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Modern information retrieval Modelling

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Introduction IR systems usually adopt index terms to process queries IR systems usually adopt index terms to process queries Index term: Index term: –a keyword or group of selected words –any word (more general) Stemming might be used: Stemming might be used: –connect: connecting, connection, connections An inverted file is built for the chosen index terms An inverted file is built for the chosen index terms

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Introduction Indexing results in records like Indexing results in records like Doc12: napoleon, france, revolution, emperor or (weighted terms) or (weighted terms) Doc12: napoleon-8, france-6, revolution-4, emperor-7 To find all documents about Napoleon would involve looking at every document’s index record (possibly 1,000s or millions). To find all documents about Napoleon would involve looking at every document’s index record (possibly 1,000s or millions). (Assume that Doc12 references another file which contains other details about the document.) (Assume that Doc12 references another file which contains other details about the document.)

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Introduction Instead the information is inverted : Instead the information is inverted : napoleon : doc12, doc56, doc87, doc99 or (weighted) or (weighted) napoloen : doc12-8, doc56-3, doc87-5, doc99-2 inverted file contains one record per index term inverted file contains one record per index term inverted file is organised so that a given index term can be found quickly. inverted file is organised so that a given index term can be found quickly.

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Introduction To find documents satisfying the query To find documents satisfying the query napoleon and revolution –use the inverted file to find the set of documents indexed by napoleon -> doc12, doc56, doc87, doc99 –similarly find the set of documents indexed by revolution -> doc12, doc20, doc45, doc99 –intersect these sets -> doc12, doc99 –go to the document file to retrieve title, authors, location for these documents.

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Introduction Docs Information Need Index Terms doc query Ranking match

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Introduction Matching at index term level is quite imprecise No surprise that users get frequently unsatisfied Since most users have no training in query formation, problem is even worst Frequent dissatisfaction of Web users Issue of deciding relevance is critical for IR systems: ranking

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Introduction A ranking is an ordering of the documents retrieved that (hopefully) reflects the relevance of the documents to the user query A ranking is based on fundamental premisses regarding the notion of relevance, such as: common sets of index terms sharing of weighted terms likelihood of relevance Each set of premisses leads to a distinct IR model

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IR Models Non-Overlapping Lists Proximal Nodes Structured Models Retrieval: Adhoc Filtering Browsing U s e r T a s k Classic Models boolean vector probabilistic Set Theoretic Fuzzy Extended Boolean Probabilistic Inference Network Belief Network Algebraic Generalized Vector Lat. Semantic Index Neural Networks Browsing Flat Structure Guided Hypertext

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IR Models The IR model, the logical view of the docs, and the retrieval task are distinct aspects of the system

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Retrieval: Ad Hoc x Filtering Ad hoc retrieval: Collection “Fixed Size” Q2Q3 Q1Q4 Q5

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Retrieval: Ad Hoc x Filtering Filtering: Documents Stream User 1 Profile User 2 Profile Docs Filtered for User 2 Docs for User 1

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Classic IR Models - Basic Concepts Each document represented by a set of representative keywords or index terms An index term is a document word useful for remembering the document main themes Usually, index terms are nouns because nouns have meaning by themselves However, search engines assume that all words are index terms (full text representation)

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Classic IR Models - Basic Concepts Not all terms are equally useful for representing the document contents: less frequent terms allow identifying a narrower set of documents The importance of the index terms is represented by weights associated to them Let ki be an index term dj be a document wij is a weight associated with (ki,dj) The weight wij quantifies the importance of the index term for describing the document contents

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Classic IR Models - Basic Concepts Ki is an index term dj is a document t is the number of index terms K = (k1, k2, …, kt) is the set of all index terms wij >= 0 is a weight associated with (ki,dj) wij = 0 indicates that term does not belong to doc vec(dj) = (w1j, w2j, …, wtj) is a weighted vector associated with the document dj gi(vec(dj)) = wij is a function which returns the weight associated with pair (ki,dj)

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The Boolean Model Simple model based on set theory Queries specified as boolean expressions precise semantics neat formalism q = ka (kb kc) Terms are either present or absent. Thus, wij {0,1} Consider q = ka (kb kc) vec(qdnf) = (1,1,1) (1,1,0) (1,0,0) vec(qcc) = (1,1,0) is a conjunctive component

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The Boolean Model q = ka (kb kc) sim(q,dj) = 1 if vec(qcc) | (vec(qcc) vec(qdnf)) ( ki, gi(vec(dj)) = gi(vec(qcc))) 0 otherwise (1,1,1) (1,0,0) (1,1,0) KaKb Kc

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The Boolean Model Example: Terms: K 1, …,K 8. Documents: 1. D 1 = {K 1, K 2, K 3, K 4, K 5 } 2. D 2 = {K 1, K 2, K 3, K 4 } 3. D 3 = {K 2, K 4, K 6, K 8 } 4. D 4 = {K 1, K 3, K 5, K 7 } 5. D 5 = {K 4, K 5, K 6, K 7, K 8 } 6. D 6 = {K 1, K 2, K 3, K 4 } Query: K 1 (K 2 K 3 ) Answer: {D 1, D 2, D 4, D 6 } ({D 1, D 2, D 3, D 6 } {D 3, D 5 }) = {D 1, D 2, D 6 }

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Drawbacks of the Boolean Model Retrieval based on binary decision criteria with no notion of partial matching No ranking of the documents is provided (absence of a grading scale) Information need has to be translated into a Boolean expression which most users find awkward The Boolean queries formulated by the users are most often too simplistic As a consequence, the Boolean model frequently returns either too few or too many documents in response to a user query

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The Vector Model Use of binary weights is too limiting Non-binary weights provide consideration for partial matches These term weights are used to compute a degree of similarity between a query and each document Ranked set of documents provides for better matching

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The Vector Model Define: wij > 0 whenever ki dj wiq >= 0 associated with the pair (ki,q) vec(dj) = (w1j, w2j,..., wtj) and vec(q) = (w1q, w2q,..., wtq) To each term ki is associated a unitary vector vec(i) The unitary vectors vec(i) and vec(j) are assumed to be orthonormal (i.e., index terms are assumed to occur independently within the documents) The t unitary vectors vec(i) form an orthonormal basis for a t-dimensional space In this space, queries and documents are represented as weighted vectors

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The Vector Model Sim(q,dj) = cos( ) = [vec(dj) vec(q)] / |dj| * |q| = [ wij * wiq] / |dj| * |q| Since wij > 0 and wiq > 0, 0 <= sim(q,dj) <=1 A document is retrieved even if it matches the query terms only partially i j dj q

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The Vector Model Sim(q,dj) = [ wij * wiq] / |dj| * |q| How to compute the weights wij and wiq ? A good weight must take into account two effects: quantification of intra-document contents (similarity) tf factor, the term frequency within a document quantification of inter-documents separation (dissi- milarity) idf factor, the inverse document frequency wij = tf(i,j) * idf(i)

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The Vector Model Let, N be the total number of docs in the collection ni be the number of docs which contain ki freq(i,j) raw frequency of ki within dj A normalized tf factor is given by f(i,j) = freq(i,j) / max(freq(l,j)) where the maximum is computed over all terms which occur within the document dj The idf factor is computed as idf(i) = log (N/ni) the log is used to make the values of tf and idf comparable. It can also be interpreted as the amount of information associated with the term ki.

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The Vector Model The best term-weighting schemes use weights which are give by wij = f(i,j) * log(N/ni) the strategy is called a tf-idf weighting scheme For the query term weights, a suggestion is wiq = (0.5 + [0.5 * freq(i,q) / max(freq(l,q)]) * log(N/ni) The vector model with tf-idf weights is a good ranking strategy with general collections The vector model is usually as good as the known ranking alternatives. It is also simple and fast to compute.

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The Vector Model Example: A collection includes 10,000 documents The term A appears 20 times in a particular document The maximum apperance of any term in this document is 50 The term A appears in 2,000 of the collection documents. f(i,j) = freq(i,j) / max(freq(l,j)) = 20/50 = 0.4 idf(i) = log(N/ni) = log (10,000/2,000) = log(5) = 2.32 wij = f(i,j) * log(N/ni) = 0.4 * 2.32 = 0.93

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The Vector Model Advantages: term-weighting improves quality of the answer set partial matching allows retrieval of docs that approximate the query conditions cosine ranking formula sorts documents according to degree of similarity to the query Disadvantages: assumes independence of index terms (??); not clear that this is bad though

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The Vector Model: Example I d1 d2 d3 d4d5 d6 d7 k1 k2 k3

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The Vector Model: Example II d1 d2 d3 d4d5 d6 d7 k1 k2 k3

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The Vector Model: Example III d1 d2 d3 d4d5 d6 d7 k1 k2 k3

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