modern information retrieval modelling. introduction ir systems usually adopt index terms to process...
TRANSCRIPT
IntroductionIntroduction
• IR systems usually adopt index terms to IR systems usually adopt index terms to process queriesprocess queries
• Index term:Index term:– a keyword or group of selected wordsa keyword or group of selected words– any word (more general)any word (more general)
• Stemming might be used:Stemming might be used:– connect: connecting, connection, connectionsconnect: connecting, connection, connections
• An inverted file is built for the chosen An inverted file is built for the chosen index termsindex terms
IntroductionIntroduction
• Indexing results in records likeIndexing results in records likeDoc12: Doc12: napoleon, france, revolution, emperornapoleon, france, revolution, emperor
or (weighted terms)or (weighted terms)Doc12: Doc12: napoleonnapoleon-8, -8, francefrance-6, -6, revolutionrevolution-4, -4, emperoremperor-7-7
• To find all documents about Napoleon To find all documents about Napoleon would involve looking at every document’s would involve looking at every document’s index record (possibly 1,000s or millions).index record (possibly 1,000s or millions).
• (Assume that Doc12 references another file (Assume that Doc12 references another file which contains other details about the which contains other details about the document.)document.)
IntroductionIntroduction
• Instead the information is Instead the information is invertedinverted : :napoleonnapoleon : doc12, doc56, doc87, doc99 : doc12, doc56, doc87, doc99
or (weighted)or (weighted)napoloennapoloen : doc12-8, doc56-3, doc87-5, doc99-2 : doc12-8, doc56-3, doc87-5, doc99-2
• inverted file contains one record per inverted file contains one record per index termindex term
• inverted file is organised so that a given inverted file is organised so that a given index term can be found quickly.index term can be found quickly.
IntroductionIntroduction
• To find documents satisfying the To find documents satisfying the query query napoleonnapoleon andand revolutionrevolution– use the inverted file to find the set of use the inverted file to find the set of
documents indexed by documents indexed by napoleonnapoleon -> -> doc12, doc12, doc56, doc87, doc99doc56, doc87, doc99
– similarly find the set of documents indexed by similarly find the set of documents indexed by revolutionrevolution -> -> doc12, doc20, doc45, doc99doc12, doc20, doc45, doc99
– intersectintersect these sets -> these sets -> doc12, doc99doc12, doc99
– go to the document file to retrieve title, go to the document file to retrieve title, authors, location for these documents.authors, location for these documents.
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
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
IR Models
Non-Overlapping ListsProximal 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
IR Models The IR model, the logical view of the docs, and the retrieval
task are distinct aspects of the system
Index Terms
Full Text
Full Text + Structure
Retrieval
Classic
Set Theoretic Algebraic
Probabilistic
Classic
Set Theoretic Algebraic
Probabilistic
Structured
Browsing
Flat
Flat
Hypertext
Structure Guided
Hypertext
LOGICAL VIEW OF DOCUMENTS
USER T A S K
Retrieval: Ad Hoc x Filtering Filtering:
Documents Stream
User 1Profile
User 2Profile
Docs Filteredfor User 2
Docs forUser 1
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)
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
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)
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
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)
Ka Kb
Kc
The Boolean Model Example:
Terms: K1, …,K8.
Documents:1. D1 = {K1, K2, K3, K4, K5}
2. D2 = {K1, K2, K3, K4}
3. D3 = {K2, K4, K6, K8}
4. D4 = {K1, K3, K5, K7}
5. D5 = {K4, K5, K6, K7, K8}
6. D6 = {K1, K2, K3, K4} Query: K1 (K2 K3) Answer: {D1, D2, D4, D6} ({D1, D2, D3, D6} {D3, D5})
= {D1, D2, D6}
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
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
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
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
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)
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.
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.
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
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
The Vector Model: Example I
d1
d2
d3d4 d5
d6d7
k1k2
k3
k1 k2 k3 q dj |dj| Sim(dj,q)d1 1 0 1 2 1.41 0.82d2 1 0 0 1 1 0.58d3 0 1 1 2 1.41 0.82d4 1 0 0 1 1 0.58d5 1 1 1 3 1.73 1d6 1 1 0 2 1.41 0.82d7 0 1 0 1 1 0.58
q 1 1 1 |q| 1.73
The Vector Model: Example II
d1
d2
d3d4 d5
d6d7
k1k2
k3
k1 k2 k3 q djd1 1 0 1 4d2 1 0 0 1d3 0 1 1 5d4 1 0 0 1d5 1 1 1 6d6 1 1 0 3d7 0 1 0 2
q 1 2 3