Estimate the Number of Relevant Images Using Two-Order Markov Chain

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Estimate the Number of Relevant Images Using
Two-Order Markov Chain

• Presented by WANG Xiaoling
• Supervisor Clement LEUNG

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Outline

• Introduction
• Objective
• Methodology
• Experiment Results
• Conclusion and Future Work

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Introduction

• Large collections of images have been made
  available on web.
• Retrieval effectiveness becomes one of the most
  important parameters to measure the performance
  of image retrieval systems.

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• Measures
• Precision
• Recall
• Significant Challenge the total number of
  relevant images is not directly observable

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• Basic Models
• Regression Model
• Markov Chain
• Two-Order Markov Chain

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Objective

• To investigate the probabilistic behavior of the
  distribution of relevant images among the
  returned results for the image search engines
  using two-order markov chain

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Methodology

• Test Image Search Engine
• Query Design
• 70 provided by authors
• One word query
• Two word query
• Three word query
• 30 suggestive term
• Suggestive term with largest returned results
• Suggestive term with least returned results

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Methodology

• Database Setup
• Stochastic process X1, X2,, XJ
• where XJ denotes the aggregate relevance of
  all the images in page J
• Equation
• where YJi1 if the i th image on page J is
  relevant, and YJi 0 if the i th image on page J
  is not relevant.

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Page J XJ
1 18
2 19
3 20
4 19
5 20
6 19
7 20
8 18
9 19
10 18
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• Forecast Using Two-Order Markov Chain
• Markov Chain Stochastic process XJ, J1
  with state space S0,1,2,20 ,
• Two-Order Markov Chain State space change to
  S2,
• Forecast the state probability distribution of
  next page p(J) based on the original state
  probability distribution p(1) and transition
  probability matrix P . An Example
• Model Test
• Mean Absolute Error

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Experiment Results

• Forecast Results Using Two-Order Markov Chain

Page Google Yahoo Bing
1 20 20 20
2 20 20 20
3 20 20 20
4 20 20 20
5 20 20 20
6 20 20 17
7 20 20 17
8 20 20 17
9 20 20 17
10 20 20 17
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Test Results--Google
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Test Results--Yahoo
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Test Results--Bing
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Measure for Forecast Accuracy

• Mean Absolute Deviation (MAD)

One-word One-word One-word Two-word Two-word Two-word Three-word Three-word Three-word
Google 2.7 2.3 1.1 0.8 0.1 0.8 1.7 1.9 0.6
Yahoo 2.0 0.1 1.1 0.5 4.8 1.1 2.2 2.2 0.4
Bing 1.3 1.9 1.2 4.5 2.0 1.2 1.2 10.5 1.1
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Comparative Results

• Best Model Two-Order Markov Chain
• Worst Model Regression Model

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Conclusion

• Two-Order Markov Chain could well represent the
  distribution of relevant images among the results
  pages for the major web image search engine.
• Two-Order Markov Chain is the best model among
  three models we have worked.

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Future Work

• Our future work will try to apply Hidden Markov
  Chain to this topic

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• Thank you!
• Q A

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Two-Order Markov Chain An example (cont)

• Suppose the stochastic process Xt, tgt0 with a
  state space SA, B, C
• As to two-order Markov chain, the state space
• S2AA, AB, AC, BA, BB, BC, CA, CB, CC
• The state probabilities distribution of period
  zero
• ? (0) (?AA, ?AB, ?AC, ?BA, ?BB, ?BC, ?CA,
  ?CB, ?CC)

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An example (cont)

• The transition probability matrix

PAA,BA0
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An example

• Therefore, the probability distribution of states
  for page J will be compute as
• p(J)p(J-1)P
• 
  Return