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List of Symbols ∆ size of window in terms of time ɛ1, ɛ2 stopping rule thresholds UCL, LCL upper and lower control limit of control chart C κ distance of control limits from center line Λ weight matrix λ threshold for calculating frequent itemset candidates µ(S) mean value of S ν threshold for calculating the support of frequent itemsets ρ probability that a T 2 control chart has chi-square distribution σ(S) standard deviation of S τ significance level ω weight for calculating moving mean and standard deviation frequent itemset Ai A complete set of frequent itemsets in S AC cover set of A ASC smallest cover set of A Acc(Ri) the accuracy of the mining result Ri C control chart C candidate list for frequent itemsets mining d number of dimensions in multi-dimensional streams Gi partitions of a distribution gS i , gE i start and end point of partition Gi h bandwidth parameter for kernel density estimation H0 Null hypnosis that asserts distribution does not change Alternative hypnosis that asserts distribution has changed H1 xxi
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 and 14: 3.62 Max duration for detecting tru
Page 15 and 16: 3.96 Mean duration for detecting tr
Page 17 and 18: 3.129Number of true changes detecte
Page 19: List of Tables 3.1 Stream types gen
Page 23 and 24: Chapter 1 Introduction 1.1 Data str
Page 25 and 26: 4. Integrate stored and streaming D
Page 27 and 28: 1.1.4 Distribution changes in data
Page 29 and 30: the email sender/receiver locations
Page 31 and 32: changing data streams. These charac
Page 33 and 34: Unlike data mining algorithms that
Page 35 and 36: to be fine-tuned to improve perform
Page 37 and 38: a large amount of sample data to ac
Page 39: • A novel technique for mining fr
Page 42 and 43: 2.1 The data stream model 2.1.1 Dat
Page 44 and 45: Many window models have been propos
Page 46 and 47: S t t 1 t 2 Fixed window Landmark w
Page 48 and 49: over dynamic streams must find a
Page 50 and 51: and dropping more elements can spee
Page 52 and 53: Aggarwal et al. proposed a framewor
Page 54 and 55: pattern or a base time series with
Page 57 and 58: Chapter 3 Distribution Change Detec
Page 59 and 60: tures. Based on this insight, a con
Page 61 and 62: change occurs to the time it is det
Page 63 and 64: would greatly reduce the efficiency
Page 65 and 66: (a) (b) (c) S t 1 Timestamp last di
Page 67 and 68: 3.2, the accuracy of this estimatio
Page 69 and 70: substream S ′ r in the updated re
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The location or scale (depends on t
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to store the representative data se
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changes mChg may not be the same as
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stream speed is stable. However, no
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Figure 3.4: Number of true changes
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Figure 3.6: Number of false changes
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Figure 3.8: Number of false changes
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Figure 3.10: Mean duration for dete
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Figure 3.12: Standard deviation of
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Figure 3.14: Standard deviation of
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0.000 0.005 0.010 0.015 0.020 0.025
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The experimental results demonstrat
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0.00 0.02 0.04 0.06 0.08 0.10 0.12
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Figure 3.21: Number of false change
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Figure 3.23: Number of false change
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Figure 3.25: Mean duration for dete
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0.00 0.05 0.10 0.15 Stream 8 − Un
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0.000 0.005 0.010 0.015 Stream 12
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0e+00 2e−04 4e−04 6e−04 8e−
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The results of the second set of ex
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0.00 0.02 0.04 0.06 0.08 0.10 0.12
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0.00 0.05 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 0.05
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0.000 0.002 0.004 0.006 0.008 0.010
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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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Since moving window method continuo
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0.00 0.05 0.10 0.15 0.20 0.00 0.05
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0.00 0.05 0.10 0.15 0.00 0.01 0.02
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0.0 0.1 0.2 0.3 0.4 0.0 0.1 0.2 0.3
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0.0 0.1 0.2 0.3 0.4 0.00 0.05 0.10
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0.00 0.05 0.10 0.15 0.20 0.00 0.02
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0.00 0.05 0.10 0.15 0.20 0.00 0.05
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0.00 0.05 0.10 0.15 0.00 0.01 0.02
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0.0 0.1 0.2 0.3 0.4 0.0 0.1 0.2 0.3
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0.00 0.05 0.10 0.15 0.00 0.05 0.10
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0.00 0.05 0.10 0.15 0.000 0.005 0.0
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0.000 0.002 0.004 0.006 0.008 0.010
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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 0.01
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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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0.000 0.002 0.004 0.006 0.008 0.000
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Note that in DMM the procedures of
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Let Acc(Ri) be the accuracy of the
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3.4 Detecting mean and standard dev
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22 20 18 16 14 12 10 8 6 4 2 1 7 13
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Significance level τ is the minimu
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where τ is the significance level,
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Algorithm 1 Mean and Standard Devia
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0.00 0.02 0.04 0.06 0.08 0.10 0.12
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0.00 0.05 0.10 0.15 Stream 5 − Mi
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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 0.00 0.01
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0.00 0.02 0.04 0.06 0.08 0.10 Strea
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0.00 0.02 0.04 0.06 0.08 0.10 Contr
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0.00 0.01 0.02 0.03 0.04 0.00 0.05
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0.00 0.01 0.02 0.03 0.04 0.05 Strea
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0.00 0.01 0.02 0.03 0.04 0.05 0.06
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0.000 0.005 0.010 0.015 0.00 0.05 0
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0.000 0.005 0.010 0.015 0.020 Strea
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0.000 0.005 0.010 0.015 Control Cha
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0.0000 0.0004 0.0008 0.0012 0.00 0.
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0.0000 0.0005 0.0010 0.0015 Stream
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0.0000 0.0005 0.0010 0.0015 Control
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These results reveal that the propo
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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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Similar conclusions as the previous
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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 0.000 0.001 0.0
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These results suggest that, increas
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0.00 0.02 0.04 0.06 0.08 0.00 0.02
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0.000 0.010 0.020 0.030 0.000 0.004
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3.5 Summary The unboundedness and h
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to take more than one attribute int
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probability distributions. However,
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weight variables on each dimension
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ta = t0. Null hypothesis H0 (i.e.,
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element Xj = (x1, x2, ..., xd) ∈
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into three sets. The first set cont
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0.00 0.02 0.04 0.06 0.08 0.10 0.12
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0.0 0.5 1.0 1.5 2.0 Num of False Ch
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0.00 0.05 0.10 0.15 Num of True Cha
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0.000 0.001 0.002 0.003 0.004 Max o
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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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Chapter 5 Mining Frequent Itemsets
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prediction window. All current freq
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the problem of mining the complete
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this approach cannot detect distrib
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A time-based tumbling window WM, ca
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• A counter for each itemset that
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e discarded from the candidate list
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Step 5.1. ∀Ak = {r} ∪ Ai, where
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• Step 1. Let A SC = φ. Build a
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Algorithm 4 MAINTAIN CANDIDATES 1:
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transactions that are missed in cou
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5.5 Experiments To evaluate TWIM’
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as existing algorithms on streams w
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Table 5.4: Mining results over S6 c
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Varying window sizes To evaluate th
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Table 5.11: Maximum counters when |
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Chapter 6 Conclusions Many of today
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ecause of these correlations. Very
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itemsets, then a polynomial algorit
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[9] F. Aparisi and J. Garcia-Diaz.
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[29] J. Cheng, Y. Ke, and W. Ng. Ma
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[49] W. Fan, Y. Huang, and P. Yu. D
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[70] A. Hyvarinen. Survey on indepe
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[92] A. Manjhi, S. Nath, and P. Gib
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[113] M. Gertz et al. A data and qu
Page 312 and 313:
[134] M. Pelikan. Hierarchical baye
Page 314 and 315:
[156] A. Wald. Sequential Analysis.
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