Information Retrieval Models: Vector Space, TF-IDF, and Fuzzy Approaches, Lecture notes of Natural Language Processing (NLP)

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NATURAL LANGUAGE

PROCESSING (21AI62)

Dr. Pushpalatha K

Professor Sahyadri College of Engineering & Management

Information Retrieval

• Information retrieval (IR) deals with the organization, storage, retrieval, and evaluation of information relevant to a user's query.
• A user in need of information formulates a request in the form of a query written in a natural language.
• The retrieval system responds by retrieving the document that seems relevant to the query.

• The actual text of the document is not used in the retrieval process.
• Instead, documents in a collection are frequently represented through a

set of index terms or keywords.

• The process of transforming document text to some representation of it is

known as indexing.

▪ There are different types of index structures.

▪ inverted index is commonly used data structure by the IR system.

▪ An inverted index is simply a list of keywords, with each keyword carrying

pointers to the documents containing that keyword.

▪ The computational cost involved in adopting a full text logical view is high.

▪ Hence, the set of representative keywords are reduced.

▪ The two most commonly used text operations are stop word elimination

and stemming.

▪ Stop word elimination removes grammatical or functional words, while

stemming reduces words to their common grammatical roots.

▪ Zipf's law can be applied to reduce the size of index set based on the

relevancy of the index term.

Indexing

• In a small collection of documents, an IR system can access a document to decide its relevance to a query.
• But a large collection of raw documents is usually transformed into an easily accessible representation which is known as indexing.
• Most indexing techniques involve identifying good document descriptors, such as keywords or terms, which describe the information content of documents. ▪ A good descriptor is one that helps describe the content of the document and discriminate it from other documents in the collection. ▪ Eg: The stemmed representation of the text, Design features of information retrieval systems, is {design, feature, inform, retrieve, system} ▪ One of the problems associated with stemming is that it may throw away useful distinctions. - In some cases, it may be useful to help conflate similar terms, resulting in increased recall. - Recall and precision are the two most commonly used measures of the effectiveness of an information retrieval system, and are explained in detail later in this chapter.

• Zipf's law on large corpuses suggest that human languages contain a small number of words that occur with high frequency and a large number of words that occur with low frequency.
• The high frequency words being common, have less discriminating power, and thus, are not useful for indexing.
• Low frequency words are less likely to be included in the query, and are also not useful for indexing.
• As there are a large number of rare (low frequency) words, dropping them considerably reduces the size of a list of index terms.
• The remaining medium frequency words are content-bearing terms and can be used for indexing. ▪ This can be implemented by defining thresholds for high and low frequency, and dropping words that have frequencies above or below these thresholds. ▪ Stop word elimination can be thought of as an implementation of Zipf's law, where high frequency terms are dropped from a set of index terms.

Information Retrieval Models

• IR models can be classified as ▪ Classical models of IR. ▪ Non-classical models of IR ▪ Alternative models of IR
• The three classical IR models-Boolean, vector, and probabilistic. ▪ These are based on mathematical knowledge that is easily recognized and well understood. ▪ These models are simple, efficient, and easy to implement.

Boolean Model

• Introduced in the 50 s, the Boolean model is the oldest of the three

classical models.

• It is based on Boolean logic and classical set theory.
• In this model, documents are represented as a set of keywords,

usually stored in an inverted file.

▪ An inverted file is a list of keywords and identifiers of the documents in which they occur.

• Users are required to express their queries as a Boolean expression

consisting of keywords connected with Boolean logical operators

(AND, OR, NOT).

• Retrieval is performed based on whether or not document contains

the query terms.

• Let T={t 1 ,t 2 ,..…,t m } be the set of all such index terms.

▪ A document is any subset of T.

• Let D={D 1 ,D 2 ,..…,D m } be the set of all documents.
• A query is a Boolean expression Q in normal form

▪ Q= ∧( ∨ Θ

i

i

∈{t

i

, ¬t

i

• The retrieval is performed in two steps:
• The set R i of documents are obtained that contain or do not contain the term t i .

▪ R

i

={d

j

i

∈ d

j

i

∈{t

i

, ∈ t

i

• Where ¬t i ∈ d j means ¬t i ∉ d j
• The set of operations are used to retrieve documents in response to Q : ∩R i

• Let the query Q be Q= information ∧ retrieval.
• First, the sets R 1 and R 2 of documents are retrieved in response to Q, ▪ where R 1 = {d j | information ∈ d j } = {d 1 , d 2 } ▪ R 2 = {d j | retrieval∈ d j } = {d 1 , d 3 } ▪ The documents retrieved in response to query Q - {d j | d j ∈ R 1 ∩R 2 } = {d 1 } - This results in the retrieval of the original document D, that has the representation d 1. ▪ If more than one document have the same representation, every such document is retrieved. ▪ With an inverted index, takes an intersection of the list of the documents associated with the keywords information and retrieval.

Drawbacks of Boolean Model

1. The model is not able to retrieve documents that are only partly relevant to user query; all information is 'to be or not to be'.
2. A Boolean system is not able to rank the returned list of documents. ▪ It distinguishes between presence and absence of keywords but fails to assign relevance and importance to keywords in a document.
3. Users seldom formulate their query in the pure Boolean expression that this model requires.

• if P(R/d) is the probability of relevance of a document d, for query q, and P(I/d) is the probability of irrelevance, then the set of documents retrieved in response to the query q is as follows. ▪S={d j |P(R/ d j ) ≥ P(I/ d j )} P(R/ d j ) ≥ α
• The probabilistic model can produce results that partly match the user query. ,
• Determination of a threshold value is the main drawback of probabilistic model IR.

Vector Space Model

• The vector space model is one of the most well-studied retrieval models.

▪ Important contribution to its development was made by Luhn ( 1959 ),

Salton ( 1968 ), Salton and McGill ( 1983 ), and van Rijsbergen ( 1977 ).

• The vector space model represents documents and queries as vectors of

features representing terms that occur within them.

• Each document is characterized by a Boolean or numerical vector.
• These vectors are represented in a multi-dimensional space, in which each

dimension corresponds to a distinct term in the corpus of documents.

▪ In its simplest form, each feature takes a value of either zero or one,

indicating the absence or presence of that term in a document or query.

▪ More generally, features are assigned numerical values that are usually a

function of the frequency of terms.

• Ranking algorithms compute the similarity between document and query

vectors, to yield a retrieval score to each document.

• This score is used to produce a ranked list of retrieved documents.

• D 1 = Information retrieval is concerned with the organization, storage,

retrieval, and evaluation of information relevant to user's query.

• D 2 = A user having an information needs to formulate a request in the

form of query written in natural language.

• D 3 = The retrieval system responds by retrieving the document that seems

relevant to the query.

• T= {information, retrieval, query}.
• The associated vector for above documents is ( 2 , 2 , 1 )

• Term document frequency matrix is 2 1 0

• To reduce the importance of the length of document vectors, document vectors can be normalized.
• Normalization changes all vectors to a standard length. ▪ Convert document vectors to unit length by dividing each dimension by the overall length of the vector. ▪ Normalized the term-document matrix:
  1. 67 0. 71 0
  2. 67 0 0. 71
  3. 33 0. 71 0. 71 ▪ Elements of each column are divided by the length of the column vector given by σ 𝑖 𝑤 2 𝑖𝑗 .