1 Weighted Partonomy-Taxonomy Trees with Local Similarity Measures for Semantic Buyer-Seller Matchmaking By: Lu Yang March 16, 2005

2 Outline Motivation Similarity Measures Partonomy Similarity Algorithm – Tree representation – Tree simplicity – Partonomy similarity Experimental Results Node Label Similarity – Inner-node similarity – Leaf-node similarity Conclusion

3 Motivation – Keywords/keyphrases – Trees e-business, e-learning … Buyer-Seller matching Metadata for buyers and sellers Tree similarity

4 Similarity measures Similarity measures apply to many research areas – CBR (Case Based Reasoning), information retrieval, pattern recognition, image analysis and processing, NLP (Natural Language Processing), bioinformatics, search engine, e- Commerce and so on In e-Commerce – Product P satisfies demand D ? Is it an “All or Nothing” question? Additional knowledge needed Bridge the gap between demand and product descriptions Now, a “How similar?” question!

5 Numerical modeling of similarity – A similarity measure on a set M is a real function sim: M 2  [0,1] – Similarity measures have following properties Reflexivity  x  M: sim(x,x) = 1 Symmetry iff  x,y  M: sim(x,y) = sim(y,x) Similarity measures (Cont’d)

6 An opposite notion of similarity measures A distance measure on a set M is a real valued function d: M 2  IR + Distance measures have following properties – Reflexivity  x  M d(x,x) = 0 – Symmetry iff  x, y  M d(x,y) = d(y,x) – Triangle Inequality iff  x, y  M d(x,y) = 0  x = y  x, y, z  M d(x,y) + d(y,z)  d(x,z) Similarity measures – distance measures

7 Transformation of similarity measures and distance measures – If a bijective, order inverting mapping f: [0,1]  [0,1] exists with f(d(x,y)) = sim(x,y) then sim and d are compatible Similarity measures – distance measures

8 Global measures are defined on the whole object – reflect the task and have a pragmatic character Local measures are defined on details (e.g. the domains of some attribute) – reflect technical and domain character – task independent Similarity measures – global and local

9 Local to global – each object A is constructed from so-called “components” A i by some construction process C(A i |i  n) = A given two objects A and B, sim i (A i, B i ) denotes the similarity of their i th components – amalgamation function f sim(A, B) is the global similarity measure of A and B sim(A, B) = f(sim i (A i, B i ) |i  n ) Similarity measures – global and local

10 Tree representation Characterises of our trees – Node-labled, arc-labled and arc-weighted – Arcs are labled in lexicographical order – Weights sum to Make Model Year 2002 Car Ford Explorer

11 Tree representation – serialization of trees – XML attributes for arc weights and subelements for arc labels – Weighted Object-Oriented RuleML Car Make Ford Model Explorer Year 2002 Tree serialization in WOO RuleML

12 Tree representation – Relfun version of tree cterm[ -opc[ctor[car]], -r[n[make],w[0.3]][ind[ford]], -r[n[model],w[0.2]][ind[explorer], -r[n[year],w[0.5]][ind[2002]] ]

13 Tree simplicity A 0.1 a ed E b B C f D c FG – Treeplicity(i,t) Depth degradation index “i” = 0.9 – Reciprocal of tree breadth – Depth degradation factor = 0.5 (0.9) (0.45) (0.225) tree simplicity:

14 Partonomy similarity – simple trees Escape Car Make Model Ford Mustang Car Make Model Ford tree ttree t´ (House) 0 1 Inner nodes 0 1 Leaf nodes

15 Partonomy similarity – complex trees  (s i (w i + w' i )/2)  (A(s i )(w i + w' i )/2) A(s i ) ≥ s i lom educational 0.5 general format platform 0.5 Introduction to Oracle t t´t´ technical edu-setgen-set tec-set language en title HTMLWinXP lom 0.1 general format platform Basic Oracle technical gen-set tec-set language en title * WinXP * : Don’t Care

16 Partonomy similarity – main recursive functions – Treesim(t,t'): Recursively compares any (unordered) pair of trees Paremeters N and i Three main recursive functions (Relfun) – Treemap(l,l'): Recursively maps two lists, l and l', of labeled and weighted arcs: descends into identical–labeled subtrees – Treeplicity(i,t): Decreases the similarity with decreasing simplicity

17 Experimental results – simple trees

18 Experimental results – simple trees (cont’d) Experiments Tree Results make auto mustang auto 0.45 model 2000 ford year t1t1 t2t2 1.0 model 0.45 explorer 0.9 make auto mustang auto 0.05 model 2000 ford year t3t3 t4t4 1.0 model 0.05 explorer

19 Experimental results – identical tree structures ExperimentsTree Results make auto ford year t2t2 model 0.5 explorer make auto 1999 ford year t4t4 model explorer make auto ford yea r t1t1 model 0.5 explorer make 2002 ford yea r t3t3 model explorer auto

20 b2 Experimental results – complex trees b c c3 c1 c2 c b3 A B C D b d b1 b4 c1 c3 d1 B1 B4 C1 C3 D1 B2B3 c4 c A B C D bd d1 B1 C1 C4 C3D E F t t´t´

21 b2 Experimental results – complex trees b c c3 c1 c2 c b3 A B C D b d b1 b4 c1 c3 d1 B1 B4 C1 C3 D1 B2B3 c4 c A B C D bd d1 B1 C1 C4 C3D E E F t t´t´

22 b2 Experimental results – complex trees b c c3 c1 c2 c b3 A B C D b d b1 b4 c1 c3 d1 B1 B4 C1 C3 D1 B2B3 c4 c A B * D bd d1 B1 C1 C4 C3D E F t t´t´

23 Node label similarity For both inner nodes and leaf nodes – Exact string matching binary result 0.0 or 1.0 – Permutation of strings “Java Programming” vs “Programming in Java” Number of identical words Maximum length of the two strings Example 1: For two node labels “a b c” and “a b d e”, their similarity is: 2 4 = 0.5

24 Example 2: Node labels “electric chair” and “committee chair” Node label similarity (cont’d) 1 2 = 0.5 meaningful? Semantic similarity

25 Node label similarity – inner nodes vs. leaf nodes Inner nodes — class-oriented – Inner node labels can be classes – classes are located in a taxonomy tree – taxonomic class similarity measures Leaf nodes — type-oriented – address, currency, date, price and so on – type similarity measures (local similarity measures)

26 Node label similarity String Permutation (both inner and leaf nodes) Exact String Matching (both inner and leaf nodes) Non-Semantic Matching Taxonomic Class Similarity (inner nodes) Type Similarity (leaf nodes) Semantic Matching

27 Inner node similarity – partonomy trees Distributed Programming Credit “Introduction to Distributed Programming” Textbook Tuition Duration $800 2months t1t1 t2t2 Object-Oriented Programming Credit “Objected-Oriented Programming Essentials” Textbook Tuition Duration $1000 3months partonomy trees

28 Inner node similarity – taxonomy tree Programming Techniques Applicative Programming General Automatic Programming Concurrent Programming Sequential Programming Object-Oriented Programming Distributed Programming Parallel Programming arc weights at the same level of a subtree do not need to add up to 1 assigned by machine learning algorithms or human experts

29 Programming Techniques Applicative Programming General Automatic Programming Concurrent Programming Sequential Programming Object-Oriented Programming Distributed Programming Parallel Programming red arrows stop at their nearest common ancestor the product of subsumption factors on the two paths (0.018) Inner node similarity – taxonomic class similarity

30 Inner node similarity – separate to encoded taxonomy tree Separate taxonomy tree – extra taxonomic class similarity measures How to compute semantic similarity without – changing our partonomy similarity algorithm – losing taxonomic semantic similarity Encode the (subsections) of taxonomy tree into partonomy trees Disjoint subsections of taxonomy lead to zero semantic similarity

31 Inner node similarity – encoding taxonomy tree into partonomy tree Programming Techniques Applicative Prgrm 0.1 General Automatic Prgrm Concurrent Prgrm Sequential Prgrm Object-Oriented Prgrm Distributed Prgrm Parallel Prgrm * * * * * * * * encoded taxonomy tree

32 Credit Title Tuition Duration $800 2months t1t1 Classification 0.65 taxonomy Object- Oriented Prgrm $1000 3months t2t2 Classification 0.65 taxonomy Distributed Prgrm course Concurrent Prgrm Parallel Prgrm Object-Oriented Prgrm course 1.0 Programming Techniques 1.0 * Distributed Prgrm Credit Title Tuition Duration Programming Techniques Sequential Prgrm * * * * * * * Inner node similarity – encoding taxonomy tree into partonomy tree (cont’d) encoded partonomy trees

33 Leaf node similarity (local similarity) 0.5 end_date Nov 3, t1t1 t 2 start_date May 3, 2004 Project 0.5 end_date Feb 18, start_date Jan 20, 2004 Project Example: “date” type leaf nodes DS(d 1, d 2 ) = { 0.0 otherwise if | d 1 – d 2 | ≥ – | d 1 – d 2 |

34 Implementation Relfun version – exact string matching – don’t care Java version – exact string matching – don’t care – string permutation – encoded taxonomy tree in partonomy tree (Teclantic) – “date” type similarity measure

35 Conclusion Arc-labeled and arc-weighted trees Partonomy similarity algorithm – Traverses trees top-down – Computes similarity bottom-up Node label similarity – Exact string matching (both inner and leaf nodes) – String permutation (both inner and leaf nodes) – Taxonomic class similarity (only inner nodes) Taxonomy tree Encoding taxonomy tree into partonomy tree – Type similarity (only leaf nodes) “date” type similarity measures

36 Questions?