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Time Series Sequence Matching. Jiaqin Wang CMPS 565. Papers. “ Fast subsequence Matching in time-series database ” Christos Faloutsos, M.Ranganathan Yannis Manolopoulos “ Skyline index for time series data ” Quanzhong Li, Ines Fernando Vega Lopez, Bongki Moon. Types of Time Series sequence.

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Time series sequence matching

Time Series Sequence Matching

Jiaqin Wang

CMPS 565


Papers
Papers

  • “Fast subsequence Matching in time-series database”Christos Faloutsos, M.Ranganathan Yannis Manolopoulos

  • “Skyline index for time series data”Quanzhong Li, Ines Fernando Vega Lopez, Bongki Moon


Types of time series sequence
Types of Time Series sequence

  • Financial, marketing area

    • Stock prices

    • Sales numbers

  • Scientific databases

    • Weather data

    • Environmental data


Categories for time series sequence matching
Categories for time series sequencematching

  • Whole matching

    • data sequences and query sequence have the same length

  • Subsequence matching

    • Query sequence and data sequence have different length


Whole matching
Whole matching

  • Given N sequences with the same length l

  • Use features extraction function to convert sequences into n-dimensional values

    • DFT

    • N-dimensional value (Q1,Q2,…,Qn)

    • Most energy in first few coefficients

      • Keep first few coefficients

      • Reduce dimensions of sequence


Whole matching1
Whole matching

  • Map each sequence as a n-dimensional point into the feature space

    • Only take first 2 coefficients

  • Organize these points into R-tree

    • For index and search in R-tree


Whole matching2
Whole matching

  • New coming query sequence

  • Use DFT convert to feature point

  • Map the query feature point into feature space

  • Find out points whose distance to query point within tolerance e

  • Consider them similar


Some pictures of time series data and dft
Some pictures of time series data and DFT

  • Discrete Fourier Transform (DFT )

  • keep first few (2-3) coefficients

  • The first few coefficients contain most energy of the feature


Feature space
Feature space

  • TS1(0.05,3)

  • TS2(0.01,12)

  • ……


Feature space1
Feature space

  • The distance e < minimum query distance


Subsequence matching
Subsequence matching

  • A collection of N sequences, each one has different length

  • A query Q with tolerance e

  • Find out all sequence Sі(1<i<N), along with the correct offsets k,such that the sequence Sі[k:k+Len(Q)-1] matches the query sequence: D(Q, Sі[k:k+Len(Q)-1] ) <= e


St index
ST-index

  • Assuming the minimum query length w

  • Using a sliding window of size w and place it on the date sequence at every possible offsets of the whole data sequences

  • Extract the features in window at each possible offset and map each feature as a point into feature space


Figure
Figure

  • Sliding window on sequence from offset 0 to Len(S)-w+1

  • The length of window is w


Figure1
Figure

  • Sliding window on sequence from offset 0 to Len(S)-w+1

  • The length of window is w


Figure2
Figure

  • Sliding window on sequence from offset 0 to Len(S)-w+1

  • The length of window is w


Figure3
Figure

  • Sliding window on sequence from offset 0 to Len(S)-w+1

  • The length of window is w


Figure4
Figure

  • Sliding window on sequence from offset 0 to Len(S)-w+1

  • The length of window is w


Result
Result

  • A series of points in the feature space is curve

  • R-tree


Time series sequence matching
MBRs

  • Store points in R-tree is inefficient

  • Divide trial into sub-trials using minimum bounding rectangles (MBRs)


Mbrs in r tree
MBRs in R-tree

  • Combine small MBRs

  • Get the index information


How to insert points into mbrs
How to insert points into MBRs

  • Group the points into MBR with a fixed-number

  • Group the points into MBR with a variable-number


I adaptive method
I-adaptive method

  • One greedy algorithm

  • number of disk access

  • cost function

  • average cost function


Algorithm
Algorithm

  • Assign the first point of the trail in a sub-trail

  • For each successive point

    • If it increases the average cost of current sub-trail

    • Then start another sub-trail

    • Else include this point in current sub-trial


Skyline index for time series data
Skyline index for time series data

  • “Skyline index for time series data”Quanzhong Li, Ines Fernando Vega Lopez, Bongki Moon



Adaptive piecewise constant approximation apca1
Adaptive Piecewise Constant Approximation (APCA)

  • Limitation of APCA

    • Internal overlap in MBRs


Skyline bounding region sbr
Skyline Bounding Region (SBR)

  • SBR

    • N time series data objects of length l

    • Specify 2-dimensional regions by top and bottom skylines


Approximate sbr
Approximate SBR

  • Many approaches

    • Equal-length constant-valued segments

    • Variance-length constant-valued segments

  • ASBR will cover the original SBR


Index approximation sbr
Index Approximation SBR

  • R-Tree based Skyline index

  • Internal node

    • Approximation SBR

    • Pointer to child node

  • Leaf node

    • Pointer to time series data


The end
The End

Thank You