Introduction to Digital Libraries

Searching

Technical View: Retrieval as Matching Documents to Queries

DocumentSpace Sample Sample

QuerySpace

Surrogates Surrogates

Terms

Vectors

Etc..

Query Form B

Etc..

MatchAlgorithm

Retrieval is algorithmic. Evaluation is typically a binary decision for each pairwise match and one or more aggregate values for a set of matches (e.g., recall and precision).

Query Form A

Human View: Information-Seeking Process

Data

Indexes

PhysicalInterface

Problem

PerceivedNeeds Queries

Results

Actions

Information seeking is an active, iterative process controlled by a human who Changes throughout the process. Evaluation is relative to human needs.

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

“Classic” Retrieval Models• Boolean

– Documents and queries are sets of index terms

• Vector– Documents and queries are documents in N-

dimensional space

• Probabilistic– Based on probability theory

Boolean Searching

• Exactly what you would expect– and, or, not operations defined

• requires an exact match

• based on inverted file

• (computer and science) and (not(animals)) would prevent a document with “use of computers in animal science research” from being retrieved

Boolean ‘AND’

• Information AND Retrieval

Information Retrieval

Example

• Draw a Venn diagram for: Care and feeding and (cats or dogs)

• What is the meaning of:Information and retrieval and performance

or evaluation

Exercise

• D1 = “computer information retrieval”

• D2 = “computer retrieval”

• D3 = “information”

• D4 = “computer information”

• Q1 = “information retrieval”

• Q2 = “information ¬computer”

Boolean-based Matching

• Exact match systems; separate the documents containing a given term from those that do not.

Doc

umen

ts

0 0 1 1 0 0 0 0 1 1 0 0 0

0 1 1 0 0 0 0 0 0 0 1 1 0

1 0 1 0 1 0 0 1 0 0 0 0 1

1 1 0 0 0 1 1 0 0 0 0 1 0

Terms

adventure

agriculture

bridge

cathedrals

disasters

flags

horticulture

leprosy

Mediterranean

recipes

scholarships

tennis

Venus

Queries

(bridge OR flags) AND tennis

flags AND tennis

leprosy AND tennis

Venus OR (tennis AND flags)

Exercise0

1 Swift

2 Shakespeare

3 Shakespeare Swift

4 Milton

5 Milton Swift

6 Milton Shakespeare

7 Milton Shakespeare Swift

8 Chaucer

9 Chaucer Swift

10 Chaucer Shakespeare

11 Chaucer Shakespeare Swift

12 Chaucer Milton

13 Chaucer Milton Swift

14 Chaucer Milton Shakespeare

15 Chaucer Milton Shakespeare Swift

((chaucer OR milton) AND (NOT swift)) OR ((NOT chaucer) AND (swift OR shakespeare))

Boolean features

• Order dependency of operators– ( ), NOT, AND, OR (DIALOG)

– May differ on different systems

• Nesting of search terms– Nutrition and (fast or junk) and food

Boolean Limitations

• Searches can become complex for the average user– too much ANDing can clobber recall– tricky syntax:

“research AND NOT computer science”“research AND NOT (computer science)” (implicit OR)

“research AND NOT (computer AND science)”

all different -- (frequently seen in NTRS logs)

Vector Model

• Calculate degree of similarity between document and query

• Ranked output by sorting similarity values

• Also called ‘vector space model’• Imagine your documents as N-dimensional

vectors (where N=number of words)• The “closeness” of 2 documents can be expressed

as the cosine of the angle between the two vectors

Vector Space Model

• Documents and queries are points in N-dimensional space (where N is number of unique index terms in the data collection)

Q

D

Vector Space Model with Term Weights

• assume document terms have different values for retrieval

• therefore assign weights to each term in each document– example:

• proportional to frequency of term in document

• inversely proportional to frequency of term in collection

Graphic Representation

Example:D1 = 2T1 + 3T2 + 5T3

D2 = 3T1 + 7T2 + T3

Q = 0T1 + 0T2 + 2T3

T3

T1

T2

D1 = 2T1+ 3T2 + 5T3

D2 = 3T1 + 7T2 + T3

Q = 0T1 + 0T2 + 2T3

7

32

5

• Is D1 or D2 more similar to Q?• How to measure the degree of

similarity? Distance? Angle? Projection?

Document and Query Vectors

• Documents and Queries are vectors of terms• Vectors can use binary keyword weights or

assume 0-1 weights (term frequencies)• Example terms: “dog”,”cat”,”house”, “sink”,

“road”, “car”• Binary: (1,1,0,0,0,0), (0,0,1,1,0,0)• Weighted: (0.01,0.01, 0.002, 0.0,0.0,0.0)

Document Collection Representation• A collection of n documents can be represented in the

vector space model by a term-document matrix.• An entry in the matrix corresponds to the “weight” of a

term in the document; zero means the term has no significance in the document or it simply doesn’t exist in the document.

T1 T2 …. Tt

D1 w11 w21 … wt1

D2 w12 w22 … wt2

: : : : : : : :Dn w1n w2n … wtn

Inner Product: Example 1

k1 k2 k3 q dj d1 1 0 1 2 d2 1 0 0 1 d3 0 1 1 2 d4 1 0 0 1 d5 1 1 1 3 d6 1 1 0 2 d7 0 1 0 1

q 1 1 1

d1

d2

d3d4 d5

d6d7

k1k2

k3

Vector Space Exampleindexed words:factors information help human operation retrieval systems

Query: human factors in information retrieval systemsVector: (1 1 0 1 0 1 1)Record 1 contains: human, factors, information, retrievalVector: (1 1 0 1 0 1 0)Record 2 contains: human, factors, help, systemsVector: (1 0 1 1 0 0 1)Record 3 contains: factors, operation, systemsVector: (1 0 0 0 1 0 1)

Simple Match

Query (1 1 0 1 0 1 1)Rec1 (1 1 0 1 0 1 0) (1 1 0 1 0 1 0) =4

Query (1 1 0 1 0 1 1)Rec2 (1 0 1 1 0 0 1) (1 0 0 1 0 0 1) =3

Query (1 1 0 1 0 1 1)Rec3 (1 0 0 0 1 0 1) (1 0 0 0 0 0 1) =2

Weighted Match

Query (1 1 0 1 0 1 1)Rec1 (2 3 0 5 0 3 0) (2 3 0 5 0 3 0) =13

Query (1 1 0 1 0 1 1)Rec2 (2 0 4 5 0 0 1) (2 0 0 5 0 0 1) =8

Query (1 1 0 1 0 1 1)Rec3 (2 0 0 0 2 0 1) (2 0 0 0 0 0 1) =3

Term Weights: Term Frequency

• More frequent terms in a document are more important, i.e. more indicative of the topic. fij = frequency of term i in document j

• May want to normalize term frequency (tf) across the entire corpus: tfij = fij / max{fij}

23

Some formulas for Sim

Dot product

Cosine

Dice

Jaccard

i i iiiii

iii

i iii

iii

i iii

iii

ii

baba

baQDSim

ba

baQDSim

ba

baQDSim

baQDSim

) * (

) * (),(

) * (2),(

*

) * (),(

) * (),(

22

22

22

t1

t2

D

Q

Example

• Documents: Austen's Sense and Sensibility, Pride and Prejudice; Bronte's Wuthering Heights

• cos(SAS, PAP) = .996 x .993 + .087 x .120 + .017 x 0.0 = 0.999• cos(SAS, WH) = .996 x .847 + .087 x .466 + .017 x .254 = 0.929

SaS PaP WHaffection 115 58 20jealous 10 7 11gossip 2 0 6

SaS PaP WHaffection 0.996 0.993 0.847jealous 0.087 0.120 0.466gossip 0.017 0.000 0.254

Extended Boolean Model

• Boolean model is simple and elegant.

• But, no provision for a ranking

• As with the fuzzy model, a ranking can be obtained by relaxing the condition on set membership

• Extend the Boolean model with the notions of partial matching and term weighting

• Combine characteristics of the Vector model with properties of Boolean algebra

The Idea • qor = kx ky; wxj = x and wyj = y

dj

dj+1

y = wyj

x = wxj(0,0)

(1,1)

kx

ky

sim(qor,dj) = sqrt( x + y ) 22 2

OR

We want a document to beas far as possible from (0,0)

Fuzzy Set Model

•Queries and docs represented by sets of index terms: matching is approximate from the start

•This vagueness can be modeled using a fuzzy framework, as follows:

–with each term is associated a fuzzy set

–each doc has a degree of membership in this fuzzy set

•This interpretation provides the foundation for many models for IR based on fuzzy theory

Probabilistic Model• Views retrieval as an attempt to answer a basic question:

“What is the probability that this document is relevant to

this query?”

• expressed as:

P(REL|D)

ie. Probability of x given y (Probability that of relevance

given a particular document D)

Probabilistic Model•An initial set of documents is retrieved somehow

•User inspects these docs looking for the relevant ones (in truth, only top 10-20 need to be inspected)

•The system uses this information to refine description of ideal answer set

•By repeting this process, it is expected that the description of the ideal answer set will improve

•Have always in mind the need to guess at the very beginning the description of the ideal answer set

•Description of ideal answer set is modeled in probabilistic terms

Recombination after dimensionality reduction

Classic IR Models

• Vector vs. probabilistic“Numerous experiments demonstrate that

probabilistic retrieval procedures yield good results. However, the results have not been sufficiently better than those obtained using Boolean or vector techniques to convince system developers to move heavily in this direction

Example

• Build the inverted file for the following document

• F1={Written Quiz for Algorithms and Techniques of Information Retrieval}

• F2={Program Quiz for Algorithms and Techniques of Web Search}

• F3={Search on the Web for Information on Algorithms}

Example• You have the collection of documents that contain the

following index terms:

• D1: alpha bravo charlie delta echo foxtrot golf

• D2: golf golf golf delta alpha

• D3: bravo charlie bravo echo foxtrot bravo

• D4: foxtrot alpha alpha golf golf delta

• Use a frequency matrix of terms to calculate a similarity matrix for these documents, with weights proportional to the term frequency and inversely proportional to the document frequency.

Terms Documents

c1 c2 c3 c4 c5 m1 m2 m3 m4

__ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __

human 1 0 0 1 0 0 0 0 0

interface 1 0 1 0 0 0 0 0 0

computer 1 1 0 0 0 0 0 0 0

user 0 1 1 0 1 0 0 0 0

system 0 1 1 2 0 0 0 0 0

response 0 1 0 0 1 0 0 0 0

time 0 1 0 0 1 0 0 0 0

EPS 0 0 1 1 0 0 0 0 0

survey 0 1 0 0 0 0 0 0 1

trees 0 0 0 0 0 1 1 1 0

graph 0 0 0 0 0 0 1 1 1

minors 0 0 0 0 0 0 0 1 1

 

Give the scores of the 9 documents for the query trees, minors using Boolean search

Give the scores of the 9 documents for the query trees, minors using the vector model.