Latent semantic indexing
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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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