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Latent Semantic Indexing. Journal Article Comparison Al Funk CS 5604 / Information Retrieval. What is LSI?. Use similarities between concepts to map documents and determine their proximity in concept space

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latent semantic indexing

Latent Semantic Indexing

Journal Article Comparison

Al Funk

CS 5604 / Information Retrieval

what is lsi
What is LSI?
  • Use similarities between concepts to map documents and determine their proximity in concept space
    • “Singular Value Decomposition” – popular statistical method for generating concept space via dimensionality reduction
  • Mapping results from SVD’s spatial analysis of a collection of documents; does not require human intervention to generate
strengths of lsi
Strengths of LSI
  • Increased relevance of information retrieval, as concepts are recognized rather than keywords
  • Larger result sets due to retrieval of texts that do not include the specific query keywords
    • LSI recognizes that keywords are related
  • Minimal human intervention to generate mappings
weaknesses of lsi
Weaknesses of LSI
  • Storage requirements for indexes
  • Computation time

In essence, high dimensionality of document representation can make searching resource intensive. LSI can reduce these costs but also can incur some of its own.

Q: Is there a way to maintain the benefits of LSI and reduce resource requirements?

two solutions identified
Two Solutions Identified?
  • Many journal articles focus on mitigating the resource intensivity of LSI by reducing dimensionality. Two approaches:
    • Article 1: Use “random projection” to lower dimensionality of the concept space, hoping to prevent erosion of vector relationships
    • Article 2: Replace SVD with “Semidiscrete Matrix Decomposition,” creating an approximation that serves to reduce dimensionality but still retain the bulk of relationships
random projection
Random Projection
  • Traditional methods of dimensionality reduction have focused means of analyzing datasets to maximize benefit and minimize loss of variation. Two such methods are:
    • Principal Component Analysis (PCA)
    • Singular Value Decomposition (SVD)
  • SVD is primary for document retrieval because it performs well with sparse matrices.
    • PCA and SVD are both computationally expensive, particularly for large datasets.
random projection1
Random Projection
  • Random Projection (RP) attempts to solve these problems by creating a random matrix and using it to project the document observation vectors onto a lower dimensional space.
  • Random projection can be used before SVD, enabling the expensive algorithm to operate on a matrix of lower dimension.
  • Bingham and Mannila’s results indicate that RP has an acceptable impact on the data while significantly reducing required computation.
sdd vs svd
SDD vs. SVD
  • Kolda and O’Leary propose to replace the expensive SVD algorithm with “Semidiscrete Matrix Decomposition”
    • Lower computation time
    • Lower storage requirements
  • Claim that methodology is as accurate as SVD but less resource intensive
what is svd
What is SVD?
  • Defined as the “closest rank-k matrix to the term-document matrix in the Frobenius measure”.
  • Essentially creates a lower-order matrix that maximizes the approximation of the original m x n document / keyword matrix.
what is sdd
What is SDD?
  • SDD is a different LSI algorithm to achieve the same goals as SVD
    • SDD creates a lower-order matrix like SVD but restricts vector item values to –1, 0 or 1
  • As a result of the restriction to these values, SDD is computationally more expensive up front
benefits of sdd
Benefits of SDD
  • Despite higher up-front processing times, updates to the matrix can be made rapidly to accommodate changing collections
  • Searching is more efficient (as much as ½ the time)
  • Storage requirements are lower, as SDD can store each matrix value in 2 bits (rather than multiple bytes for a floating-point value)
conclusions
Conclusions
  • Both articles provide for a quantifiable increase in performance over traditional LSI techniques
  • Techniques could potentially be used together, as both tackle the related issues of performance and dimensionality reduction
article links
Article Links
  • http://doi.acm.org/10.1145/291128.291131
  • http://doi.acm.org/10.1145/502512.502546
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