Discovering partial periodic pattern on discrete spatiotemporal data

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Discovering partial periodic pattern on discrete
spatio-temporal data

• Huiping Cao
• Sep. 26, 2003

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Outline

• Background
• Problem definition
• Solution
• Experiments
• Future work
• References

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Background

• More spatio-temporal data are generated with the
  development of moving computing equipments
• Most provided methods support queries on such
  kind of data efficiently by making use of index
• We are trying to find some periodic patterns from
  the data to facilitate the queries (3same
  motivation).

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Related Work

• Partial period patterns discovered from
  spatio-temporal data refer to those location
  series that appear periodically and frequently.
• Existing works on periodic pattern mining
• Either assume that the periods are given in
  advance by the user
• Or could not efficiently find the periods
  automatically

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Pre-handling of data

• Continuous spatio-temporal data sequence is
  converted to discrete symbol data sequence
• Discrete data is defined in advance. E.g., some
  district name in the real world.
• (x,y) sequence (20,20),(21, 20) (21,21)
• Discrete symbol sequence A A B
• Where A and B are predefined by the user

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Problem definition

• Given discrete value sequence S D1, D2, ...,
  Dn where sampling rate is fixed.
• Partial pattern s s1 ... sp . Here, si is
  defined over (2L-??) where L is the
  underlying set of features and refers to the
  dont care character.

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Problem definition

• s pattern length
• L-length of s number of si which contains
  letters from L.
• Sub-pattern of a pattern s a pattern s s1
  ... sp such that si si and si ?si for
  every position i where si ?.
• E.g. s aa,cde
• s5,
• L-length is 4(also called 4-pattern)
• aa,c and cde are all its sub-patterns

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Problem definition

• A patterns s s1 ... sp is true in some period
  segment if
• for each position i, either si is or all the
  letters in si occur in the ith set of the
  features in the segment.
• E.g., Pattern ab is true in segment acb, but
  not true in bcb
• frequency_count(s) in sequence SD1, D2, ..., Dn
• frequency_count(s) i0?iltm, and string s is
  true in Dis1, Diss, ..., Diss.

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Problem definition

• support(s) frequency_count(s)/m
• m maximum number of periods of length s
  contained in the sequence.(ms? nlt(m1)s).
• E.g. In ab,cbaebaced, freq_count(ab) 2,
  sup(ab) 2/3
• frequent partial periodic pattern s
• sup(s) ? min_conf, which is a user specified
  threshold

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Problem definition

• Input
• A discrete data sequence, S
• min_support , min_sup
• Time window, w
• Goal
• Find the periods automatically in window w
• Discover all the frequent patterns for one period
  or some periods

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Solution

• Step1
• scans the sequence and constructs a memory based
  structure, abbreviated list table, to find the
  potential periods.
• Create disk-based inverted lists for the typical
  data points in the sequence
• Step2
• Find all the frequent patterns taking advantage
  of the disk-based inverted lists gotten from the
  first step and the max sub-pattern tree

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Step 1

• Abbreviated list table
• For each value v and each possible period p(1?p ?
  w), count the occurrences of v at position 0, 1,
  ..., p-1
• Example.

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Example

• E.g.
• SABAAACCAAE
• min_sup 0.8
• w5

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Example(cont.)

• Possible periods
• 2,4,5
• F1
• p2 A
• p4 A, A
• p5 A, A

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Analysis on step1

• Time complexity O(n)
• where n is the sequence length
• Space O(Dw2)
• Space Dw(w1)/2
• D domain size
• w window
• Suppose w 1000, w2 is about 1M
• absolute value is acceptable

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Analysis on step1(cont.)

• Compare with the circular autocorrelation method
• generate F1 in the same time
• n could be unknown in advance
• avoid generating useless period
• e.g.
• S AAAAA ( dont care), min_sup0.8
• bitmap of A 1010100110
• f(0).f(4) ? (1010100110).(0110101010) ?
• 3 gt 210/40.8 frequent
• However, p4 is not frequent

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Step 2

• Construct max sub-pattern tree by scanning the
  disk-based inverted list
• access disk with less cost
• E.g.,
• Domain A,B,C,D,E,F,G,H
• The symbols that appear in F1 are A and C
• Just need scan the inverted list of A and C but
  neednt access other symbols
• Traverse max sub-pattern tree to get frequent
  ones

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Step2(cont.)
1
abd
a
d
b
1
0
1
ab
bd
ad

• F1 a, b, d
• s tbydi abbdd abccc
• sup(abd)1
• sup(bd) 11 2
• sup(ad) 01 1
• sup(ab) 11 2

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Analysis

• Advantages
• Find periods efficiently(Experiments) compared
  with the circular autocorrelation method
• Mine frequent patterns more efficiently(Experiment
  s)
• Disadvantage
• Inverted list uses the same space as the sequence

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Experiments

• data24192 data points
• min_sup0.7
• Varying window

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Experiments(cont.)

• window24
• min_sup0.7
• Varying data volume

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Experiments(cont.)

• data24192 data points
• window 48
• Varying min_sup

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Experiments(cont.)

• window24
• min_sup0.7
• Varying data volume

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Experiments(cont.)

• data 67200 data points
• min_sup0.7
• Varying window

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Experiments(cont.)

• data 67200 data points
• window48
• Varying min_sup

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Future work

• Finding new kind of patterns
• How to store patterns more efficiently
• How to facilitate queries when using patterns

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References

• J. Han, G. Dong, Y. Yin. Efficient Mining of
  Partial Periodic Patterns in Time Series
  Database. In ICDE99.
• C.Berberidis, I. Vlahavas, W. G. Aref. etc. On
  the Discovery of Weak Periodicities in Large Time
  Series. In PKDD02.
• L.H. Yang, M. L. Lee, W. Hsu. Efficient Mining of
  XML Query Patterns for Caching. In VLDB04.

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Suggestions Questions