Lecture 3 Modeling.pdf

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Fuzzy Set Theorya class• A fuzzy subset A of a universe of discourseU is characterized by a membershipfunction µ A : U→[0,1] which associates witheach element u of U a number µ A (u) in theinterval [0,1]– complement:– union: A∪B– intersection:a documentμ ( u)= 1−μ ( u)Aμ ( u)= max( μ ( u),μ ( u))Aμ ( u)= min( μ ( u),μ ( u))A∩BAABB3-52
Examples• Assume U={d 1 , d 2 , d 3 , d 4 , d 5 , d 6 }• Let A and B be {d 1 , d 2 , d 3 } and {d 2 , d 3 , d 4 },respectively.• Assume μ A ={d 1 :0.8, d 2 :0.7, d 3 :0.6, d 4 :0, d 5 :0, d 6 :0} andμ B ={d 1 :0, d 2 :0.6, d 3 :0.8, d 4 :0.9, d 5 :0, d 6 :0}μ( u)= 1−μ ( u)• A ={d 1 :0.2, d 2 :0.3, d 3 :0.4, d 4 :1, d 5 :1, d 6 :1}A• μ A∪B( u)= max( μ A(u),μB( u))={d 1 :0.8, d 2 :0.7, d 3 :0.8, d 4 :0.9,d 5 :0, d 6 :0}μ ( u)= min( μ ( u),μ ( u))• A∩BA B ={d 1 :0, d 2 :0.6, d 3 :0.6, d 4 :0,d 5 :0, d 6 :0}3-53
Page 1 and 2: Lecture 3 Modeling3-1
Page 3 and 4: Information Retrieval Models• Cla
Page 5 and 6: Taxonomy of Information Retrieval M
Page 7 and 8: Combinations of these issuesUSERTAS
Page 9 and 10: User profile• Simplistic approach
Page 11 and 12: Formal Definition of IR Models(cont
Page 13 and 14: Boolean Model• The index term wei
Page 15 and 16: Boolean Model (Continued)• advant
Page 17 and 18: Document representation in vector s
Page 19 and 20: Similarity Measure (Continued)• v
Page 21 and 22: Sample query-documentsimilarity com
Page 23 and 24: Vector Model• w i,j : a positive,
Page 25 and 26: document ranking• Similarity (i.e
Page 27 and 28: Definition of tf• N: total number
Page 29 and 30: Analysis of vector model• advanta
Page 31 and 32: Probabilistic Model (Continued)•
Page 33 and 34: Probabilistic Principle• w i,j
Page 35 and 36: 3-35independence assumption ofindex
Page 37 and 38: Initial guess• P(k i |R) is const
Page 39 and 40: Small values of V and V i• altern
Page 41 and 42: • Initial GuessProbabilistic Mode
Page 43 and 44: No Interaction with User• Retriev
Page 45 and 46: No Interaction with User• Retriev
Page 47 and 48: Interaction with User• Alternativ
Page 49 and 50: Analysis of Probabilistic Model•
Page 51: Alternative Set Theoretic Models-Fu
Page 55 and 56: Fuzzy OR3-55
Page 57 and 58: Fuzzy Information Retrieval• basi
Page 59 and 60: Fuzzy Information Retrieval(Continu
Page 61 and 62: ExampleQuery q=k a ∧ (k b ∨¬k
Page 63 and 64: Fuzzy Set Model3-63
Page 65 and 66: Fuzzy Set Model• Sim(q,d): Altern
Page 67 and 68: Review• Two vectors u and v are l
Page 69 and 70: Generalized Vector Space Model(Cont
Page 71 and 72: t=3cccminterm m r m r vectorm 1 =(0
Page 73 and 74: Generalized Vector Space Model(Cont
Page 75 and 76: 3-7523,823,623,423,283,863,63,423,2
Page 77 and 78: asic idea• Map each document and
Page 79 and 80: Singular Value DecompositionA∈R(1
Page 81 and 82: A=QDQtAQ=tQDQ Q=QDwhere Q=[ q q21Kq
Page 83 and 84: M=tM= ( K S D= ( DSDSM M=K St22: do
Page 85 and 86: Ranking in LSI• query: a pseudo-d
Page 87 and 88: Non-Overlapping Lists• divide the
Page 89 and 90: Inverted Files• File is represent
Page 91 and 92: Inverted-file process (Continued)
Page 93 and 94: Extensions of Inverted Index Operat
Page 95 and 96: Model Based on Proximal Nodes• hi
Page 97 and 98: Model Based on Proximal Nodes(Conti
Page 99 and 100: Models for Browsing• Flat organiz

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