IR c5-c6

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Questions and Answers

What is indicated by the term 'document frequency' in the vector space model?

The number of times a term appears in a specific document.

The total number of documents in a collection.

The average frequency of a term across all documents.

The number of documents containing a term at least once. (correct)

Which formula correctly represents the calculation of inversed document frequency (idf) for a term?

idf(t) = N / df(t)

idf(t) = log_10(df(t) / N)

idf(t) = df(t) * N

idf(t) = log_10(N / df(t)) (correct)

How does the term frequency (tf) relate to the overall tf-idf score?

It has no effect on the score.

It is only used for rare terms.

It increases the score with higher term frequency. (correct)

It decreases the score when term frequency is high.

What is the impact of using inverse document frequency (idf) in multi-term queries?

Idf helps to rank documents based on the rarity of search terms. Signup and view all the answers

What is a characteristic of rare terms in the vector space model?

Rare terms should have higher weights. Signup and view all the answers

What does the term 'add-one smoothing' aim to address in the context of term frequency?

It avoids zero term frequency for unseen terms. Signup and view all the answers

In the context of tf-idf, what does a higher collection frequency imply about a term?

The term is less important for distinguishing documents. Signup and view all the answers

What is the primary purpose of using tf-idf scoring in information retrieval?

To identify the most relevant documents based on term significance. Signup and view all the answers

What does a lower document frequency indicate about a term's significance in a document collection?

The term should be assigned a higher weight. Signup and view all the answers

Which statement correctly describes the effect of idf on document ranking?

Idf influences rankings in queries containing two or more terms. Signup and view all the answers

In the calculation of tf-idf, what does the term frequency (tf) primarily represent?

The frequency of a term in a specific document. Signup and view all the answers

What is the purpose of logarithmic term frequency in wf-idf scoring?

To simplify computation and reduce extreme values. Signup and view all the answers

Which of the following statements about the weight matrix in the vector space model is true?

Each column corresponds to a specific term. Signup and view all the answers

What does the 'inverse document frequency' (idf) score reflect about a term in a document collection?

How common or rare the term is, influencing its weight. Signup and view all the answers

What is the main advantage of utilizing rare terms in vector space modeling?

They contribute more weight to the tf-idf score. Signup and view all the answers

Which concept helps to improve the scoring when certain terms do not appear in the documents?

Add-one smoothing. Signup and view all the answers

Study Notes

Vector Space Model

A method for representing documents and queries as vectors in a multi-dimensional space.
Documents and terms are represented as vectors.
Columns in the matrix represent documents, rows represent terms.
Term Frequency (tf): the number of times a term appears in a document.
Collection Frequency: the number of times a term appears across all documents.
Document Frequency: the number of documents in which a term appears.
Inversed Document Frequency (idf): a measure of how important a term is across the entire collection.
Higher idf value, higher the weight
A higher idf value means the term is less frequent in the corpus and therefore more informative.
Scoring a document's relevance to a query (score(q, d)): sum of tf-idf over all terms (t): (tf multiplied by idf)
Normalization: Adjusting vector magnitudes for comparison.

Ranking Documents

Ranking documents by relevance to a query can be done using different metrics.
Euclidean Distance: Measures the straight-line distance between two vectors.
Cosine Similarity: Measures the cosine of the angle between two vectors. A higher cosine similarity score indicates a higher degree of similarity.
Methods for ranking documents are based on comparing the similarity between terms in the query and terms in documents.

Add-one smoothing

Incorporating an extra occurrence of a term that isn't in a document, or not present in the document.
This method adds 1 to each term's frequency in each document to avoid having zero frequencies for certain terms.
Score is a measure of the weight of a term in a document based on both its frequency in that document and its importance across all documents.
tf-idf = frequency * idf

Index Compression

Techniques to reduce the storage space required to store an index, while maintaining query performance.
Methods include storing gaps between document identifiers instead of absolute values.
The goal of compression is to reduce storage memory
Reduces memory and disk space needs by up to 75% for indexes.

Zipf's Law

Describes the frequency distribution of words in a natural language text.
Highly frequent words appear more often than less frequent ones.
The frequency of a word is inversely proportional to its rank in a frequency table.

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Description

Test your understanding of the Vector Space Model, a method for representing documents and queries in multi-dimensional space. This quiz covers key concepts like term frequency, inverse document frequency, and the scoring of document relevance. Prepare to explore how these elements work together to rank documents effectively.