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CS 430 / INFO 430 Information Retrieval

Lecture 2

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Course Administration

Web site:

http://www.cs.cornell.edu/courses/cs430/2006fa

Notices:

See the home page on the course Web site

Sign-up sheet:

If you did not sign up at the first class, please sign up now.

Programming assignments:

The web site require Java or C++. Other languages are under consideration.

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Course Administration

Please send all questions about the course to:

cs430-l@lists.cs.cornell.edu

The message will be sent to

William ArmsTeaching Assistants

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Course Administration

Discussion class, Wednesday, August 30Phillips Hall 203, 7:30 to 8:30 p.m.

Prepare for the class as instructed on the course Web site.

Participation in the discussion classes is one third of the grade, but tomorrow's class will not be included in the grade calculation.

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Discussion Classes

Format:

Questions.

Ask a member of the class to answer.

Provide opportunity for others to comment.

When answering:

Stand up.

Give your name. Make sure that the TA hears it.

Speak clearly so that all the class can hear.

Suggestions:

Do not be shy at presenting partial answers.

Differing viewpoints are welcome.

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Discussion Class: Preparation

You are given two problems to explore:

• What is the medical evidence that red wine is good or bad for your health?

• What in history led to the current turmoil in Palestine and the neighboring countries?

In preparing for the class, focus on the question: What characteristics of the three search services are helpful or lead to difficulties in addressing these two problems? The aim of your preparation is to explore the search services, not to solve these two problems.

Take care. Many of the documents that you might find are written from a one-sided viewpoint.

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Discussion Class: Preparation

In preparing for the discussion classes, you may find it useful to look at the slides from last year's class on the old Web site:

http://www.cs.cornell.edu/Courses/cs430/2005fa/

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Similarity Ranking Methods

Similarity ranking methods: measure the degree of similarity between a query and a document.

Query DocumentsSimilar

Similar: How similar is a document to a query?

[Contrast with methods that look for exact matches (e.g., Boolean). Those methods assume that a document is either relevant to a query or not relevant.]

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Similarity Ranking Methods: Use of Indexes

Query DocumentsIndex database

Mechanism for determining the similarity of the query to the document.

Set of documents ranked by how similar they are to the query

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Term Similarity: Example

Problem: Given two text documents, how similar are they?

A documents can be any length from one word to thousands. The following examples use very short artificial documents.

Example

Here are three documents. How similar are they?

d1 ant ant beed2 dog bee dog hog dog ant dogd3 cat gnu dog eel fox

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Concept: Two documents are similar if they contain some of the same terms.

Term Similarity: Basic Concept

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Term Vector Space: No Weighting

Term vector space

n-dimensional space, where n is the number of different terms used to index a set of documents (i.e. size of the word list).

Vector

Document i is represented by a vector. Its magnitude in dimension j is tij, where:

tij = 1 if term j occurs in document itij = 0 otherwise

[This is the basic method with no term weighting.]

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A Document Represented in a 3-Dimensional Term Vector Space

t1

t2

t3

d1

t13

t12t11

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Basic Method: Term Incidence Matrix

(No Weighting)

document text termsd1 ant ant bee ant bee

d2 dog bee dog hog dog ant dog ant bee dog hog

d3 cat gnu dog eel fox cat dog eel fox gnu

ant bee cat dog eel fox gnu hog

d1 1 1

d2 1 1 1 1

d3 1 1 1 1 1

tij = 1 if document i contains term j and zero otherwise

3 vectors in 8-dimensional term vector space

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Similarity between two Documents

Similarity

The similarity between two documents, d1 and d2, is a function of the angle between their vectors in the term vector space.

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Two Documents Represented in 3-Dimensional Term Vector Space

t1

t2

t3

d1 d2

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Vector Space Revision

x = (x1, x2, x3, ..., xn) is a vector in an n-dimensional vector space

Length of x is given by (extension of Pythagoras's theorem) |x|2 = x1

2 + x22 + x3

2 + ... + xn2

If x1 and x2 are vectors:

Inner product (or dot product) is given by x1.x2 = x11x21 + x12x22 + x13x23 + ... + x1nx2n

Cosine of the angle between the vectors x1 and x2:

cos () =

x1.x2 |x1| |x2|

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Example: Comparing Documents (No Weighting)

ant bee cat dog eel fox gnu hog length

d1 1 1 2

d2 1 1 1 1 4

d3 1 1 1 1 1 5

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Example: Comparing Documents

d1 d2 d3

d1 1 0.71 0

d2 0.71 1 0.22

d3 0 0.22 1

Similarity of documents in example:

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Similarity between a Query and a Document

Consider a query as another vector in the term vector space.

The similarity between a query, q, and a document, d, is a function of the angle between their vectors in the term vector space.

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Similarity between a Query and a Document in 3-Dimensional Term Vector Space

t1

t2

t3

q d

cos() is used as a measure of similarity

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Similarity of Query to Documents(Term Incidence Matrix: no Weighting)

ant bee cat dog eel fox gnu hog

q 1 1 d1 1 1 d2 1 1 1 1 d3 1 1 1 1 1

queryq ant dogdocument text termsd1 ant ant bee ant bee

d2 dog bee dog hog dog ant dog ant bee dog hog

d3 cat gnu dog eel fox cat dog eel fox gnu

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Calculate Ranking

d1 d2 d3

q 1/2 1/√2 1/√10 0.5 0.71 0.32

Similarity of query to documents in example:

If the query q is searched against this document set, the ranked results are:

d2, d1, d3

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Simple Uses of Vector Similarity in Information Retrieval

Threshold

For query q, retrieve all documents with similarity above a threshold, e.g., similarity > 0.50.

Ranking

For query q, return the n most similar documents ranked in order of similarity.

[This is the standard practice.]

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An improved measure of similarity might take account of:

(a) Whether the terms are common or unusual

(c) How many times each term appears in a document

(d) The lengths of the documents

(e) The place in the document that a term appears

(f) Terms that are adjacent to each other (phrases)

Term Extending the Basic Concept with Term Weighting

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Term Vector Space with Weighting

Term vector space

n-dimensional space, where n is the number of different terms used to index a set of documents (i.e. size of the word list).

Vector

Document i is represented by a vector. Its magnitude in dimension j is tij, where:

tij > 0 if term j occurs in document itij = 0 otherwise

tij is the weight of term j in document i.