OVERVIEW OF DATA VISUALIZATION

Definitions

• Visualization is the graphical presentation of information, with the goal of providing the viewer with a qualitative understanding of the information contents.
• Information may be data, processes, relations, or concepts.
• Graphical presentation may entail manipulation of graphical entities (points, lines, shapes, images, text) and attributes (color, size, position, shape).
• Understanding may involve detection, measurement, and comparison, and is enhanced via interactive techniques and providing the information from multiple views and with multiple techniques.

Characteristics of Data

• Numeric, symbolic (or mix)
• Scalar, vector, or complex structure
• Various units
• Discrete or continuous
• Spatial, quantity, category, temporal, relational, structural
• Accurate or approximate
• Dense or sparce
• Ordered or non-ordered
• Disjoint or overlapping
• Binary, enumerated, multilevel
• Independent or dependent
• Multidimensional
• Single or multiple sets
• May have similarity or distance metric
• May have intuitive graphical representation (e.g. temperature with color)
• Has semantics which may be crucial in graphical consideration

What is the dimension of data?

f(x, y) -> (t, p)

f1(x, y) -> t, f2(x, y) -> p

f3(x, y, t) -> 0 or 1, f4(x, y, p) -> 0 or 1

f5(x, y, t, p) -> 0 or 1

The key is that the mapping must go to a single value (or vector), e.g. f(x, t) -> 0 or more values of elements with position x and temp t, therefore losing information (e.g. hidden surfaces in projection). This is OK for statistics (e.g. histogram).

Graphical entities and attributes

• Entity: point, line, polyline, glyph, surface, solid, image, text
• Attribute: color/intensity, location, style, size, relative position/motion

What do we see and how well do we see it?

• Different viewers perceive different graphical/spatial/color in different degrees
• Context varies our sensitivity
• According to one researcher (Cleveland), in increasing inaccuracy
  1. Position along a common scale
  2. Position along identical, non-aligned scales
  3. Length
  4. Angle/slope
  5. Area
  6. Volume
  7. Hue/saturation/intensity (informally derived)
• Weber's law - detection is proportional to percent change, not scale
• Stevens' law - perceived scale is proportional to a power of the actual scale. power is .9 - 1.1 for length, .6 - .9 for area, .5 - .8 for volume

What makes a good visualization?

• Effective: the viewer gets it (ease of interpretation)
• Accurate: sufficient for correct quantitative evaluation. Lie factor = size of visual effect/size of data effect
• Efficient: minimize data-ink ratio and chart-junk, show data, maximize data-ink ratio, brase non-data-ink, brase redundant data-ink
• Aesthetics: must not offend viewer's senses (e.g. moire patterns)
• Adaptable: can adjust to serve multiple needs

Mapping data to graphics

• Examine cardinality of dimension with detectible variations in graphics (see below for evaluation under human perception)
• Use scaling and offset to fit in range
• Use derived values (residuals, logs) to emphasize changes
• Use projections, other combinations, to compress information, get statistics
• Use random jiggling to separate overlaps
• Use multiple views to handle hidden relations, high dimensions
• Use effective grids, keys and labels to aid understanding

Interacting with the data

• Dynamically adjust mapping
• Tour data by varying views
• Labeling to get original data
• Deleting to eliminate clutter
• Brushing/Highlighting to see correspondence in multiple views
• Zooming to focus attention
• Panning to explore neighborhoods

Common Techniques

• Charts: bar or pie
• Graphs: good for structure, relationships
• Plots: 1- to n-dimensional
• Maps: one of most effective
• Images: use color/intensity instead of distance (surfaces)
• 3-D surfaces and solids
• isosurfaces/slices
• translucency
• stereopsis
• animation