Transcript Information Search
INFORMATION SEARCH
Presenter: Pham Kim Son
Saint Petersburg State University
Overview
Introduction Overview of IR system and basic terminologies Classical models of Information Retrieval Boolean Model Vector Model Modern models of Information Retrieval Latent Semantic Indexing Correlation Method Conclusion
Introduction
People need information to solve problem Very simple thing Complex thing “Perfect search machine” defined by Larry Page is something that understand exactly what you mean and return exactly what you want.
Challenges to IR
Introduction of www www is large Heterogeneous Gives challenges to IR
Overview of IR and basic terminologies
IR can be divided in to 3 components Query Input Processor Processor Input Output Output Documents
Input
Input The main task: Obtain a good representation of each document and query for computer to use A document representative: a list of extracted keywords Idea: Let the computer process the natural language in the document
Input (cont)
Obstacles Theory of human language has not been sufficiently developed for every language Not clear how to use it to enhance information retrieval
Input (cont)
Representing documents by keywords Step1:Removing common words Step2: Stemming
Step1: Removing common words words By So comparing with stop-list cent (C.J. van Rijsbergen)
Step2:Stemming Def: Stemming : The process of chopping the ending of a term, e.g. removing “ed”, ”ing” Algorithm Porter
Processor
Processor This part of the IR system are concerned with the retrieval process Structuring the documents in an appropriate way Performing actual retrieval function, using a predefined model
output
Output
Input Processor The output will be a set of documents, assumed to be relevant to users.
Purpose of IR: Retrieved all relevant documents Retrieved irrelevant documents as few as possible
Definition Relevant docs retrieved relevant docs
recall
Number of relevant Total number of documents retrieved relevant documents
Relevant docs retrieved All docs retrieved
precision
Number of relevant Total number of documents retrieved documents retrieved
Returns relevant documents but misses many useful ones too 1 The ideal 0 Recall 1 Returns most relevant documents but includes lots of junk
Information Retrieval Models
Classical models Boolean model Vector model Novel models Latent semantic indexing model Correlation method
Boolean model
Earliest and simplest method, widely used in IR systems today Based on set theories and Boolean algebra.
Queries are Boolean expressions of keywords, connected by operators AND, OR, ANDNOT Ex: (Saint Petersburg AND Russia) | (beautiful city AND Russia)
Inverted files are widely used Ex: Term1 : doc 2 , doc 5, doc6 ; Term2 : doc 2, doc4, doc5; Query : q = (term1 AND term2) Result: doc2, doc5 Term-document matrix can be used
Thinking about Boolean model
Advantages: Very simple model based on sets theory Easy to understand and implement Supports exact query Disadvantages: Retrieval based on binary decision criteria , without notion of partial matching Sets are easy, but complex Boolean expressions are not The Boolean queries formulated by users are most often so simplistic Retrieves so many or so few documents Gives unranked results
Vector Model
Why Vector Model ?
Boolean model just takes into account the existence or nonexistence of terms in a document Has no sense about their different contributions to documents
Overview theory of vector model
Documents and queries are displayed as vectors in index-term space Space dimension is equal to the vocabulary size Components of these vectors: the weights of the corresponding index term, which reflects its significant in terms of representative and discrimination power Retrieval is based on whether the “query vector” and “document vector” are closed enough.
Set of document:
D
{
D D
1 , 2 ,...,
D m
} A finite set of terms :
T
t t
1 2
t n
Every document can be displayed as vector:
d j
(
w
1
j
,
w
2
j
,...,
w nj
) the same to the query:
q
(
w
1
q
,
w
2
q
,...,
w nq
)
j dj
q i
Similarity of query q and document d: (||
d
Given a threshold , all documents with similarity > threshold are retrieved
Compute a good weight
A variety of weighting schemes are available They are based on three proven principles: Terms that occur in only a few documents are more valuable than ones that appear in many The more often a term occur in a document, the more likely it is to be important to that document A term that appears the same number of times in a short document and in a long one is likely to be more available for the former
tf-idf-dl (tf-idf) scheme
The term frequency of a term t i in document d j :
ij
i j
The length of document d j : DL j = total number of terms occurrences in document d j Inverted document frequency: collection of N documents, inverted document frequency of a term t i that appears in n document is : Weight:
IDF i
log
N n w ij
TF ij
*
IDF i DL j
Think about Vector model
Advantages: Term weighting improves the quality of the answer Partial matching allows to retrieve the documents that approximate the query conditions Cosine ranking formula sorts the answer Disadvantages Assumes the independences of terms Polysemy and synonymy problem are unsolved
Modern models of IR
Why ?
Problems with polysemy: Bass (fish or music ?) Problems with synonymy: Car or automobile ?
These failures can be traced to : The way index terms are identified is incomplete Lack of efficient methods to deal with polysemy Idea to solve this problem: take the advance of implicit higher order structure(latent) in the association terms with documents .
Latent Semantic Indexing (LSI)
LSI overview Representing documents roughly by terms is unreliability, ambiguity and redundancy Should find a method , which can : Documents and terms are displayed as vectors in a k-dim concepts space. Its weights indicating the strength of association with each of these concepts That method should be flexible enough to remove the weak concepts, considered as noises
Document-term matrix A[mxn] are built
t 1 t 2
:
w w d 1 11 21 d w w 2 12 22 …. d m … w 1m … w 2m
: : :
t n
:
w
: : :
n1 w n2 … w nm
Matrix A is factored in to 3 matrices, using Singular value decomposition SVD U,V are orthogonal matrices
diag
( 1 , 2 ,...,
n
)
T U U
T V V
Let ( ) 1 2
r
r
1
I n
n
0
T
These special matrices show a break down of the original relationship (doc-term) to a linearly independent components (factors) Many of these components are very small: ( considered as noises) and should be ignored 1 0 ...
0 0 ...
...
0 ...
0
r
...
0 ...
...
0
V T
Criteria to choose k: Ignore noises Important information are not lost Documents and terms are displayed as vectors in k dim space Theory Eckart & Young
A k
ensures us about not losing important information min ||
k
|| 2
F
||
A
A k
|| 2
F
k
2 1
U k
V k T
r
2
Query
Should find a method to display a query to k-dim space Query q can be seen as a document.
From equation: We have
q k
A k T q U k
U k
k
1
V k T
Similarity between objects
Term-Term: Dot product between two rows vector of matrix A k reflects the similarity between two terms
T
Term-term similarity matrix :
A A k k T
U k
k k T V V k
k U k T
(
U k k k U k T
) Can consider the rows of matrix as coordinate of
k
k
terms.
The relation between taking rows of as coordinate
k U k
k
Document-document
D
Dot product between two columns vectors of matrix A k reflect the similarity between two documents.
k T A A k
k k k T U U k
k V k T
(
V k k k V k T
) documents.
Term-document This value can be obtained by looking at the element of matrix A k
A k
U k
k V k T
U k k k
1/ 2
V k
Drawback: between and within comparisons can not be done simultaneously without resizing the coordinate.
Example
q1:
human
machine
interface
for Lab ABC computer applications q2: a survey of user opinion of
computer system response time.
q3: the EPS user
interface
management
system
q4:
System
and
human system
engineering testing of EPS q5:Relation of user-perceived
response time
to error measurement q6: The generation of random, binary, unordered
tree
q7: The intersection
graph
of paths in
trees
q8:
Graph minors
IV: Widths of
trees
and well-quasi-ordering q9:
Graph minors
: A survey
A k
Numerical results
0.22
0.20
0.24
0.40
0.64
0.27
0.27
0.30
0.21
0.01
0.04
T
A k
U k
k V k T
0.11
0.07
0.04
0.06
0.17
0.11
0.11
0.14
0.27
0.49
0.62
3.34
0 0 2.54
0.20
0.06
A
human interface computer user system response time EPS survey trees graph minors
0.61
0.
17 0.46
0.13
q
1 1 1 1 0 0 0 0 0 0 0 0 0
q
2 0 0 1 1 1 1 1 0 1 0 0 0 0.54
0.23
q
3 0 1 0 1 1 0 0 1 0 0 0 0 0.28
q
4 1 0 0 0 2 0 0 1 0 0 0 0
q
5 0 0 0 1 0 1 1 0 0 0 0 0 0.00
0.11 0.19
0 0 0 0 0 0 0 0 0 1 0 0
q
6 0.03
0.45
0.02
0.44
q
7 0 0 0 0 0 0 0 0 0 1 1 0
q
8 0 0 0 0 0 0 0 0 0 1 1 1 0.02
0.62
q
9 0 0 0 0 0 0 0 0 1 0 1 1 0.08
0.53
Query: human computer interaction
Updating
Folding in New document
k d new
d T new U k
k
1 New terms and docs has no effect on the presentation of pre-existing docs and terms Re-computing SVD Re-compute SVD Requires times and memory Choosing one of these two methods
Think about LSI
Advantages: Synonymy problem is solved Displaying documents in a more reliable space: Concepts space Disadvantages: Polysemy problem is still unsolved A special algorithms for handling with large size matrices should be implemented
Correlation Method
Idea: If a keyword is present in the document, correlated keywords should be taken into account as well. So, the concepts containing in the document aren’t obscured by the choices of a specific vocabulary.
In vector space model: similarity vector :
T r
A q
Depend on the user query q, we now build the best query, taking the correlated keyword into account as well.
The correlation matrix is built based on the term-document matrix Let: A is the term-document matrix D : number of document, is the mean vector. Clearly that :
d
1
D j D
1
d j d
Covariance matrix is computed:
D C
D
1 1
j
1 (
d
Correlation Matrix S :
j
S j
d
)
ij c ij s ij
c c ii jj
Better query:
q better
Sq
We now use SVD to reduce noises in the correlation of keywords: We choose the first k largest factors to obtain the k dimensional of S
S k
X k
k X k T
Generate our best query:
q best
S q k
Vector of similarity :
r
k
k
k k
k k
Define a projection, defined by : 1/ 2
k P k
1/ 2
k X k T
Strength of correlation method
In real world, correlation between words are static. Number of terms has a higher stability level when comparing with number of documents Number of documents are many times larger than number of keywords.
This method is able to handle database with a very large number of documents and doesn’t have to update the correlation matrix every time adding new documents.
Its importance in the electronic networks.
Conclusion
IR overview Classical IR models : Boolean model Vector model Modern IR models : LSI Correlation methods
Any questions ?
References
Gheorghe Muresan: Using document Clustering and language modeling in mediated IR.
Georges Dupret: Latent Concepts and the Number Orthogonal Factors in Latent Semantic Indexing C.J. van RIJSBERGEN: Information Retrieval Ricardo Baeza-Yates: Modern Information Retrieval Sandor Dominich: Mathematical foundation of information retrieval.
IR lectures note from : www.cs.utexas.edu
Scott Deerwester, Susan T.Dumais: Indexing by Latent Semantic Analysis
Desktop Search
Design the desktop search that satisfies Not affects computer’s performance Privacy is protected Ability to search as many types of files as possible( consider music file) Multi languages search User-friendly Support semantic search if possible