Download Polaris: Query, Analysis, and Visualization of Large Hierarchical

Polaris
Query, Analysis, and Visualization
of
Large Hierarchical Relational Databases
Pat Hanrahan
With Chris Stolte and Diane Tang
Computer Science Department
Stanford University
Motivation
Large databases have become very common

Corporate data warehouses


Amazon, Walmart,…
Scientific projects:

Human Genome Project

Sloan Digital Sky Survey
Need tools to extract meaning from these databases
Related Work
Formalisms for graphics

Bertin’s “Semiology of Graphics”

Mackinlay’s APT

Roth et al.’s Sage and SageBrush

Wilkinson’s “Grammar of Graphics”
Visual exploration of databases

DeVise

DataSplash/Tioga-2
Visualization and data mining

SGI’s MineSet

IBM’s Diamond
Formalism
Polaris Formalism
UI interpreted as visual specification that defines:

Table configuration

Type of graphic in each pane

Encoding of data as visual properties of marks

Data transformations and queries
Schema
Ordinal fields
(categorical)
Market
State
Year
Quarter
Month
Product Type
Product
Profit
Sales
Payroll
Quantitative fields Marketing
(measures) Inventory
Margin
COGS
...
Coffee chain data
[Visual Insights]
Polaris Visual Encodings
Principle of Importance Ordering: Encode the most important
information in the most effective way [Cleveland & McGill]
The Pivot Table Interface

Common interface to statistical packages/Excel


Cross-tabulations
Simple interface based on drag-and-drop
Data Cubes
Structure relation as n-dimensional cube
Each cell
aggregates
all measures for
those dimensions
Each cube axis
corresponds to a dimension
in the relation
Table Algebra: Operands
Ordinal fields: interpret domain as a set that partitions
table into rows and columns:
Quarter = {(Qtr1),(Qtr2),(Qtr3),(Qtr4)} 
Quantitative fields: treat domain as single element set
and encode spatially as axes:
Profit = {(Profit)} 
Concatenation (+) Operator
Ordered union of two sets
Quarter + ProductType
= {(Qtr1),(Qtr2),(Qtr3),(Qtr4)}+{(Coffee),(Espresso)}
= {(Qtr1),(Qtr2),(Qtr3),(Qtr4),(Coffee),(Espresso)}
Profit + Sales
= {(Profit),(Sales)}
Cross () Operator
Direct-product of two sets
Quarter  ProductType =
{(Qtr1,Coffee), (Qtr1, Tea), (Qtr2, Coffee), (Qtr2, Tea),
(Qtr3, Coffee), (Qtr3, Tea), (Qtr4, Coffee), (Qtr4,Tea)}
ProductType  Profit =
SQL Dataflow
Sort
Relational Table
Tuples in Panes
Marks in Panes
Notes

Aggregation operators applied after sort

Only one layer is shown; additional z-sort
Multiscale Visualization
Hierarchical Structure
Challenge: these databases are very large

Queries/Vis should not require all the records
Augment database with hierarchical structure

Provide meaningful levels of abstraction

Derived from domain or clustering

Provides metadata (missing data for context)
Hierarchies and Data Cubes
Each dimension in the cube is structured as a tree
Each level in tree corresponds to level of detail
Schema: Star Schema
Existence Table
Location
Market
State
Products
Product Type
Product Name
Generalizations
• Snowflake schemas
• Lattices (DAGs)
Fact table
State
Month
Product
Profit
Sales
Payroll
Marketing
Inventory
Margin
...
Time
Year
Quarter
Month
Measures
Categorical Hierarchies
Quarter  Month

Direct product of two sets

Would create twelve entries for each quarter, i.e.
(Qtr1, December)
Quarter / Month

Based on tuples in database not semantics

Would only create three entries per quarter

Can be expensive to compute
Quarter . Month

Based on tuples in existence tables (not db)
Cartographic Generalization
Canterbury and East Kent
1:50,000
1:625,000
Generalization: Techniques
Selection
Simplification
Exaggeration
Regularization
Displacement
Aggregation
Summary
Polaris

Spreadsheet or table-based displays

Simple drag-and-drop interface

Built on a formalism that allows algebraic
manipulation of visual mapping of tuples to marks

Multiscale visualizations using data and visual
abstraction

Connects to SQL/MDX servers
See http://www.graphics.stanford.edu/projects/polaris
Future Work

Articulate full-set of multiscale design patterns

Transition between levels of detail

Develop system infrastructure for browsing VLDB

Support layers/lenses/linking with tuple flow

Device independence through graphical encodings

Extend formalism to 3D

Couple scientific and information visualization

…