estimate the number of relevant images using two-order markov chain presented by: wang xiaoling...
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![Page 1: Estimate the Number of Relevant Images Using Two-Order Markov Chain Presented by: WANG Xiaoling Supervisor: Clement LEUNG](https://reader030.vdocuments.mx/reader030/viewer/2022032523/56649d7a5503460f94a5df7e/html5/thumbnails/1.jpg)
Estimate the Number of Estimate the Number of Relevant Images Using Two-Relevant Images Using Two-
Order Markov Chain Order Markov Chain
Presented by: WANG XiaolingPresented by: WANG Xiaoling
Supervisor: Clement LEUNGSupervisor: Clement LEUNG
![Page 2: Estimate the Number of Relevant Images Using Two-Order Markov Chain Presented by: WANG Xiaoling Supervisor: Clement LEUNG](https://reader030.vdocuments.mx/reader030/viewer/2022032523/56649d7a5503460f94a5df7e/html5/thumbnails/2.jpg)
OutlineOutline
IntroductionIntroduction Objective Objective MethodologyMethodology Experiment ResultsExperiment Results Conclusion and Future WorkConclusion and Future Work
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IntroductionIntroduction
Large collections of images have Large collections of images have been made available on web.been made available on web.
Retrieval effectiveness becomes one Retrieval effectiveness becomes one of the most important parameters to of the most important parameters to measure the performance of image measure the performance of image retrieval systems. retrieval systems.
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Measures: Measures: PrecisionPrecision Recall Recall
Significant Challenge: the total number of Significant Challenge: the total number of relevant images is relevant images is not directly observablenot directly observable
databasetheinimagesrelevantofnumbertotal
retrievedimagesrelevantofnumberR
returnedimagesofnumbertotal
retrievedimagesrelevantofnumberP
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Basic ModelsBasic Models Regression ModelRegression Model Markov ChainMarkov Chain Two-Order Markov ChainTwo-Order Markov Chain
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ObjectiveObjective
To investigate the probabilistic To investigate the probabilistic behavior of the distribution of behavior of the distribution of relevant images among the returned relevant images among the returned results for the image search engines results for the image search engines using two-order markov chainusing two-order markov chain
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MethodologyMethodology
Test Image Search Engine: Test Image Search Engine: Query DesignQuery Design
70% provided by authors70% provided by authors One word queryOne word query Two word queryTwo word query Three word queryThree word query
30% suggestive term30% suggestive term Suggestive term with largest returned resultsSuggestive term with largest returned results Suggestive term with least returned resultsSuggestive term with least returned results
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MethodologyMethodology
Database Setup:Database Setup: Stochastic process {Stochastic process {XX11, X, X22,…,,…, XXJJ } }
where where XXJJ denotes the aggregate relevanc denotes the aggregate relevance of all the images in page e of all the images in page J J Equation:Equation:
where where YYJiJi=1=1 if the if the i i th th image on page image on page JJ is re is relevant, andlevant, and Y YJiJi =0 if the =0 if the i i thth image on page image on page JJ is not relevant. is not relevant.
20
1J YX
iJi
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Page Page JJ XXJJ
11 1818
22 1919
33 2020
44 1919
55 2020
66 1919
77 2020
88 1818
99 1919
1010 1818
18YX20
1J
iJi
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Forecast Using Two-Order Markov ChainForecast Using Two-Order Markov Chain Markov Chain: Stochastic process {XMarkov Chain: Stochastic process {XJJ, J, J≥1≥1} with state s} with state s
pace S={0,1,2,…20} pace S={0,1,2,…20} ,, Two-Order Markov Chain: State space change to STwo-Order Markov Chain: State space change to S22 ,, Forecast the state probability distribution of next page Forecast the state probability distribution of next page
ππ(J) (J) based on the original state probability distributiobased on the original state probability distribution n ππ(1) (1) and transition probability matrix and transition probability matrix PP . . An ExampleAn Example
Model TestModel Test Mean Absolute ErrorMean Absolute Error
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Experiment ResultsExperiment Results Forecast Results Using Two-Order Markov ChainForecast Results Using Two-Order Markov Chain
PagePage GoogleGoogle YahooYahoo BingBing
11 2020 2020 2020
22 2020 2020 2020
33 2020 2020 2020
44 2020 2020 2020
55 2020 2020 2020
66 2020 2020 1717
77 2020 2020 1717
88 2020 2020 1717
99 2020 2020 1717
1010 2020 2020 1717
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Test Results--GoogleTest Results--Google
1 2 3 4 5 6 7 8 9 1010
15
20
Page Number
( i )
1 2 3 4 5 6 7 8 9 1010
15
20
Page Number
( j )
1 2 3 4 5 6 7 8 9 1010
15
20
Page Number
( a )
1 2 3 4 5 6 7 8 9 1010
15
20
Page Number
( b )
1 2 3 4 5 6 7 8 9 1010
15
20
Page Number
Num
ber o
f Rel
evan
t Im
ages ( c )
1 2 3 4 5 6 7 8 9 1010
15
20
Page Number
Num
ber o
f Rel
evan
t Im
ages ( d )
1 2 3 4 5 6 7 8 9 1010
15
20
Page Number
( e )
1 2 3 4 5 6 7 8 9 1010
15
20
Page Number
( f )
1 2 3 4 5 6 7 8 9 1010
15
20
Page Number
( g )
1 2 3 4 5 6 7 8 9 1010
15
20
Page Number
( h )
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Test Results--YahooTest Results--Yahoo
1 2 3 4 5 6 7 8 9 1010
15
20
( i )
Page Number1 2 3 4 5 6 7 8 9 10
10
15
20
( j )
Page Number
1 2 3 4 5 6 7 8 9 1010
15
20( a )
Page Number1 2 3 4 5 6 7 8 9 10
10
15
20( b )
Page Number
1 2 3 4 5 6 7 8 9 1010
15
20( c )
Page Number
Num
ber o
f Rel
evan
t Im
ages
1 2 3 4 5 6 7 8 9 1010
15
20( d )
Page Number
Num
ber o
f Rel
evan
t Im
ages
1 2 3 4 5 6 7 8 9 1010
15
20( e )
Page Number1 2 3 4 5 6 7 8 9 10
10
15
20( f )
Page Number
1 2 3 4 5 6 7 8 9 1010
15
20( g )
Page Number1 2 3 4 5 6 7 8 9 10
10
15
20( h )
Page Number
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Test Results--BingTest Results--Bing1 2 3 4 5 6 7 8 9 10
1 2 3 4 5 6 7 8 9 100
10
20(c)
Page Number
Num
ber o
f Rel
evan
t Im
ages
1 2 3 4 5 6 7 8 9 100
10
20(e)
Page Number
1 2 3 4 5 6 7 8 9 100
10
20(g)
Page Number
1 2 3 4 5 6 7 8 9 100
10
20(a)
Page Number
1 2 3 4 5 6 7 8 9 100
10
20
(i)
Page Number1 2 3 4 5 6 7 8 9 10
0
10
20
(j)
Page Number
1 2 3 4 5 6 7 8 9 100
10
20(b)
Page Number
1 2 3 4 5 6 7 8 9 100
10
20(d)
Page Number
Num
ber o
f Rel
evan
t Im
ages
1 2 3 4 5 6 7 8 9 100
10
20(f)
Page Number
1 2 3 4 5 6 7 8 9 100
10
20(h)
Page Number
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Measure for Forecast AccuracyMeasure for Forecast Accuracy
MMeanean A Absolute bsolute DDeviationeviation ( (MADMAD)) ::
n
errorforecast MAD
One-wordOne-word Two-wordTwo-word Three-wordThree-word
GooglGooglee
2.2.77
2.2.33
1.11.1 0.80.8 0.10.1 0.80.8 1.1.77
1.91.9 0.60.6
YahooYahoo 2.2.00
0.0.11
1.11.1 0.50.5 4.84.8 1.11.1 2.2.22
2.22.2 0.40.4
BingBing 1.1.33
1.1.99
1.21.2 4.54.5 2.02.0 1.21.2 1.1.22
10.10.55
1.11.1
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Comparative ResultsComparative Results
Best Model: Two-Best Model: Two-Order Markov Order Markov ChainChain
Worst Model: Worst Model: Regression ModelRegression Model
0
1
2
3
4
5
Googel Yahoo Bi ng
Image Search Engi ne
Mean
Abs
olut
e Er
ror
Regreesi onModelMarkov Chai n
Two-OrderMarkov Chai n
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ConclusionConclusion
Two-Order Markov Chain could well Two-Order Markov Chain could well represent the distribution of relevant represent the distribution of relevant images among the results pages for images among the results pages for the major web image search engine.the major web image search engine.
Two-Order Markov Chain is the best Two-Order Markov Chain is the best model among three models we have model among three models we have worked.worked.
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Future WorkFuture Work
Our future work will try to apply Hidden Our future work will try to apply Hidden Markov Chain to this topicMarkov Chain to this topic
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Thank you!Thank you!
Q & AQ & A
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Two-Order Markov Chain Two-Order Markov Chain An example (cont’)An example (cont’)
Suppose the stochastic process {XSuppose the stochastic process {Xtt, t>=0} with , t>=0} with a state space S={A, B, C}a state space S={A, B, C}
As to two-order Markov chain, the state space:As to two-order Markov chain, the state space: SS22={AA, AB, AC, BA, BB, BC, CA, CB, CC} ={AA, AB, AC, BA, BB, BC, CA, CB, CC} The state probabilities distribution of period zThe state probabilities distribution of period z
ero: ero: (0)= ((0)= (AAAA, , ABAB, , ACAC, , BABA, , BBBB, , BCBC, , CACA, , CBCB, , CCCC))
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An example (cont’)An example (cont’)
The transition probability matrix:The transition probability matrix:
CCCCCBCCCACC
BCCBBBCBBACB
ACCAABCABCCA
CCBCCBBCCABC
BCBBBBBBBABB
ACBAABBAAABA
CCACCBACCAAC
BCABBBABBAAB
ACAAABAAAAAA
ppp
ppp
ppp
ppp
ppp
ppp
ppp
ppp
ppp
p
,,,
,,,
,,,
,,,
,,,
,,,
,,,
,,,
,,,
000000
000000
000000
000000
000000
000000
000000
000000
000000
PAA,BA=0
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An exampleAn example
Therefore, the probability distribution of Therefore, the probability distribution of states for page states for page J J will be compute as:will be compute as:
ππ(J)=(J)=ππ(J-1)*P(J-1)*P
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