Chaotic Mining: Knowledge Discovery Using the Fractal Dimension

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Chaotic Mining Knowledge Discovery Using the
Fractal Dimension

• Daniel Barbara
• George Mason University
• Information and Software Engineering Department
• dbarbara_at_gmu.edu
• By
• Dhruva Gopal

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Fractals

• What are fractals
• Property of a fractal
• Self Similarity

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Uses of fractals

• Geologic activity
• Planetary orbits
• Weather
• Fluid flow
• databases

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Fractal Dimensions

• Number of possible dimensions?
• Fractal dimension computation
• Dq 1/(q-1)(logSi piq)/(log r)
• Hausdorff dimension
• Information dimension
• Correlation dimension

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Examples

• Event Anomalies in time series
• Self similarity in association rules
• Analyzing patterns in datacubes
• Incremental clustering

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Event Anomalies

• Time series
• Stock price changes
• TCP connection occurrence
• Example
• Half open TCP connections
• Network Spoofing

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Methodology

• Half open connections are self similar
• Collect data points every d seconds
• Moving window of k d (k is an integer)
• Fractal dimension will show a drastic decrease in
  case of spoofing
• Other applications of fractals with time series
• Password port in FTP service

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Self Similarity in Association Rules

• Parameters associated with a rule
• Support
• Confidence
• Distribution of these transactions???
• Seasonal
• Promotional
• Regular

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Fractals in Association rules

• Compute Fractal dimension of a k-itemset while
  computing its support
• Information about the fractal dimension should be
  kept for use when computing k1th itemset

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Analyzing Patterns in datacubes

• Patterns
• Null cells (no aggregate)
• Compute fractal dimension of null cells
• Drastic changes imply anomalous trends

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Incremental Clustering

• Clustering algorithms are needed to deal with
  large datasets
• Extended K means algorithm
• Use a variation of extended K means algorithm
  using fractal dimensions for deciding point
  membership

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Conclusions

• Fractals are powerful parameters used to uncover
  anomalous patterns in the databases
• Paper discusses techniques that can be used, but
  none are implemented.

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References

• Fast Discovery of Association rules,R. Agrawal,
  H. Mannila, R. Srikant, H. Toivonen, A.I. Verkamo
• John Sarraille and P. DiFalco, FD3,
  http//tori.postech.ac.kr/softwares/
• http//www.math.umass.edu/mconnors/fractal/simila
  r/similar.html
• http//tqd.advanced.org/3288/julia.html
• http//www.tsi.enst.fr/marquez/FRACTALS/fdim/node
  7.html
• http//www.physics.unlv.edu/thanki/thesis/node14.
  html

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