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3.76 Standard deviation of the duration for detecting true changes in Stream1 and Stream17 using XI-merged with different windows size . . . . . . . . . . . . . . . . . . . . . . . . . . 136 3.77 Max duration for detecting true changes in Stream1 and Stream17 using XI-merged with different windows size . . 137 3.78 Example of a control chart . . . . . . . . . . . . . . . . . . 145 3.79 Number of true changes detected for Stream1 and Stream2 153 3.80 Number of true changes detected for Stream3 and Stream4 154 3.81 Number of true changes detected for Stream5 and Stream6 155 3.82 Number of true changes detected for Stream7 and Stream8 156 3.83 Number of true changes detected for Stream9 and Stream10157 3.84 Number of true changes detected for Stream11 and Stream12158 3.85 Number of false changes detected for Stream1 and Stream2 159 3.86 Number of false changes detected for Stream3 and Stream4 160 3.87 Number of false changes detected for Stream5 and Stream6 161 3.88 Number of false changes detected for Stream7 and Stream8 162 3.89 Number of false changes detected for Stream9 and Stream10163 3.90 Number of false changes detected for Stream11 and Stream12164 3.91 Mean duration for detecting true changes in Stream1 and Stream2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 3.92 Mean duration for detecting true changes in Stream3 and Stream4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 3.93 Mean duration for detecting true changes in Stream5 and Stream6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 3.94 Mean duration for detecting true changes in Stream7 and Stream8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 3.95 Mean duration for detecting true changes in Stream9 and Stream10 . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 xiv
3.96 Mean duration for detecting true changes in Stream11 and Stream12 . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 3.97 Standard deviation of the duration for detecting true changes in Stream1 and Stream2 . . . . . . . . . . . . . . . . . . 171 3.98 Standard deviation of the duration for detecting true changes in Stream3 and Stream4 . . . . . . . . . . . . . . . . . . 172 3.99 Standard deviation of the duration for detecting true changes in Stream5 and Stream6 . . . . . . . . . . . . . . . . . . 173 3.100Standard deviation of the duration for detecting true changes in Stream7 and Stream8 . . . . . . . . . . . . . . . . . . 174 3.101Standard deviation of the duration for detecting true changes in Stream9 and Stream10 . . . . . . . . . . . . . . . . . . 175 3.102Standard deviation of the duration for detecting true changes in Stream11 and Stream12 . . . . . . . . . . . . . . . . . 176 3.103Max duration for detecting true changes in Stream1 and Stream2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 3.104Max duration for detecting true changes in Stream3 and Stream4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178 3.105Max duration for detecting true changes in Stream5 and Stream6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 3.106Max duration for detecting true changes in Stream7 and Stream8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 3.107Max duration for detecting true changes in Stream9 and Stream10 . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 3.108Max duration for detecting true changes in Stream11 and Stream12 . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 3.109Number of true changes detected for Stream13 and Stream14184 3.110Number of true changes detected for Stream15 and Stream16185 3.111Number of true changes detected for Stream17 and Stream18186 3.112Number of false changes detected for Stream13 and Stream14187 xv
Page 1 and 2: Mining Time-Changing Data Streams b
Page 3 and 4: Abstract Streaming data have gained
Page 5 and 6: Contents List of Figures ix List of
Page 7 and 8: 4 Change Detection in Multi-dimensi
Page 9 and 10: List of Figures 1.1 Abstract archit
Page 11 and 12: 3.30 Max duration for detecting tru
Page 13: 3.62 Max duration for detecting tru
Page 17 and 18: 3.129Number of true changes detecte
Page 19: List of Tables 3.1 Stream types gen
Page 22 and 23: I, Ii set of items for transactiona
Page 24 and 25: • Financial and market activities
Page 26 and 27: Figure 1.1: Abstract architecture o
Page 28 and 29: change detection and incremental ma
Page 30 and 31: preliminary analysis over the data
Page 32 and 33: streams is a continuous process and
Page 34 and 35: these approaches may achieve high p
Page 36 and 37: Under the assumption that attribute
Page 38 and 39: itemsets mining. A task-specific st
Page 41 and 42: Chapter 2 Background This chapter s
Page 43 and 44: • Due to performance and storage
Page 45 and 46: S t s i s i+1 s i s i+j W W W W’
Page 47 and 48: Figure 2.3: Example of continuous d
Page 49 and 50: samples so that it can be stored in
Page 51 and 52: Change detection As discussed in Se
Page 53 and 54: Frequency counting and association
Page 55: Integration of stream mining system
Page 58 and 59: Only a few distribution change-dete
Page 60 and 61: method is inclined to be conservati
Page 62 and 63: the distribution change cannot refl
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that the probability of a value tha
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|Wr| from Wr + Wt, such that: Discr
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To partition (Wr + Wt) into a numbe
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tings, an experiment framework is d
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Table 3.1: Stream types generated S
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By combining the three window movin
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• Standard deviation of durations
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Figure 3.3: Number of true changes
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0.00 0.02 0.04 0.06 0.08 0.10 0.12
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Figure 3.7: Number of false changes
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Figure 3.9: Mean duration for detec
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Figure 3.11: Mean duration for dete
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Figure 3.13: Standard deviation of
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0.0000 0.0004 0.0008 0.0012 0.00 0.
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0.000 0.002 0.004 0.006 0.000 0.005
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Figure 3.18: Number of true changes
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0.00 0.02 0.04 0.06 0.08 0.10 0.12
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Figure 3.22: Number of false change
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Figure 3.28: Standard deviation of
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0.0000 0.0004 0.0008 0.0012 0.00 0.
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0.000 0.005 0.010 0.015 0.020 0.000
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than fixed window method. Fixed win
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0.00 0.05 0.10 0.15 0.00 0.02 0.04
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0.00 0.05 0.10 0.15 0.00 0.02 0.04
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0.00 0.02 0.04 0.06 0.08 0.10 0.12
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0.000 0.010 0.020 0.030 0.000 0.004
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0.000 0.001 0.002 0.003 0.004 0.005
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0.000 0.002 0.004 0.006 0.008 0.000
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0.000 0.001 0.002 0.003 0.004 0e+00
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The following observations can be m
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technique with smaller τ setting o
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0.00 0.05 0.10 0.15 0.00 0.01 0.02
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0.00 0.05 0.10 0.15 0.20 0.25 0.30
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0.00 0.05 0.10 0.15 0.00 0.05 0.10
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0.00 0.02 0.04 0.06 0.08 0.10 0.12
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0.00 0.01 0.02 0.03 0.04 0.05 0.06
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0.00 0.05 0.10 0.15 0.00 0.01 0.02
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0.00 0.05 0.10 0.15 0.20 0.25 0.30
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These results show that larger τ v
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0.00 0.02 0.04 0.06 0.08 0.10 0.12
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0.00 0.02 0.04 0.06 0.08 0.10 0.12
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0.00 0.02 0.04 0.06 0.08 0.10 0.00
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0.00 0.01 0.02 0.03 0.04 0.000 0.00
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0.000 0.005 0.010 0.015 0.020 0.025
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0.00 0.02 0.04 0.06 0.08 0.10 0.00
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0.00 0.02 0.04 0.06 0.08 0.10 0.00
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3.3.7 Mining streams with periodica
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Choosing important distributions Fo
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containing the representative sets
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an important feature for detecting
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that have arrived in S in the last
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significance level τ. Tables in [9
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Full algorithm The full algorithm o
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values of the change detection dura
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Stream 3 − Exponential Distributi
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0.00 0.02 0.04 0.06 0.08 0.10 0.12
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0.00 0.02 0.04 0.06 0.08 0.10 0.12
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0.00 0.02 0.04 0.06 0.08 0.10 0.00
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0.00 0.02 0.04 0.06 0.08 0.10 Strea
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0.00 0.01 0.02 0.03 0.04 0.00 0.02
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0.00 0.02 0.04 0.06 0.00 0.01 0.02
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0.000 0.002 0.004 0.006 0.008 0.010
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0.00 0.02 0.04 0.06 0.08 0.10 0.000
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0.0000 0.0004 0.0008 0.0012 0.00 0.
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0.000 0.005 0.010 0.015 0.020 0.000
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0.00 0.02 0.04 0.06 0.08 0.10 0.00
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0.00 0.05 0.10 0.15 0.00 0.02 0.04
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0.00 0.02 0.04 0.06 0.08 0.00 0.02
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0.000 0.004 0.008 0.012 0.000 0.005
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0.000 0.005 0.010 0.015 0.020 0.000
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0.00 0.02 0.04 0.06 0.000 0.002 0.0
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0e+00 2e−04 4e−04 6e−04 8e−
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0e+00 2e−04 4e−04 6e−04 0e+00
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0.00 0.05 0.10 0.15 0.00 0.02 0.04
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0.00 0.02 0.04 0.06 0.08 0.000 0.00
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0.000 0.005 0.010 0.015 0.020 0e+00
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0.00 0.05 0.10 0.15 0.00 0.05 0.10
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0.00 0.02 0.04 0.06 0.000 0.004 0.0
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0.0000 0.0010 0.0020 0.0030 0e+00 2
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Chapter 4 Change Detection in Multi
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Recall that the original approach i
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4.3.1 Building the multi-dimensiona
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4.3.2 Detecting changes When data f
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Algorithm 2 Mean Change Detection f
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For each stream type, there are a t
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0.0 0.1 0.2 0.3 Num of False Change
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0.00 0.01 0.02 0.03 0.04 0.05 0.06
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0.00 0.05 0.10 0.15 0.20 0.25 SD of
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0.00 0.02 0.04 0.06 0.08 0.10 Mean
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4.5.2 Performance comparison with o
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0.00 0.02 0.04 0.06 0.08 0.10 Mean
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Note that KD is a generic approach
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items is too large for memory-inten
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time t and a set of items I = {a, b
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than three) [163]. When the sizes o
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according to certain criteria (Sect
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When the end of WM is reached, it t
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Similarly, if one infrequent item r
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the new frequent itemset with all c
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Step 2.5. No new frequent itemset d
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Updating candidate support For any
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Algorithm 5 UPDATE CANDIDATE SUP 1:
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esult at time t1 may not be consist
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The sizes of the tumbling windows u
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Table 5.2: Results for varying ν v
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Table 5.5: Results for varying λ o
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5.5.5 Memory usage The major memory
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5.6 Summary Mining frequent itemset
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Two techniques are proposed in this
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change detection and mining process
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Bibliography [1] G. Abdulla, T. Cri
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[19] S. Chandrasekaran and M. Frank
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[39] F. David. The moments of the z
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[60] X. Gu, S. Papadimitriou, S. Yu
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[81] J. Kramer and B. Seeger. Seman
Page 309 and 310:
[102] B. Park et al. Reservoir-base
Page 311 and 312:
[124] T. Dasu et al. An information
Page 313 and 314:
[144] W. Shewhart. Statistical Meth
Page 315:
[166] J. Yu, Z. Chong, H. Lu, and A
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