From Tessellations to Table Interpretation

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From Tessellations to Table Interpretation

• R. C. Jandhyala1, M. Krishnamoorthy1,
• G. Nagy1, R. Padmanabhan1,
• S. Seth2, W. Silversmith1
• 1DocLab, Rensselaer Polytechnic Institute
• 2Computer Science and Engineering, University of
  Nebraska-Lincoln
• (Supported by NSF Grants 044114854 and 0414644,
  and Rensselaer Center for Open Source Software)

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Goal Construction of a narrow-domain ontology
from semi-structured web data (table
understanding )
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Outline
Tilings (rectangular tessellations) X-Y trees
(1984)
Grammars
Tables
Wang Categories (1996)
A B C D
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Outline
Tilings (rectangular tessellations) X-Y trees
(1984)
Grammars
Tables
Wang Categories (1996)
A B C D
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Web tables

• Cannot precisely define human-understandable
  tables.
• Convert to smaller set of admissible tables.
• Why? Algorithmic ease.

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Admissible Tables

• Have stub, headings and data cells.

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Factor out layout-equivalent tables
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Outline
Tilings (rectangular tessellations) X-Y trees
(1984)
Grammars
Tables
Wang Categories (1996)
A B C D
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Rectangular Tessellations

• Partition of an isothetic rectangle into
  rectangles.
• Uniquely defined by junction points (location and
  type).
• Number of tessellations increases rapidly with
  table size.

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XY Tessellations

• Special case of rectangular tessellations.
• Successive horizontal and vertical cuts.
• Easily represented by trees.

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A tiling and its X-Y Tree(aka slicing structure,
puzzle tree, tree map)
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Non-slicing structures No XY tree
In fact, X-Y tilings are an infinitesimal
fraction of all tilings. This helps, because
tables never contain this spiral structure.
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Fundamental Idea

• Use XY trees to automate table processing and
  understanding.

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Table to XY tree EX2XY

• Applicable to any XY tessellation.
• Input Excel Table
• Copy and paste or Import.
• Edit to make admissible.
• Output XY tree
• as XML for portability.
• as parenthesized string for grammars.

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Example
(http//www40.statcan.ca/l01/cst01/econ50-eng.htm)
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After import into Excel
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After Editing
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Output - XML

• ltblock id'1.1.2.1' range'17,230,2'gt
• ltcontentgt
• Real gross domestic product, expenditure-based,
  by province and territory (millions of chained
  (2002) dollars)
• lt/contentgt
• lt/blockgt

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Outline
Tilings (rectangular tessellations) X-Y trees
(1984)
Grammars
Tables
Wang Categories (1996)
A B C D
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Table Grammars

• Can characterize entire families of tables.
• Developed grammar for one family.
• Input - Nested parenthesized notation .
• Output Accept/Reject as example of family.

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Grammar

• For parsing column headers
• S A (Rule 1)
• A B (Rule 2)
• B c X B c X (Rules 3 and 4)
• X c X A X A c (Rules 5, 6, 7 and
  8)
• S is start symbol.
• A generates all admissible column headers.
• B generates category trees.
• c is a root category.
• X generates sub-categories.

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Table Grammars

• Cannot check if table is consistent.
• Need further geometric alignment and lexical
  checks.

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Outline
Tilings (rectangular tessellations) X-Y trees
(1984)
Grammars
Tables
Wang Categories (1996)
A B C D
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Logical Structure of Tables

• How to interpret a table?
• Describe relationship between header cells and
  content cells Wang, U. Waterloo,1996.
• Wang notation
• Elegant description.
• Dimensionality Number of category trees.
• Cartesian product maps categories to data.

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Layout independent Wang Notation
Different layout and same information means same
Wang Notation
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Wang Category Trees for either table

• characteristic
• gonsity
• hepth
• fleck burlam falder multon
• Any data cell can be designated by a path
  through each category tree.
• Leaves correspond to row or column headings.

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Real Table Understanding

• Analyzing logical structure not sufficient.
• Need additional information from title,
  footnotes, captions, etc.
• Semantic analysis of the labels also important
  need external knowledge.

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Does Wang Notation always exist?

• Not always!
• Inconsistent tables do not have Wang Notation.
• Others can be edited using virtual headers.

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XY tree to Wang Notation Algorithm

• Input XY trees.
• Output XML version of Wang Notation.
• Checks for table consistency.

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Algorithm

• Locate principal regions - stub, headers and
  content cells.
• Extract Wang categories.
• Compute Cartesian product of category paths.
• Match each key to the content of a delta cell.

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Conclusions

• Admissible layouts identified for ease of
  processing.
• Algorithms developed for
• extracting XY trees from tables.
• extracting Wang notation from XY trees.
• Family of tables identified using a grammar.

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Future work

• Augmentations - captions, aggregates, units, etc.
  
• Expand the grammar.
• Automate conversion of table to admissible
  formats.

(http//www40.statcan.ca/l01/cst01/agri111a-eng.ht
m)
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THANK YOU
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Goal construction of a narrow-domain
ontologyfrom semi-structured web data(table
understanding )

• Currently multon is the best choice for rapitting
  velters. It is about 25 better than burlam or
  falder, which have the same girby (hepth/gonsity
  ratio).
• Check another table to see whether elmer is even
  better.
• NOT TODAY!

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H-first tree can be transformed into V-first
tree(and vice-versa)
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EX2XY Algorithm

• Two workhorses
• Vertical_cut returns leftmost sub-rectangle of
  a given rectangle.
• Horizontal_cut returns topmost sub-rectangle of
  a given rectangle.

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EX2XY Algorithm (contd.)

• Used in a pair of procedures P1 and P2.
• P1 cuts vertically and submits first
  sub-rectangle to P2 for horizontal cuts.
• Similarly with P2.

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Parenthesized notation

• P-notation has 11 correspondence with general
  trees.
• For above table, the XY tree sentence is
• Sxy c c c c c c c c c c c c.

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A table with six Wang dimensions
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XY2WANG Other features

• Handles more complex scenarios
• Higher dimensionality.
• Deeper nesting of headers.
• Repetitive headers.

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(http//www40.statcan.ca/l01/cst01/econ50-eng.htm)
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Table Augmentations Example
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Raghavs Experiment
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Results
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Results (Contd.)
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Conclusion

• Average total time to process a table - 231
  seconds.
• Average table size - 587 cells before
  preprocessing.
• Average preprocessing time - 104 seconds.
• 3 category tables took approximately 27 seconds
  more than 2 category tables.

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Conclusion (Contd.)

• Tables with aggregates and footnotes - more time
  to process.
• Strong correlation between processing time and
  table size.
• For future automatically segmenting
  augmentations, categories and delta cells using
  visual cues.