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?

<p>Idf helps to rank documents based on the rarity of search terms. (C)</p> Signup and view all the answers

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

<p>Rare terms should have higher weights. (B)</p> Signup and view all the answers

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

<p>It avoids zero term frequency for unseen terms. (B)</p> Signup and view all the answers

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

<p>The term is less important for distinguishing documents. (D)</p> Signup and view all the answers

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

<p>To identify the most relevant documents based on term significance. (A)</p> Signup and view all the answers

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

<p>The term should be assigned a higher weight. (C)</p> Signup and view all the answers

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

<p>Idf influences rankings in queries containing two or more terms. (A)</p> Signup and view all the answers

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

<p>The frequency of a term in a specific document. (B)</p> Signup and view all the answers

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

<p>To simplify computation and reduce extreme values. (B)</p> Signup and view all the answers

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

<p>Each column corresponds to a specific term. (A)</p> Signup and view all the answers

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

<p>How common or rare the term is, influencing its weight. (D)</p> Signup and view all the answers

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

<p>They contribute more weight to the tf-idf score. (D)</p> Signup and view all the answers

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

<p>Add-one smoothing. (D)</p> Signup and view all the answers

Flashcards

Vector Space Model (VSM)

A method for representing documents and queries as vectors in a multi-dimensional space, enabling similarity calculations.

Term-Frequency (tf)

The frequency of a term in a single document.

Collection Frequency

The total count of a term across all documents.

Document Frequency

The number of documents containing a specific term at least once.

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Inverse Document Frequency (idf)

A weighting factor that increases with the rarity of a term in a collection.

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Tf-idf Weight

The product of term frequency and inverse document frequency, defining how important a term is.

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Add-one Smoothing

A technique to handle terms not present in some documents by adding a small constant to their count.

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Wf-idf

An alternative to tf-idf that uses a logarithmic scale for term frequencies to give higher weight to more frequent words.

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What is a counter vector?

A counter vector represents a document in a vector space model. It's created by combining all terms in a document with their respective term frequencies (tf).

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Why are rare terms more important?

Rare terms are more valuable for searching because they indicate specific content. Their occurrence in a document suggests the document is more likely relevant to a search query involving that rare term.

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What is 'Collection Frequency'?

Collection Frequency refers to the total number of times a term appears across all documents in a collection.

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What is 'Document Frequency'?

Document Frequency (df) counts the number of documents in a collection that contain a particular term at least once.

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What is 'Inverse Document Frequency' (idf)?

idf is a weight assigned to a term based on its rarity in a collection. Rarity means fewer documents contain the term. Higher df leads to lower idf.

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How is idf calculated?

idf(t) = log10(N/df(t)), where N is the total number of documents and df(t) is the document frequency of the term 't'.

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What is 'Add-one smoothing'?

A technique used to handle terms that don't appear in certain documents. It simply adds a small constant (often 1) to the term frequency to ensure every document has at least a small weight for a term.

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What is the 'tf-idf score'?

The tf-idf score is a weight assigned to a term in a document, calculated by multiplying the term frequency (tf) by the inverse document frequency (idf). It reflects the importance of a term in a document.

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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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