1. Polaris Query, Analysis, and Visualization of Large Hierarchical Relational Databases Pat Hanrahan With Chris Stolte and Diane Tang Computer Science Department Stanford University

2. 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

3. 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

4. Formalism

5. 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

6. Schema Market State Year Quarter Month Product Type Product Profit Sales Payroll Marketing Inventory Margin COGS... Ordinal fields (categorical) Quantitative fields (measures) Coffee chain data [Visual Insights]

7. Polaris Visual Encodings Principle of Importance Ordering: Encode the most important information in the most effective way [Cleveland & McGill]

8. The Pivot Table Interface Common interface to statistical packages/Excel Cross-tabulations Simple interface based on drag-and-drop

10. 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

11. 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)} 

12. 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)}

13. 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 =

18. SQL Dataflow Notes Aggregation operators applied after sort Only one layer is shown; additional z-sort Relational TableTuples in PanesMarks in Panes Sort

19. Multiscale Visualization

20. 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)

21. Hierarchies and Data Cubes Each dimension in the cube is structured as a tree Each level in tree corresponds to level of detail

22. Schema: Star Schema State Month Product Profit Sales Payroll Marketing Inventory Margin... Measures Location Market State Time Year Quarter Month Products Product Type Product Name Fact table Existence Table Generalizations Snowflake schemas Lattices (DAGs)

23. 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)

24. Cartographic Generalization Canterbury and East Kent 1:50,0001:625,000

25. Generalization: Techniques Selection Simplification Exaggeration Regularization Displacement Aggregation

30. 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

31. 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 …