1. 1 Weighted-Tree Simplicity Algorithm for Similarity Matching of Partial Product Descriptions Lu Yang, Biplab Sarker, Virendra C. Bhavsar and Harold Boley IASSE Talk, July 21, 2005

2. 2 Outline Buyer-Seller AgentMatcher in e-Markets Product Descriptions : Arc-Labeled, Arc-Weighted Trees Tree Similarity Tree Simplicity Computational Results Use Case Conclusion

3. 3 Buyer-Seller AgentMatcher in e-Markets Main Server User Info User Profiles User Agents … … Agents … … e-Market To other sites (network) Web Browser User Matcher 1 Matcher n

4. 4 Buyer-Seller AgentMatcher in e-Markets Seller RankSimilarity 10.9845 20.7210 30.6232 40.4197 50.2058 n0.0745 Recommendations for a buyer Buyer 1Seller 1 Buyer 2 Seller m Seller 2 Matcher i Buyer n

5. 5 Product Descriptions : Arc-Labeled, Arc-Weighted Trees 0.8 Car Ford Sedan 10000SmallTaurusV-8 1999 Category Year Make Engine Model Size 0.1 0.90.10.30.7 Kms Buyer TreeSeller Tree 0.4 Car Ford Sedan 160000SmallTaurus 2000 Category Year Make Model Size 0.20.4 1.00.5 Kms Scenario: Used-car buying/selling Similarity = 0.6232 missing subtree Missing subtree represents partial product description

6. 6 Tree Similarity Algorithm Recursively traverse (sub)trees top-down Compute similarity bottom-up S(T 1, T 2 ) =  S i (w i + w' i )/2 When a subtree of a tree is missing in the other tree, compute the simplicity of the subtree

7. 7 Tree simplicity measure computes the simplicity of a single (sub)tree Tree simplicity contributes to tree similarity Takes into account: Arc weights Out-going degree of non-leaf nodes (tree breadth) Depth of leaf nodes Wider and deeper trees lead to smaller tree simplicity values Tree Simplicity Algorithm (Cont’d)

8. 8 : the simplicity value of a single tree T : depth degradation index : depth degradation factor d : depth of a leaf node m : root node degree of tree T that is not a leaf node w j : arc weight of the j th outgoing arc from the root node of tree T T j : subtree connected to the j th arc with arc weight w j Tree Simplicity Algorithm (Cont’d) if T is a leaf node, otherwise.

9. 9 Tree Simplicity — Extreme Cases The simplest tree is a single-node tree with simplicity 1.0 The most complex tree is an infinite tree (our previous tree complexity measure made the tree complexity go toward infinite in this case) Š(T) = 0 or Š(T) = 0 or

10. 10 Tree Simplicity — Example A B F b 0.8 0.2 0.5 CDE c d e f g hij GHI J 0.1 0.3 0.4 0.1 1.0 0.5 0.25 0 1 2 d DIDI Š(T) = (0.2· Š(T B ) +0.1· Š(T C ) + 0.3· Š(T D ) + 0.4· Š(T E ) ) Š(T) = 0.6667 Š(T E ) =(0.5 · Š(T I ) +0.5 · Š(T J ) ) Š(T B ) = (0.8 · Š(T F ) +0.1 · Š(T G ) + 0.1 · Š(T H ) ) = =

11. 11 Tree Simplicity — Analysis of k-ary trees A A1A1 l1l1 1/k lklk AkAk k-ary tree k-ary trees: Each node (except the leaf nodes) has k children Each path from the root to a leaf node has the same length

12. 12 Computational Results Simplicity as a function of depth d

13. 13 Simplicity as a function of root-node degree k Computational Results

14. 14 Simplicity as a function of root-node degree k and depth d Computational Results

15. 15 Use Case — Learning Object Tree classification lom 0.16667 taxonpath 1.0 taxon Applied Sciences, Technology classification -set taxon- set 1.0 0.16667 general 0.33334 0.3333 title language en Introduction To Oracle general- set keyword 0.3333 keyword -set database 0.5 0.16667 lifeCycle Contribute- set 1.0 educational 0.16667 language learning Resource Type 0.2 context 0.2 educational- set intende dEndUs erRole 0.2 typicalAge Range 0.2 course Learner 0.2 18- 25    lifeCycle- set contribute entity  0.16665 technical rights 0.16667 format technical- set 0.5 copyrightAnd Other Restrictions 0.5 rights- set descriptions 0.5   otherPlatform Requirements oracle 0.5 YesHTML   Don’t care

16. 16 Use Case — Learner Query Tree classification lom 0.16667 taxonpath 1.0 taxon Applied Sciences, Technology classification -set taxon- set 1.0 0.16667 lifeCycle Contribute- set 1.0 educational 0.16667 language learning Resource Type 0.2 context 0.2 educational- set intende dEndUs erRole 0.2 typicalAge Range 0.2 course Learner 0.2 45- 60   lifeCycle- set contribute entity  0.16665 technical rights 0.16667 format technical- set 0.5 copyrightAnd Other Restrictions 0.5 rights- set descriptions 0.5   otherPlatform Requirements NoHTML Similarity = 0.7323 Simplicity = 0.3750

17. 17 Conclusion Arc-labeled, arc-weighed tree representations for buyer-seller product descriptions Tree similarity measure for buyer-seller matching Allows partial product description Tree simplicity measure for partial product description matching Simpler missing (sub)trees lead to greater simplicity values and thus greater similarity values Applications eduSource: learner and learning object matching http://www.cs.unb.ca/agentmatcher Teclantic: project profile matching http://teclantic.ca

18. 18 Thank you! Questions?