Mining Multiple Data Streams

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Mining Multiple Data Streams

• Ahmet Bulut
• Department of Computer Science
• University of California, Santa Barbara

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Stock Market

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Trend Related Analysis, You would like to...

• identify the stocks that move in a similar trend.
  
• find the stocks that move similar to your stock
• know aggregates related to your stock
• AVG closing price in time interval (t1,t1?)
• NUM days where daily_volumegt threshold

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Single Stream

• Find a method to keep statistics of a stream,
  that is
• space efficient Storing the stream in memory is
  a no-no
• run-time efficient Incremental, low update cost
• adaptive Dynamically adapting to changing
  conditions

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Summarization using Wavelet based Approximation
Tree
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Is it a method that we are looking for?

• space efficient For a stream of size O(N), it
  keeps O(log N) summaries (approximations)
• run-time efficient For each incoming data, the
  amortized update cost is O(1)
• adaptive We can change the number of summaries
  at each level, increase the resolution

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Multiple Streams

• Keep a summary structure for each of the streams
• You can answer trend-related questions by
  examining these structures
• However, a way to query the summaries ,
  irrelevant of the individual streams is useful

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Stardust (R a DUet with STreams)
S3
S2
S1
Level 3
Level 2
Level 1
Level 0
R-tree 0
R-tree 1
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Is this a method? ?

• space-efficient Underlying structure is space
  efficient
• run-time efficient M Streams, O(M) R Insertion
• adaptiveWe can change the lowest level to start
  keeping summaries

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Competing Technique

• Similarity Search in Sequence Databases Agrawal
  et al. 1993
• Fast Subsequence Matching Faloutsos et al. 1994
  
• We keep a single index structure for all the
  streams
• When (a new value arrives)
• Apply DFT on the window covering new value.
• Keep only a few of the coefficients
• Trail on the reduced dimensional space
• Put a fixed number of points in a box I-fixed
• Use marginal cost for inclusion in a box
  I-adaptive

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Range Queries (radius ?)

• Search(radius)
• Apply DFT, keep a few of the coefficients
• Do range query with radius ?
• Post Process
• Prefix Search
• Queries longer than window
• Extract the prefix of window size
• Search(?)
• Multi-piece Search
• Queries multiple of window, say k
• Extract k window size portions
• Search(?/?k))

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Search in Stardust

• Prefix Search has the same flavor
• Multi-piece Search

?/?2
?/2
?/2?2
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Experimental Results
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Experimental Results contd
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Future Work

• Find correlations between streams
• Thank the audience!

• Take a vacation...