Which One Is Better: Presentation-Based or Content-Based Math - - PowerPoint PPT Presentation

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Which One Is Better: Presentation-Based or Content-Based Math - - PowerPoint PPT Presentation

Oct 24, 2023 294 likes •491 views

Which One Is Better: Presentation-Based or Content-Based Math Search? Minh-Quoc NGHIEM, Giovanni Yoko KRISTIANTO, Goran TOPC, Akiko AIZAWA Outline Introduction Math Search Systems Method Evaluation Conclusion 2

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SLIDE 1

Which One Is Better: Presentation-Based or Content-Based Math Search?

Minh-Quoc NGHIEM, Giovanni Yoko KRISTIANTO, Goran TOPÍC, Akiko AIZAWA

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SLIDE 2

Outline

  • Introduction
  • Math Search Systems
  • Method
  • Evaluation
  • Conclusion

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SLIDE 3

Introduction

  • Math Search

– Presentation-based

  • LaTeX
  • Presentation MathML

– Content-based

  • Content MathML
  • OpenMath
  • NTCIR Math Track

– http://ntcir-math.nii.ac.jp/

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SLIDE 4

Introduction

  • Content-based systems use SnuggleTeX or

LaTeXML for semantic enrichment

  • No evaluation of how semantic enrichment

module contribute to search system

  • Which one is better: content-based search or

presentation-based search

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Mathematical Search Systems

  • Presentation-based systems

– Springer LaTeX Search – MathFind – The Digital Library of Mathematical Functions – EgoMath – Math Indexer and Searcher – ActiveMath – …

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Mathematical Search Systems

  • Content-based systems

– Wolfram Function – MathWebSearch – MathGO! – MathDA – The system of Nguyen et. al – …

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SLIDE 7

Method

  • Use Semantic Enrichment module to convert

Presentation to Content MathML

  • Use Content MathML for Indexing
  • Allow user to input query in Presentation

MathML

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SLIDE 8

System framework

Content MathML expressions

Presentation MathML expressions Indexing Semantic Enrichment Ranking

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Semantic Enrichment

  • Semantic Enrichment method of Nghiem et. al

(CICM 2013)

– Segmentation rules: segment Presentation MathML trees into smaller trees – Translation rules: translate Presentation MathML trees to Content MathML trees – Each rule is associated with a probability

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SLIDE 10

Indexing

  • Indexing method of Topic et. al (NTCIR 2013)

– Opaths: path in XML tree with order – Upaths: no order – Sisters: sister nodes in subtree

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Evaluation

  • Data

– 20k Math expressions in WFS – 15 queries (modified from NTCIR)

  • Systems

– Presentation MathML (PMathML) – Content MathML (CMathML) – Semantic Enrichment (SE)

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Evaluation

  • Metrics

– Precision at 10 (P@10)

  • Precision in top k results

– Normalize Discounted Cumulative Gain (nDCG)

  • Ranking quality

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Queries

∞

𝑦𝑒𝑦 𝑦2 + 𝑧2

∞

ⅇ−𝑦2 𝑒𝑦 𝑏𝑠𝑑𝑡𝑗𝑜(𝑦) 𝑙2 coshⅇ𝑨 + sinhⅇ𝑨 ⅇ ℛ𝑨𝜔𝜉(𝑨), ∞

~

∫ 𝑏𝑒+𝑐𝑨 𝑨 𝑒𝑨 lim

𝜉→∞

𝑀𝛽+𝜉 𝑀𝜉 ℬ𝒬

𝑨𝔔𝜉 𝜈(𝑨)

𝜉 ∈ ℕ 𝜔𝜉(𝑨) log(𝑨 + 1) 𝐼𝑜(𝑨) 1 𝜌

𝜌

cos𝑢𝑜 − 𝑨sin𝑢 𝑒𝑢

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SLIDE 14

Evaluation: search performance

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Using content markup improve search performance

0.6 0.7 0.8 0.9 1 PMathML CMathML SE

nDCG and Precision at 10

nDCG P@10

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Evaluation: search performance

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Using content markup improve search performance Relevant results are ranked higher

0.6 0.7 0.8 0.9 1 1 3 5 7 9

Precision at k

PMathML CMathML SE

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PMathML and SE systems

  • SE system is better

– Functions have specific meanings

  • Poly-Gamma, Hermite-H

– More than one way to represent math expression

  • Sin-1 and Arcsin
  • PMathML system is better

– Elementary functions

  • Power, Logarithm, Trigonometric functions
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Summary

  • Content-based math search is better than presentation-based

math search

  • Performance of semantic enrichment module affect the math

search performance

  • Both presentation-based and content-based systems have

their strong points

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Tⱨ∆∩ⱪ y○u

∫○r y○ur ∆tte∩ti○∩!

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