ORDER INDEPENDENT INCREMENTAL EVOLVING   FUZZY GRAMMAR FRAGMENT LEARNER <ul><li>Nurfadhlina Mohd Sharef , </li></ul><ul><l...
OUTLINE <ul><li>Introduction </li></ul><ul><li>Text Fragment Learning </li></ul><ul><li>Fuzzy Grammar Fragment </li></ul><...
** Source from World Incidents Tracking System Human is able to understand a class without following a strict pattern
SUMMARY EXAMPLES <ul><li>“ On  27 May 2004 , in Nadapuram, Kerala, India, a bomb exploded at a store, causing moderate dam...
TEXT FRAGMENT LEARNING learn the  underlying grammar patterns of similar texts ;  exploiting both syntactical and semantic...
BOMBING TEXT FRAGMENT <ul><li>“ On 1 January 2004, in Srinagar, Jammu and Kashmir, India, an assailant on a bicycle was ca...
Learning Fuzzy Grammar Fragments <ul><li>“ To investigate  </li></ul><ul><li>an  incremental  evolving fuzzy grammar  frag...
FUZZY GRAMMAR FRAGMENT  **  Grammar derivation  is done using a set of  predefined terminal sets  of type  regular express...
EVOLVING GRAMMAR ISSUES Grammar Class Text Class <ul><li>How to  recognize  the fragment </li></ul><ul><li>How to  represe...
GRAMMAR SIMILARITY Table 1: Example of  string  edit distance operation (*I:Insert, D:Delete, S:Substitute) Table 2: Examp...
GRAMMAR COMBINATION Start s=new string maxMem=membership(s,TG) maxMem<1? costST=costTS=1 Y gx=Combine(sg,tg) costST=1 && c...
MINIMAL COMBINATION RULES Source  Grammar Target  Grammar Cost (Source, Target) Cost (Target, Source) Combination  Operati...
ORDER INDEPENDENT IEFG <ul><li>Let α be a triplet α =< S, GS,GT> where S is a finite  permutation of strings i.e. a sequen...
THEOREM 1:  FOR  α   =< S,GS,GT>  EXT(GS)=EXT(GT) <ul><li>Proof by induction </li></ul><ul><li>Basis  n=1 </li></ul><ul><l...
Let: Ext(GS j ) = Ext(GS j-1 ) ∪ Ext(gs j )  g x =Combine(gs j ,gt i ) Ext(g x ) = Ext(gs j ) ∪ Ext (gt i ) Case1: Combine...
LEMMA 2.1 <ul><li>For any two permutations S and S*, giving derived  grammars  GS and GS* </li></ul><ul><li>Ext(GSj) = Ext...
<ul><li>Theorem 2 : Given α =< S, GS ,GT>  and  α * =< S*, GS* ,GT*>,  </li></ul><ul><li>Then Ext(GTi) = Ext(GTi*)  </li><...
EXAMPLE <ul><li>generated results  may not be syntactically identical but rather yield same (approximate) parsing coverage...
CONCLUSION <ul><li>An algorithm that  features independent training order  can ensure robust results.  </li></ul><ul><li>T...
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ORDER INDEPENDENT INCREMENTAL EVOLVING FUZZY GRAMMAR FRAGMENT LEARNER

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  • Minimal Combination for Incremental Grammar Fragment Learning-IFSA/EUFSLAT 2009 Minimal Combination for Incremental Grammar Fragment Learning-IFSA/EUFSLAT 2009
  • Minimal Combination for Incremental Grammar Fragment Learning-IFSA/EUFSLAT 2009 Minimal Combination for Incremental Grammar Fragment Learning-IFSA/EUFSLAT 2009
  • ORDER INDEPENDENT INCREMENTAL EVOLVING FUZZY GRAMMAR FRAGMENT LEARNER

    1. 1. ORDER INDEPENDENT INCREMENTAL EVOLVING FUZZY GRAMMAR FRAGMENT LEARNER <ul><li>Nurfadhlina Mohd Sharef , </li></ul><ul><li>Department of Computer Science, </li></ul><ul><li>Faculty of Computer Science and Information Technology, </li></ul><ul><li>University Putra Malaysia, </li></ul><ul><li>Malaysia. </li></ul><ul><li>[email_address] , </li></ul><ul><li>[email_address] , </li></ul><ul><li>Trevor Martin, </li></ul><ul><li>Yun Shen </li></ul><ul><li>Artificial Intelligence Group, </li></ul><ul><li>Intelligent System Lab, </li></ul><ul><li>University of Bristol </li></ul><ul><li>Bristol, United Kingdom </li></ul><ul><li>[email_address] , </li></ul><ul><li>[email_address] </li></ul>
    2. 2. OUTLINE <ul><li>Introduction </li></ul><ul><li>Text Fragment Learning </li></ul><ul><li>Fuzzy Grammar Fragment </li></ul><ul><li>Order Independent </li></ul>
    3. 3. ** Source from World Incidents Tracking System Human is able to understand a class without following a strict pattern
    4. 4. SUMMARY EXAMPLES <ul><li>“ On 27 May 2004 , in Nadapuram, Kerala, India, a bomb exploded at a store, causing moderate damage to the establishment but no casualties. No group claimed responsibility.” </li></ul><ul><li> “ On 27 May 2004 , at about 7:30 AM , in the Tanahu District, Nepal, a press vehicle ran over a landmine, killing the driver and injuring two passengers. No group claimed responsibility, although it is widely believed the Communist Party of Nepal (Maoist)/United People's Front was responsible.” </li></ul><ul><li>“ On 27 May 2004 , at night , in Pulwama, Jammu and Kashmir, India, armed assailants fired upon and killed a former Special Police Officer in his home. No group claimed responsibility.” </li></ul><ul><li>** Source from World Incidents Tracking System </li></ul>date date date time time victim victim
    5. 5. TEXT FRAGMENT LEARNING learn the underlying grammar patterns of similar texts ; exploiting both syntactical and semantic properties Text Fragment Examples XML Tag: Event Type - Bomb exploded - Explosion occurred - detonated a bomb -detonated a timed improvised explosive device Bombing - Attacks to occur - Attackers threw a grenade - Assailants attacked a security vehicle - Gunmen killed a member Armed Attack
    6. 6. BOMBING TEXT FRAGMENT <ul><li>“ On 1 January 2004, in Srinagar, Jammu and Kashmir, India, an assailant on a bicycle was carrying a bomb, which prematurely exploded , injuring six civilians. No group claimed responsibility.” </li></ul><ul><li>“ On 27 May 2004, in Nadapuram, Kerala, India, a bomb exploded at a store, causing moderate damage to the establishment but no casualties. No group claimed responsibility.” </li></ul><ul><li>“ On 2 February 2004, in Khowst, Nader Shah Kot District, Afghanistan, an explosion occurred at a concert, frightening the crowd, but causing no injuries. No group claimed responsibility.” </li></ul><ul><li>“ On 1 March 2004, in Burgos, Italy, an attacker detonated a bomb outside the apartment home of the mayor of Burgos, killing the official's father. The mayor had been a target of several attacks and threats, including a recent bombing at his mother's grave. No group claimed responsibility.” </li></ul><ul><li>** Source from World Incidents Tracking System </li></ul>
    7. 7. Learning Fuzzy Grammar Fragments <ul><li>“ To investigate </li></ul><ul><li>an incremental evolving fuzzy grammar fragment learning </li></ul><ul><li>with independent-order feature” </li></ul>
    8. 8. FUZZY GRAMMAR FRAGMENT ** Grammar derivation is done using a set of predefined terminal sets of type regular expression , enumeration and compound learn the underlying structure of the data convert the texts into a more structured form + Text Fragment Grammar Fragment <ul><li>Bomb exploded </li></ul><ul><li>Explosion occurred </li></ul><ul><li>detonated a bomb </li></ul><ul><li>a timed improvised explosive device detonated </li></ul><ul><li>detonated explosives </li></ul><ul><li>bombers threw grenades </li></ul><ul><li>BombType-BombAction </li></ul><ul><li>BombAction </li></ul><ul><li>BombAction-Article-Bomb Type </li></ul><ul><li>Article-Bomb Type- BombAction </li></ul><ul><li>BombAction-Bomb Type </li></ul><ul><li>CriminalList-anyword- Bomb Type </li></ul>
    9. 9. EVOLVING GRAMMAR ISSUES Grammar Class Text Class <ul><li>How to recognize the fragment </li></ul><ul><li>How to represent the grammar </li></ul><ul><li>? How to generalize the grammar </li></ul>Text Fragment1 Word 1 -Word 2 -…-Word n Grammar1 Term 1 -Term 2 -…-Term n Text Fragment2 Word 1 -Word 2 -…-Word n Grammar2 Term 1 -Term 2 -…-Term n <ul><li>Automatic Generation </li></ul><ul><li>How to tell one grammar is better ? </li></ul>Grammar1 Term 1 -Term 2 -…-Term n
    10. 10. GRAMMAR SIMILARITY Table 1: Example of string edit distance operation (*I:Insert, D:Delete, S:Substitute) Table 2: Example of Grammar Edit Distance Operation (*I:Insert, D:Delete, S:Substitute) Cost(sg ,tg) = <I D S Rs Rt>=<1 1 1 null null> I:Insert D:Delete S:Substitute Rs: remaining in Source Rt: remaining in Target Source string W E D N E S D A Y Target string T U E S D A Y Edit distance* S=1 S=1 D=1 D=1 = = = = = Source grammar, sg Number Word Word Streetending Placename Target grammar, tg Number Placename Streetending Placename Countyname Edit distance* = S=1 D=1 = = I=1
    11. 11. GRAMMAR COMBINATION Start s=new string maxMem=membership(s,TG) maxMem<1? costST=costTS=1 Y gx=Combine(sg,tg) costST=1 && costTS=0 gx=sg N Y N costST=0 && costTS=1 gx=tg Y Update TG: GTj={GTj-1-gti} union {gx} gx=sg N sg=deriveGrammar(s) tg=target grammar with maxMem costST=grammarSimilarity(sg,tg) costTS=grammarSimilarity (tg,sg) End Y N
    12. 12. MINIMAL COMBINATION RULES Source Grammar Target Grammar Cost (Source, Target) Cost (Target, Source) Combination Operation Combined grammar a-b-c a-b 0 1 0 - - 1 0 0 - - Insert a-b-[c] a-b a-b-c 1 0 0 - - 0 1 0 - - Insert a-b-[c] a-b-c a-B-c 0 0 0 - - 0 0 1 - - Merge a-B-c, B>b a-B-c a-b-c 0 0 1 - - 0 0 0 - - Merge a-B-c, B>b a-F-c a-G-c 0 0 1 - - 0 0 1 - - Create a-X-c , X:=F||G,
    13. 13. ORDER INDEPENDENT IEFG <ul><li>Let α be a triplet α =< S, GS,GT> where S is a finite permutation of strings i.e. a sequence in which each string appears exactly once. </li></ul><ul><li>parse) S. </li></ul><ul><li>GT is the set of combined grammars that represents (can </li></ul><ul><li>parse) S. </li></ul><ul><li>In order to show GS = GT we note that </li></ul><ul><li>GS ≤ GT ↔ Ext(GS) ⊆ Ext(GT) </li></ul><ul><li>GT ≤ GS ↔ Ext(GT) ⊆ Ext(GS) </li></ul><ul><li>where </li></ul><ul><li>Ext(GS) is the set of strings parse-able by GS </li></ul><ul><li>Ext(GT) is the set of strings parse-able by GT </li></ul><ul><li>Hence it suffices to show that </li></ul><ul><li>Ext(GS) = Ext(GT) </li></ul>
    14. 14. THEOREM 1: FOR α =< S,GS,GT> EXT(GS)=EXT(GT) <ul><li>Proof by induction </li></ul><ul><li>Basis n=1 </li></ul><ul><li>Clearly GS = {gs1} = GT, so Ext(GS) = Ext(GT) </li></ul><ul><li>Inductive step </li></ul><ul><li>We assume that Ext(GSj-1) = Ext(GTi-1) for some arbitrary value i=j and j>1 and show that </li></ul><ul><li>Ext(GSj) = Ext(GTi) </li></ul><ul><li>Note that </li></ul><ul><li>Ext(GSj) = Ext(GSj-1)∪ Ext(gsj) </li></ul>
    15. 15. Let: Ext(GS j ) = Ext(GS j-1 ) ∪ Ext(gs j ) g x =Combine(gs j ,gt i ) Ext(g x ) = Ext(gs j ) ∪ Ext (gt i ) Case1: Combine( gs j ,gt i ) if Cost(gs j ,gt i )=Cost(gt i , gs j )= 1 In this case, Ext(GT i ) = Ext(GT i-1 - {gt i }) ∪ Ext(g x ) Hence Ext(GT i ) = (Ext(GTi-1) - (Ext(gt i )) ∪ Ext(g x ) = Ext(GT x-1 ) ∪ Ext(gs j ) Case2: Combine( gs j ,gt i ) if gs j is more general than gt i i.e. Ext(gt i ) ⊆ Ext(gs j ) In this case, Ext(GT i ) = Ext(GT i-1 ) ∪ Ext(gs j ) Case3: Combine( gs j ,gt i ) if gt i is more general than gs j i.e. Ext(gs j ) ⊆ Ext (gt i ) In this case, Ext(GT i ) = Ext(GT i-1 ) Therefore Ext(GS j-1 ) = Ext(Gt j-1 ) implies Ext(GS j ) = Ext(Gt i ) Thus in all cases the inductive hypothesis is true and Ext(GSj)=Ext(Gti) ■
    16. 16. LEMMA 2.1 <ul><li>For any two permutations S and S*, giving derived grammars GS and GS* </li></ul><ul><li>Ext(GSj) = Ext(GSj*) </li></ul><ul><li>Proof </li></ul><ul><li>Each example string sj leads to a derived grammar gsi. Clearly from the definition </li></ul><ul><li>Ext(GS) = Ext(gs1) ∪ Ext(gs2) ∪ … </li></ul><ul><li>This is independent of the order in which the example strings are presented. </li></ul>
    17. 17. <ul><li>Theorem 2 : Given α =< S, GS ,GT> and α * =< S*, GS* ,GT*>, </li></ul><ul><li>Then Ext(GTi) = Ext(GTi*) </li></ul><ul><li>Proof </li></ul><ul><li>By lemma 2.1, Ext(GSj) = Ext(GSj*) </li></ul><ul><li>By theorem 1, Ext(GSj) = Ext(Gti) and Ext(GSj*) = Ext(GTi*) </li></ul><ul><li>Hence Ext(GTi) = Ext(GTi*) </li></ul><ul><li>Corollary 2 </li></ul><ul><li>Cost( GT,GT*) = Cost(GT*,GT)= <0 0 0 null null> </li></ul><ul><li>This ends the proof of Theorem 2■ </li></ul>To show that the IEFG process is independent of the order in which examples are presented, we consider a different permutation S* leading to  * =<S*, GS* ,GT*> and show that Ext(GTi) = Ext(GTi*)
    18. 18. EXAMPLE <ul><li>generated results may not be syntactically identical but rather yield same (approximate) parsing coverage even when the pattern instances are presented in different orders. </li></ul>
    19. 19. CONCLUSION <ul><li>An algorithm that features independent training order can ensure robust results. </li></ul><ul><li>This paper discusses an order-independent fuzzy grammar fragment learning method which is implemented using incremental evolving method. </li></ul><ul><li>The formalized theory is supported with empirical evidence which generates grammars that have equal (approximated) parsing coverage of the trained dataset regardless of the orders . </li></ul>

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