[Data Visualization] What - Data Abstraction

The Big Picture

• What data does the user see? (data abstraction)
• Why does the user use the system? (task abstraction)
• How are the visual encoding and interaction idioms constructed? (idiom abstraction)

What - Data Abstraction

Why Data Abstraction?

• There are an infinite number of datasets.
• Thus, it would be inefficient to design a visualization system for every dataset.
• We will categorize and characterize data types that a visualization system aims to visualize.
• Insights gained from such analysis can be used to design a visualization system in the future.

Why Data Semantics and Types?

1, 4.5, -3, 10001, 2, 0

• What does this sequence of six numbers mean?
• Multiple interpretations are possible.

Basil, 7, S, Pear

• Same for this record

• The type of the data is its structural or mathematical interpretation.
• The semantics of the data is its real-world meaning.
• Metadata: additional data required for correctly interpreting data
  • Types
  • Semantics
  • Syntax of a data file (e.g., CSV, TSV, or JSON)

Data, Dataset, and Attributes

• We will learn three concepts: data types, dataset types, and attribute types.
• Data types: what kind of thing is the data?
  • e.g., an item, a link, or an attribute
• Dataset types: how are these data types combined into a larger structure?
  • e.g., a table, a tree, or a field of sampled values
• Attribute types: what kinds of mathematical operations are meaningful for an attribute?
  • e.g., quantity, category, $\dots$

Data Types

• Five Basic Data Types: Items, Attributes, Links, Positions, and Grids
• An item is an individual entity that is discrete.
  • e.g., a row in a simple table or a node in a network.
• An attribute is some specific property that can be measured, observed, or logged.
  • Sometimes, called variable or dimension
  • e.g., salary, price, or number of sales
• A link is a relationship between items typically within a network.
  • e.g., marriage relationship
• A grid specifies the strategy for sampling continuous data in terms of both geometric and topological relationships between its cells.
• A position is spatial data, providing a location in two-dimensional (2D) or three-dimensional (3D) space.
  • e.g., a latitude–longitude pair describing a location on the Earth’s surface
  • e.g., three numbers specifying a location within the region of space measured by a medical scanner

Dataset Types

• Let’s combine these five basic data types.
• One of the most common dataset type is a table.
• A table dataset type includes item (rows) and attribute (columns) data types.
• A network dataset type consists of three data types: items (nodes), links (links), and attributes (attributes of node links).

• Four dataset types: tables, networks and trees, fields, and geometry
  • • clusters, sets, and lists

Tables

• A table is made up of rows and columns.
  • Usually, 2D
• A row represents an item.
• A column represents an attribute.
• A cell is specified by the combination of a row and a column.
  • e.g., stores a value specified by an item and an attibute.
• A multidimensional table has a more complex structure for indexing into a cell, with multiple keys.

Networks and Trees

• A network is made up of nodes and links and specifies the relationship between two or more nodes.
• Nodes and links can have attributes independently.
• Example: social network on Facebook
  • Node: accounts (people, organizations, or pages)
  • Link: friendship (or subscription)
  • Node attributes: name, photo, website_url, …
  • Link attributes: last interaction time, …

• Networks with hierarchical structure are more specifically called trees.
• In contrast to a general network, trees do not have cycles.
  • Each child node has only one parent node pointing to it.
• Networks are sometimes called graphs.
  • e.g., graph drawing and graph theory
• But, the term graphs is also used for charts.
  • e.g., bar graph and line graph
  • It is confusing. So, we will use the term charts for this

• Two popular visualizations for networks: a node-link diagram and an adjacency matrix.
• There are a lot of network visualizations!

Fields

• The field dataset type contains attribute values associated with cells.
• What is the difference between 2D tables and 2D fields?
• In a 2D field, each cell contains measurements or calculations from an continuous domain.
  • So if you want, you can draw an infinite number of measurements!
  • In a table, rows and columns are discrete.

• Consider a field dataset representing a medical scan of a human body.
  • This is a 3D field, because our body is continuous.
• We can determine the resolution of the scan (i.e., granularity)
  • A low resolution (a coarser grid): 64 * 64 * 64 cells
  • A high resolution (a finer grid): 256 * 256 * 256 cells

• Since it is impossible to measure an infinite number of cells, sampling and interpolation techniques are important in the field dataset type.
• Sampling: how frequently to take the measurements?
• Interpolation: how to show values in between the sampled points in a way that does not mislead.
• Interpolating appropriately between the measurements allows you to reconstruct a new view of the data.

• Grid geometry: the location of cells in space
• Grid topology: how each cell connects with its neighboring cells

SciVis vs InfoVis

• If we want to visualize a 2D field, an obvious choice for visual encoding would be to keep the spatialization of the data in the visualization.
  • e.g., longitude -> horizontal position, latitude -> vertical position
• Scientific visualization (SciVis) is concerned with situations where spatial position is given with the dataset.
• Information visualization (InfoVis) is concerned with situations where the use of space in a visual encoding is chosen by the designer.

Geometry

• The geometry dataset type specifies information about the shape of items with explicit spatial positions.
  • Items + positions
  • e.g., points, one-dimensional lines or curves, or 2D surfaces or regions, or 3D volumes
• e.g., cartography

Other Dataset Types

• Set: an unordered group of items
• List: an ordered group of items
• Cluster: grouping based on attribute similarity, where items within a cluster are more similar to each other than to ones in another cluster

InfoVis Subfields

• (Dataset type) + “visualization”
• Table visualization
• Network visualization
• Field visualization (usually, vector or tensor visualization in SciVis)
• Set visualization
• Cluster visualization
• $\dots$

Dataset Availability

• Any of dataset types can be static or dynamic.
• The default approach to visualization assumes that the entire dataset is available all at once, as a static file (static datasets, offline).
• Recently, it becomes more frequent to visualize dynamic datasets that change over the course of the visualization session (dynamic datasets, online).
• e.g., monitoring, …

Attribute Type

• The type of an attribute

• Categorical data do not have an implicit ordering (sometimes, nominal or qualitative).
  • But they often have hierarchy structure.
  • e.g., movie genres, file types, and city names
  • Operators: == and !=
• Ordered data have an implicit ordering.
  • Ordinal data have an ordering but artihmetic is not meaningful (e.g., shirt sizes, ranks)
  • Quantitative data have an ordering and arithmetic makes sense (e.g., length, stock prices)
  • Operators: ==, !=, >, <, and (+ and – only for quantitative data)
• Quantitative data can be further divided into two types: interval and ratio.
• In interval data, distances are meaningful but there is no absolute zero.
  • e.g., temperature in Celsius or Fahrenheit
  • Multiplication and division does not make sense. 60°C is not twice as hot as 30°C.
• In ratio data, distances are meaningful and there is an absolute zero.
  • e.g., temperature in Kelvin
  • 60°K is twice as hot as 30°K.

Summary: Attribute Types

• Categorical (sometimes nominal or qualitative): movie genres, file types, …
  • Operators: ==, !=
• Ordinal: shirt sizes, ranks, …
  • Operators: ==, !=, <, >
• Interval: temperature in Celsius, …
  • Operators: ==, !=, <, >, +, -
• Ratio: temperature in Kelvin, number of people, …
  • Operators: ==, !=, <, >, +, -, *, /

• For ordered data, we can consisder the ordering direction.
  • i.e., where is the origin?
• Sequential: there is a homogeneous range from a minimum to a maximum value, such as height.
• Diverging: data can be deconstructed into two sequences pointing in opposite directions that meet at a common zero point, such as elevation.
• Cyclic: the values wrap around back to a starting point rather than continuing to increase indefinitely, such as the day of the week.

• Color schemes for ordering directions

Semantics

• Two types of attribute semantics: key and value
• A key attribute acts as an index that is used to look up value attributes.
  • Key: your student ID
  • Value: your name
  • Keys are sometimes called independent attributes or dimensions, and values are sometimes called dependent attributes or measures.
• Types and semantics are cross-cutting.
  • A categorical attribute can be value attributes, and a quantitative attribute can be key attributes.

• Name is a categorical attribute that might appear to be a reasonable key at first.
• But it is not a good choice since there are two people (Amy) have the same name.
• The quantitative attribute of Age and the ordinal attribute of Shirt Size have many duplicates so they are not a good choice.
• ID can serve as a key attribute.

• For multidimensional tables or fields, multiple keys are required to look up an item.
  • The combination of all keys must be unique for each item, even though an individual key attribute may contain duplicates!
  • (ID, Name)
• Multidimensional: data have multiple keys.
  • one-dimensional, two-dimensional, …
• Multivariate: data have multiple values.
  • univariate, bivariate, …
• Many people do not separate these two terms but they are DIFFERENT!
  • 다차원 vs 다변량

• Suppose you measured the temperature of a 3D space.
• You have three keys: x, y, and z
• For each cell, you have one value (temperature)
• So, you have 3 dimensions and one attribute for each cell!
  • Three-dimensional univariate dataset!

• Keys: one-dimensional, two-dimensional, three-dimensional, …, multidimensional
• Values: univariate (scalar), bivariate (vector), trivariate (tensor), …, multivariate
• Measuring the wind direction at some locations in a region: twodimensional (lat and long) vector fields (the direction of the wind)
• Can you imagine a 4-dimensional univariate dataset?

Summary: Data Abstraction