Compact Encodings for All Local Path Information in Web Taxonomies with Application to WordNet

1
Compact Encodings for All Local Path Information
in Web Taxonomies with Application to WordNet

• Svetlana Strunja-Yoshikawa
• Joint with Fred Annexstein and
• Kenneth Berman
• strunjs,annexste,berman_at_ececs.uc.edu
• University of Cincinnati

2
Introduction

• Consider Lowest Common Ancestor Query Problem
• Find most specific common generalization or
  least common subsumer among 2 or more terms or
  attributes in a large hierarchical/classification
  data sets
• Constraint Evaluate queries without indirection
• Goal Compact labeling schemes for taxonomies

3
Introduction (contd)

• Applications
• Fast classification of sets and similarity, e.g.
  prediction sets similar to Google Sets (given
  Bush" and Clinton it predicts all other US
  presidents)
• Fast answers to ancestor queries in XML search,
  e.g., test if 2 terms share a parent node without
  loading XML file (see1,2)
• Fast navigation through voluminous web taxonomies
  (see 3)

4
Data Model

• Structural properties found in well-known web
  taxonomies
• large variance out-degree(?), i.e., some nodes
  have many subclasses
• small in-degree (d) range and variance
• small depth (s) (logarithmic)
• small number (gt1) of paths from root
• See paper for table of statistical values for
  Wordnet, ODP, and Math taxonomies

5
Our Approach

• Given large, rooted web taxonomies represented
  abstractly as Directed Acyclic Graph or DAG with
  above statistics
• Problem Label each node of the DAG so that all
  local path information for each taxonomy element
  is preserved in the encoding
• Our labeling scheme is a variable-length,
  prefix-based scheme, and built up in two stages

6
Our Approach (contd)

• 1.Greedy Dewey Labeling for Trees
• (TGDL)
• -Identifies a Breadth-First tree T in a DAG
• -Encodes path information for the paths in T
• -Label nodes with concatenation of edge labels

7
GDL example
8
TGDL example
9
Analysis of the Length for TGDL Labels

• Performed in 2 steps
• First step assume that delimiting labels are
  empty -- each node v labeled with
  bits at most
• Second step Using different edge delimiting
  schemes estimated upper bound of node labels

10
Delimiting schemes

• They encode length of each tree-edge label
• Two approaches tested
• Unary Length Encoding
• Fixed Binary Length Encoding

11
Unary Length Encoding (ULE)

• Comparable to Elias Gamma Code
•     Gamma             ULE    1    
  1              10        2    
  010            113     011            
  0100 4     00100          01015    
  00101          01106     00110         
  01117     00111       0010008    
  0001000        001001
• ULE assigns e-1 bits long zero prefix to an
  edge label e with GDL label of the length e

12
Unary Length Encoding (ULE) Analysis

• Theorem
• Upper bound on TGDL label length with
• ULE of delimiters is
• bits, for an arbitrary node v in a tree T
• - is the depth of v in T
• - n is number of nodes in T

13
Fixed Binary Length Encoding (FBLE)

• For an edge e, this encoding is the binary
  representation of the length for GDL(e)
• Encoded with a fixed number of bits
• - is the maximum node out-degree in T
• - uses 4 bits in our application

14
FBLE example

• - 4 bits will encode delimiters for any T with
  maximum out-degree lt 216
• - Let e is an edge in T with a given GDL
• label, e.g. GDL(e)0000111111
• Then FBLE produces delimiter 1010,
• so label for e is 10100000111111

15
Fixed Binary Length Encoding (FBLE) Analysis

• Upper bound on TGDL label length with FBLE of
  delimiters is
• bits, for an arbitrary node v in a tree T

16
Our Approach (contd2)

• 2.Extended Greedy Dewey Labeling for DAGs (EGDL)
• -Augment codes generated from step 1
• -Used for inferring paths not part of the
  Breadth-First tree
• -Adds TGDL node label pairs of non-tree edges

17
EGDL Labeling - Example
.01.0.01 .01.0.0
.0.01.0.01
18
Experimental Results for Wordnet taxonomy (n
80K)
19
Experimental Results-Label Lengths
Encoding Length
Wordnet 2.1 Statistics
20
References

• 1 Budanitsky, A., Hirst, G. Semantic distance
  in WordNet An
• experimental, application-oriented evaluation of
  five
• measures. Workshop on WordNet and Other Lexical
  Resources,
• Second meeting of the North American Chapter of
  the Association for
• Computational Linguistics, Pittsburgh,PA, 2001.
• 2 Resnik, F. Using Information Content to
  Evaluate Semantic
• Similarity in a Taxonomy. In Proceedings of the
  14th International
• Joint Conference on Artificial Intelligence
  (IJCAI), pages 448453,
• 1995.
• 3 Christophides, V., Plexousakis, D. On
  Labeling Schemes for the Semantic Web. In
• Proceedings of the 12th international conference
  on World Wide Web, pages 544555,
• Budapest, Hungary.
• 4 Abiteboul., S., Kaplan, H., Milo, T. Compact
  labeling schemes for ancestor
• queries. In Proceedings of the twelfth annual
  ACM-SIAM symposium on
• Discrete algorithms, pages 547556, Washington,
  D.C., 2001.
• 5 Strunjas-Yoshikawa, S., Annexstein, F.,
  Berman, K. Compact Encodings for All Local
• Path Information in Web Taxonomies with
  applications to WordNet . In Proceedings of the
• 32nd International Conference on Current
  Trends in Theory and Practice of Computer
• Science, Merin, Czech Republic, January 21-27,
  2006.