High-dimensional Data?

Tabular data, containing

rows (items) columns (attributes or items) rows >> columns Age Gender Height Bob 25 M 181 Alice 22 F 185 Chris 19 M 175

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High-Dimensional Data Visualization

How many dimensions?

~50 – tractable with “just” vis ~1000 – need analytical methods

How many records?

~ 1000 – “just” vis is fine >> 10,000 – need analytical methods

Homogeneity

Same data type? Same scales?

Age Gender Height Bob 25 M 181 Alice 22 F 185 Chris 19 M 175 BPM 1 BPM 2 BPM 3 Bob 65 120 145 Alice 80 135 185 Chris 45 115 135

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Analytic Component

no / little analytics strong analytics 
 component

Scatterplot Matrices


[Bostock]

Parallel Coordinates


[Bostock]

Pixel-based visualizations /
 heat maps Multidimensional Scaling

[Doerk 2011] [Chuang 2012]

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Geometric Methods

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Parallel Coordinates (PC)

Axes represent attributes Lines connecting axes represent items

Inselberg 1985

A B X Y X Y A B A B

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Parallel Coordinates

Each axis represents dimension Lines connecting axis represent records Suitable for

all tabular data types heterogeneous data

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PC Limitation: 
 Scalability to Many Dimensions

500 axes

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PC Limitation: Scalability to Many Items

Solutions:

Transparency Bundling, Clustering Sampling

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PC Limitations 


Correlations only between adjacent axes

Solution: Interaction

Brushing Let user change order

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PC Limitation: 
 Ambiguity

Solutions:

Brushing Curves

Graham and Kennedy 2003

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Parallel Coordinates

Shows primarily relationships between adjacent axis Limited scalability (~50 dimensions, ~1-5k records)

Transparency of lines

Interaction is crucial

Axis reordering Brushing Filtering

Algorithmic support: Choosing dimensions Choosing order Clustering & aggregating records

http://bl.ocks.org/jasondavies/1341281

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Star Plot

Similar to parallel coordinates Radiate from a common origin

[Coekin1969]

http://www.itl.nist.gov/div898/handbook/eda/section3/starplot.htm http://start1.jpl.nasa.gov/caseStudies/autoTool.cfm

http://bl.ocks.org/kevinschaul/raw/8833989/

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Multiple Line Charts

http://square.github.io/cubism/

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Combining Various Charts

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Scatterplot Matrices (SPLOM)

Matrix of size d*d Each row/column is one dimension Each cell plots a scatterplot of two dimensions

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Scatterplot Matrices

Limited scalability (~20 dimensions, ~500-1k records) Brushing is important Often combined with “Focus Scatterplot” as F+C technique Algorithmic approaches: Clustering & aggregating records Choosing dimensions Choosing order

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SPLOM Aggregation - Heat Map

Datavore: http://vis.stanford.edu/projects/datavore/splom/

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SPLOM F+C, Navigation

[Elmqvist]

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Flexible Linked Axes (FLINA)

Claessen & van Wijk 2011

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Web-based implementation of 
 FLINA concept

http://vis.pku.edu.cn/mddv/val/ ¡

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Connected Charts

Viau ¡& ¡McGuffin ¡2012 ¡

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  • rigin

ARTISTS Australia Europe North America studio albums WcountH continent first album WyearH number one hits

5 Countries 5 Artists

start of career WyearH career status in business at first album inactive gender gender ∩ inactive sold albums WabsoluteH COUNTRIES population WmillionH Barbados Ireland Sweden UK US

Rihanna U2 ABBA Elton John The Beatles Whitney Houston The Black Eyed Peas Britney Spears Eminem Michael Jackson Madonna Elvis Presley Australia France Italy Sweden Span Austria Germany Netherlands Ireland UK US Canada

inactive active male group female

Artists Countries 12 12 1

Domino

Gratzl ¡et ¡al. ¡2014 ¡

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Data Reduction

Sampling

Don’t show every element, show a (random) subset Efficient for large dataset Apply only for display purposes Outlier-preserving approaches

Filtering

Define criteria to remove data, e.g.,

minimum variability > / < / = specific value for one dimension consistency in replicates, …

Can be interactive, combined with 
 sampling

[Ellis & Dix, 2006]

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Filter Example

http://square.github.io/crossfilter/

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Pixel Based Methods

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Pixel Based Displays

Each cell is a “pixel”, value 
 encoded in color / value Meaning derived from ordering If no ordering inherent, 
 clustering is used Scalable – 1 px per item Good for homogeneous data

same scale & type

[Gehlenborg & Wong 2012]

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3D Pitfall: Occlusion & Perspective

[Gehlenborg and Wong, Nature Methods, 2012]

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3D Pitfall: Occlusion & Perspective

[Gehlenborg and Wong, Nature Methods, 2012]

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Heterogeneous Data?

[Verhaak 2012]

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Bad Color Mapping

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Good Color Mapping

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Color is relative!

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Clustering

Classification of items into “similar” bins Based on similarity measures

Euclidean distance, Pearson correlation, ...

Partitional Algorithms

divide data into set of bins # bins either manually set (e.g., k- means) or automatically determined (e.g., affinity propagation)

Hierarchical Algorithms Produce “similarity tree” – dendrogram Bi-Clustering Clusters dimensions & records Fuzzy clustering allows occurrence of elements in multiples clusters

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Clustering Applications

Clusters can be used to

  • rder (pixel based techniques)

brush (geometric techniques) aggregate

Aggregation

cluster more homogeneous than whole dataset statistical measures, distributions, etc. more meaningful

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Clustered Heat Map

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F+C Approach, with Dendrograms

[Lex, PacificVis 2010]

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Cluster Comparison

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Aggregation

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Design Critique

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EdgeMaps: http://goo.gl/q8Cv7t

http://mariandoerk.de/edgemaps/demo/#music

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Dimensionality Reduction

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Dimensionality Reduction

Reduce high dimensional to lower dimensional space Preserve as much of variation as possible Plot lower dimensional space Principal Component Analysis (PCA)

linear mapping, by order of variance

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PCA Example – CS 171 Project 2013

[Mercer & Pandian] http://mu-8.com/

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Multidimensional Scaling

Nonlinear, better suited for some DS Popular for text analysis

[Doerk 2011]

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Can we Trust Dimensionality Reduction?

http://www-nlp.stanford.edu/projects/dissertations/browser.html

Topical distances between departments in a 2D projection Topical distances between the selected Petroleum Engineering and the others.

[Chuang et al., 2012]