• How are visualizations perceived by different humans?
• How do we know that a given visualization is correctly interpreted?

Perception:

• Recognizing
• Organizing (gathering, storing)
• Interpreting (binding to knowledge)

• Human perceptual system is not perfect

• Preattentive
  • Fast (250 ms)
  • Performed in parallel
• Attentive
  • Slow
  • Uses short term memory
  • Transforms simple visual features into structured objects
  • Compares to memory models (ex. door)

• Preattentive feature= shape
• How quickly do you see a red circle?

• Important: Combination (conjuction) of nonunique features can not be detected preattentively
  • Many red objects
  • Many circle objects
• How quickly can you find a unique object here?

• Length
• Width
• Size
• Curvature (shape)
• Hue
• Intensity
• Flicker
• Direction of motion
• 3D depth
• Lighting direction

• Presense or absense of object with a unique visual feature among distractors is detected preattentively
• Boundary between two groups of elements with the same visual feature is detected preattentively
• Movement of an object with a unique visual feature is tracked preattentively
• Amount of elements with a unique visual feature is estimated preattentively

• A figure is processed in parallel by checking individual feature maps
• A specific preattentive task is performed in each feature map
• Conjuction of features requires searial search between maps - takes time

• How quickly can you identify a boundary?

• What graphical features can be accurately perceived by humans?
• How many distinct entities can be visualized without confusion?
• How should we use color?
• How should we combine features in a complex phenomenon?

Channel capacity: how many different levels of a feature we can perceive

• 8 levels = 3 bits

• Position on a line: 10-15 levels (3.25 bits)
• Size of squares: 4-5 levels (2.2 bits)
• Color: hue 10 levels, brightness: 5 levels (3.1 bits, 2.1 bits)
• Line length: 2.8 bits
• Line orientation: 3 bits
• Line curvature: 1.6-2.2 bits

Summary: 6-7 unique values max.

Note: Combining metrics does not sum up the capacity!…

• Hue and saturation: 3.6 bits
• Size, brightness and hue: 4.1 bits
• Position in a square: 4.6 bits

Relative judgement: comparing two values of a feature

Errors (in increasing order)

• Position along a common scale
• Length
• Angle
• Area
• Volume
• Color hue

–> Pie charts are less effective than Bar Charts

• Use intuitive mapping to aesthetics
  • Visualization type is adopted to user's background
  • Geographical coordinates –> X,Y, temperature–>color
  • Use correct mapping
    • Ordinal variables- X,Y, saturation, orientation
    • Nominal variables - shape, texture, hue
• Support view modifications
  • Scrolling, zooming
  • Color map
  • Mapping aesthetics
  • Scales
  • Level of details

• Do not put too much information in the display (occlusion)
• Add keys, labels, legends, grids with care
• Use display efficiently (0%-100% scale vs actual domain)

Color:

• Keep the number of colors low (5-6 distinct)
• Use redundant mappings (color+size)
• Include labeled color key
• Use resonant colors

Aesthetics:

• Important findings should be visually emphasized
• Most important components in the center
• Do not put much information into one display

Other:

• The size of the plot should be normally Horizontal:Vertical=1.5:1
• Text in the graph is normally horizontal
• Caption and Source should be present and informative
• In bar charts, bars are normally sorted
• Axis labels present

• Scaling and perspective problem

• Scaling and perspective problem

Abusing dimensionality/wrong mapping

• A scalar is mapped to a size of a cube
• Mapping is wrong: a scalar is mapped to radius, not area
  • R1=2R2, A1=4A2 !

• Mixing data of different nature/scales
  • Ex: One time series plots with two series: Price and Amount both on Y axis
• Smoothed/filtered data interpreted as raw data
  • How good was the smoothing?
• Using of insufficient sampled data

• Quantiative variable:
  1. Computing summaries (ex. frequencies)
  2. Visualizing as bar or pie charts
• What to analyse:
  • Largest and smallest bar or slice
  • For sorted bars, sudden shifts in level
  • Compare first within groups and then difference between groups

Example: Visualizing number of gears and number of cylinders in cars

• Dimension reduction
  • PCA
  • MDS
  • Correspondence analysis (nominal)
  • Other techniques (ex. ICA, Autoencoders), welcome to Machine Learning course..

• Meaning of "two objects are close"?

• Measure of proximity (ex: quantiative vars, Euclidian distance)

• Similarity measure \(s_{rs}\) (=1 if same object, <1 otherwise)
  • Ex: correlation
• Dissimilarity measure \(\delta_{rs}\) (=0 if same object, >0 otherwise)
  • Ex: euclidian distance
• Problem of cosntructing the measures of proximity:
  • What if the variable is qualitative?
  • What if the object is a text document?

Given \(n\) objects with known matrix of similarities or dissimilarities. Each object \(i\) is characterized by \(p\)-dimensional vector \(X_i\)

• Present these objects in lower dimensions (\(p'=2\) or 3) such that the distance between the new points \(d_{rs}\) would reflect the matrix of similarities (or dissimilarities \(\delta_{rs}\))
• See neighbour observations
• See clusters and outliers
• Have a "map" of your data

Two types of MDS:

• Metric MDS
• Non-metric MDS

(algorithm is not discussed here)

Seaching for points \(\chi_1, \ldots, \chi_n\), such that distances between \(||\delta_{rs}||\) and \(||d_{rs}||\) are minimized

Given \(n\) objects \(X_1, \ldots, X_n\) with known matrix of similarities \(||\delta_{rs}||\) of dissimilarities.

For some configuration \(\chi_1, \ldots, \chi_n\) (in lower dimension) with matrix \(||d_{rs}||\) , define stress \(S(\chi_1, \ldots, \chi_n)\) by

1. Computing \(d'_{rs}\) as a a monotonic regression of \(||d_{rs}||\) on \(||\delta_{rs}||\)
2. Computing \(S=\sqrt{\frac{\sum_{r,s} \left(d_{rs}-d'_{rs}\right)^2)}{\sum_{r,s} d^2_{rs}}}\)

How to find optimal configuration?

• Use numeric optimization to minimize \(S(\chi_1, \ldots, \chi_n)\)

• Artist (abba. Beatles. Wiwaldi, Mozart, Beethoven, Enya)
• Type (rock, classical, new wave)
• lvar, lave, lmax, lfener, lfreq - parameters of the music signal

• Mapping into two dimensions and using scatterplot

• Mapping into three dimensions, coloring by Artist and using 3D-scatter:

• Plot of \(d_{rs}\) vs \(\delta_{rs}\)
• Displays also \(\delta'_{rs}\) for non-metric MDS
• Shows the quality of MDS fit-> Best if scatter reminds a monotonic curve

• Book, chapters 3.1, 3.3, 3.5, 13
• Cox, AA, and Cox, T.F.: "Multidimensional scaling." Handbook of data visualization. Springer, Berlin, Heidelberg, 2008. 315-347.
• Plotly book, ch 2.3