Polaris A System for Query, Analysis and Visualization of Multidimensional Relational Databases

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Polaris A System for Query, Analysis and
Visualization of Multidimensional Relational
Databases

• Ugur YENIER

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Introduction

• Need for data interfaces emerging with
• Data warehousing
• Scientific Computation
• Business Analysis
• Graphic Representations are more effective
• Allowing multiple views of the same data
• Easy discovery on massive data

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Introduction

• Meaning of data
• Discover Structure
• Find Patterns
• Derive Casual Relationships
• n-Dimensional Data Cubes
• Cube Dimension Relational Schema Dimension

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Introduction

• Most popular method PIVOT TABLE
• Allow data cube to be rotated, pivoted
• Dimensions Rows or Columns
• Remaining Dimensions are aggregated
• Cross-tabulations and summaries are provided
• Further exploit Graphs
• Projections of data cubes in
• Bar Charts
• Scatter points
• Parallel Coordinate Displays

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Introduction

• POLARIS
• Interface for exploring multi-dimensional
  databases
• Extends Pivot Table to directly generate rich
  graphical displays
• Builds tables using algebraic formalism involving
  fields of the database
• Each table contains layers and panes

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Overview

• Support interactive exploration of large
  multidimensional relational databases
• A relational database may contain heterogeneous
  but interrelated tables
• Field Characteristics
• Nominal
• Ordinal
• Quantitative
• Interval

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Overview

• Polaris Field Categorization
• Intervals Quantitative
• (Ordered) Nominal Ordinal
• Dimension Product Name
• Measure Product Prize, Size
• Ordinal Fields ?Dimensions
• Quantitative ? Measure

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Overview

• Target Specifications
• Data-dense displays
• Multiple display types
• Exploratory Interface
• Polaris meets specs. providing rapidly and
  incrementally generating table-based displays
• Table Rows, Columns LAYERS

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Overview

• Each table axis may contain multiple nested
  dimensions
• Each table entry (pane) consists a set of records
  represented with marks
• Sample Polaris Interface

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Interface Characteristics

• Multivariate Multiple dimension of data can be
  explicitly encoded
• Comparative Small-multiple displays to compare,
  exposing patterns and trends
• Familiar Statisticians are accustomed to using
  tabular display of graphics

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Visualization

• Multiple data sources may be combined in a single
  visualization
• Dimensions are displayed in x,y,z shelves
• Record partitioning and layering
• Grouping information
• Graphic Type
• Field mappings to retinal properties

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Visualization

• Selecting a mark pops up detail window displaying
  specified tuples
• It is possible to draw a rubber band around a set
  of marks to brush
• (will be discussed later)

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Generating Graphics

• There are three components
• Specifications of the different table
  configurations
• Type of graphics inside each pane
• Details of the visual encodings

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Table Algebra

• Formal mechanism to specify table configurations
• When a field is placed in a shelf, algebra
  expression is generated
• x,y axes partition into rows and columns, z
  partitions to layers

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Table Algebra

• A,B,C representing ordinal fields
• P,Q,R representing quantitative fields

• Assignment of sets to symbols reflect difference
  in how two types of fields will be encoded in the
  structure of the tables
• Ordinal fields into rows and columns
• Quantitative fields into axes within the panes

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Table Algebra

• Valid expression is an ordered sequence of one or
  more symbols
• Between each adjacent symbol there are operators
• Operators (in order of precedence)
• (X) Cross
• (/) Nest
• () Concatenation

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Concatenation

• Performs union operations

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Cross

• Performs Cartesian product operations

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Nest

• Similar to cross operator, but only creates set
  entries for which there exist records with those
  domain values.

• Interpretation is B within A
• For example, given the fields quarter and month,
  the expression quarter/month would be interpreted
  as months within each quarter

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Table Algebra

• Every expression in the algebra can be reduced to
  a single set
• Each entry in the set being an ordered
  concatenation of zero of more ordinal values with
  zero or more quantitative field names
• This set evaluation of an expression is
  normalized set form

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Normalized Set Form

• Table axis is partitioned into columns (rows or
  layers) so that there is a one-to-one
  correspondence between set entries in the set and
  columns

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Normalized Set Form
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Types of Graphics

• Once the table configuration is specified, next
  step is to specify the type of graphic in each
  pane
• Three graphic families
• ordinal-ordinal
• ordinal-quantitative
• quantitative-quantitative
• Each family contains a number of ways to mark
  records

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Type of Graphics

• Supported Polaris types
• Rectangle
• Circle
• Glyph
• Text
• Gantt bar
• Line
• Polygon
• Image

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Types of Graphics

• Dependent and independent dimensions are
  interpreted differently
• By default dimensions are treated as independent
  dimensions
• Aggregations affect the type of graphics

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Ordinal-Ordinal

• Axis variables are typically independent of each
  other
• Task is focused on understanding patterns and
  trends in some function
• ƒ(Ox,Oy) ? R
• Typical example is studying sales and margin as a
  function of product type, month and state of
  items sold by a coffee chain

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Ordinal-Quantitative

• Typically bar chart, possibly clustered or
  stacked, the dot plot and Gantt Chart
• Quantitative variable is often dependent on the
  ordinal variable and the aim is to understand or
  compare the properties of some function
• ƒ(O) ? Q

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Ordinal-Quantitative

• Matrix of bar charts used to study several
  functions of the independent variables product
  and month

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Ordinal-Quantitative

• The cardinality of the record set does affect the
  structure of the graphics
• When the cardinality of the record is set is one,
  the graphics are simple bar or dot plots
• When the cardinality of the record is set to
  greater than one, the graphic is stacked bar chart

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Ordinal-Quantitative

• Major wars over the past 500 year shown as a
  Gantt chart
• Additional layer in figure displays pictures of
  major scientists plotted as a function of the
  independent variables country of birth and date
  of birth

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Quantitative- Quantitative

• Used to understand the distribution of data as a
  function of one or both quantitative variables
  and to discover casual relationships between the
  two quantitative variables

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Quantitative-Quantitative

• Typical Map
• Flight scheduling varies with the region of the
  country in which the flight originated
• Number of flights between major airports has been
  plotted as a function of latitude and longitude
• Plotted in two layers, the location plots and the
  geography of each state as a polygon

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Visual Mappings

• Each record in a pane is mapped to a mark
• Two Components
• Type of graphic and mark
• Encoding of fields of the records into visual or
  retinal properties of the selected mark
• Visual properties in Polaris are based on
  Bertin's retinal variables
• Shape
• Size
• Orientation
• Color (value and hue)
• Texture (not supported in the current version of
  Polaris)

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Retinal Properties

• The different retinal properties that can be used
  to encode fields of the data and examples of the
  default mappings that are generated when a given
  type of data field is encoded in each of the
  retinal properties

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Visual Mappings

• Retinal properties of the display greatly
  enhances the data density and the variety of
  displays that can be generated
• Analysts should not be required to construct the
  mappings
• Instead, they should be able to simply specify
  that a field be encoded as a visual property
• System should then generate an effective mapping
  from the domain of the field to the range of the
  visual property

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DATA TRANSFORMATIONS AND VISUAL QUERIES

• Rapidly change the table configuration, type of
  graphic, and visual encodings used to visualize a
  data set for interactive exploration
• Resulting display is also manipulable
• Analyst is able to sort, filter, and transform
  the data to uncover useful relationships and
  information
• Also form ad hoc groupings and partitions that
  reflect this newly uncovered information

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Data Transformations and Visual Queries

• Polaris supports four features to perform visual
  queries
• Deriving additional fields
• Sorting and filtering
• Brushing and tool tips
• Undo and Redo

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Deriving Additional Fields

• The generated fields are aggregates or
  statistical summaries
• Polaris currently provides five methods for
  deriving additional fields
• Simple aggregation of quantitative measures
• Counting of distinct values in ordinal dimensions
• Discrete partitioning of quantitative measures
• Ad hoc grouping within ordinal dimensions
• Threshold aggregation

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Deriving Additional Fields Simple Aggregation

• Basic aggregation operations (that are applied to
  a single quantitative field)
• Summation
• Average
• Minimum
• Maximum
• Right-Click and apply, change type
• Easily extended to provide any statistical
  aggregate that can be generated from relational
  data

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Deriving Additional FieldsCounting of Ordinal
Dimensions

• Counting of distinct values for an ordinal field
  within the data set
• Right-Click and apply
• Applying the count operator changes the field
  type (to quantitative) and thus change the table
  configuration and graph type in each pane

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Deriving Additional FieldsDiscrete Partitioning

• Used to discretize a continuous domain
• Polaris provides two discretization methods
• Binning, allows the analyst to specify a regular
  bin size in which to aggregate the data, useful
  for creating graphs, such as histograms, in which
  there are many regularly sized bins
• Partitioning, allows the user to individually
  specify the size and name of each bin, useful for
  encoding additional categorizations into the data
  
• Right-Click and apply

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Deriving Additional FieldsAd hoc Grouping

• Ordinal version of quantitative partitioning,
  where the user can choose to group together
  different ordinal values
• Allows the analyst to add own domain knowledge to
  the analysis and to change the groupings as the
  exploration uncovers additional patterns
• Right-Click and apply

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Deriving Additional FieldsThreshold Aggregation

• It is derived from two source fields an ordinal
  field and a quantitative field
• If the quantitative field is less than a certain
  threshold value for any values of an ordinal
  field, those values are aggregated together to
  form an "Other" category
• Allows the user to specify threshold values below
  which the data is considered uninteresting
• Right-Click and apply

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Sorting and Filtering

• Filtering allows the user to choose which values
  to display so that he can focus on and devote
  more screen space and attention to the areas of
  interest
• For ordinal fields, a listbox with all possible
  values is shown and the user can check or uncheck
  each value to display it or not
• For quantitative fields, a dynamic query slider
  allows the user to choose a new domain
• Additionally, there are textboxes showing the
  chosen minimum and maximum values that the user
  can use to directly enter a new domain.

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Sorting and Filtering

• Sorting allows the user to uncover hidden
  patterns by changing the order of values within a
  field's domain or the ordering of tuples in the
  data
• The ordering of tuples affects the drawing order
  of marks within a pane.
• Polaris provides three ways for a user to sort
  the domain.
• User can bring up the filter window and drag-and
  drop the values within that window to reorder the
  domain
• If the field has been used to partition the table
  into rows or columns, the user can drag-and-drop
  the table row or column headers to reorder the
  domain values
• Polaris provides programmatic sorting, allowing
  the user to sort one field based on the value in
  another field

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Brushing and Tooltips

• Analysts want to directly interact with the data,
  visually querying the data to highlight
  correlated marks or getting more details on
  demand
• Brushing allows the user to choose a set of
  interesting data points by drawing a rubberband
  around them
• Tooltips allow the user to get more details on
  demand.

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Brushing

• The user selects a single field whose values are
  then used to identify related marks and tuples
• All marks corresponding to tuples sharing
  selected field values with the selected tuples
  are subsequently highlighted in all other panes
  or linked Polaris views
• Allowing correlation between different
  projections of the same data set or relationships
  between distinct data sets.

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Tooltips

• If the user hovers over a data point or pane,
  additional details, such as specific field values
  for the tuple corresponding to the selected mark,
  are shown
• Analysts can use tooltips to understand the
  relationship between the graphical marks and the
  underlying data

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Undo and Redo

• Unlimited undo and redo within an analysis sessio
• Users can use the "Back" and "Forward" buttons on
  the top toolbar to either return to a previous
  visual specification or to move forward again.

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GENERATING DATABASE QUERIES
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Results

• Throughout the analyses users want to see data
  and how they want to see it change continually
• Analysts
• form hypotheses
• create new views to perform tests and experiments
  
• Certain displays enable an understanding of
  overall trends, whereas others show causal
  relationships
• As the analysts better understand the data, they
  may want to drill-down in the visible dimensions
  or display entirely different dimensions
• Polaris supports this exploratory process through
  its visual interface
• By formally categorizing the types of graphics,
  Polaris is able to provide a simple interface for
  rapidly generating a wide range of displays
• This allows analysts to focus on the analysis
  task rather than the steps needed to retrieve and
  display the data

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Discussions

• Comparison with similar work is omitted in this
  presentation
• Interpretation of visual specifications as
  database queries
• Interactivity and performance of Polaris

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Interpretation of Visual Specifications as
Database Queries

• Polaris generates the SQL query for each table
  pane
• Similar to CUBE operator generating the queries
  to create the cross-tab and Pivot Table displays
• However the CUBE operator is not applicable for
  Polaris because it assumes that the sets of
  relations partitioned into each table pane do not
  overlap

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Interactivity and Performance of Polaris

• Polaris at its first implementations focuses on
  the techniques, semantics and formalism rather
  then the interactivity
• It has been experienced that the query response
  time does not need to be real-time in order to
  maintain a feeling of exploration (several tens
  of seconds)

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Interactivity and Performance of Polaris

• Test Data
• A subset of a packet trace of a mobile network
  over a 13 week period, approx. 6 million tuples
• A subset of the data collected from Sloan Digital
  Sky Survey (approx. 650MB)
• Both stored on MS SQL Server 2000
• Paper does not provide numeric data on
  performance but the personal experiences of the
  testers

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Conclusion

• Polaris extends the well known Pivot Table
  interface to display relational query results
  using a rich inexpensive set of graphical
  displays
• Succinct visual specification for describing
  table-based graphical displays of relational data
  
• Interpretation of visual specifications as a
  precise sequence of relational database operations

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Future Work

• Performance evaluation
• Hierarchical data cubes
• Correspondence of marks to data tuples (dynamic
  mark generation)
• Animation shelf to display sequencing data

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• Thank You