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Chaotic Mining: Knowledge Discovery Using the Fractal Dimension. Daniel Barbara George Mason University Information and Software Engineering Department [email protected] By Dhruva Gopal. Fractals. What are fractals Property of a fractal Self Similarity. Uses of fractals.

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Chaotic mining knowledge discovery using the fractal dimension l.jpg

Chaotic Mining: Knowledge Discovery Using the Fractal Dimension

Daniel Barbara

George Mason University

Information and Software Engineering Department

[email protected]

By

Dhruva Gopal


Fractals l.jpg
Fractals

  • What are fractals

  • Property of a fractal

    • Self Similarity


Uses of fractals l.jpg
Uses of fractals

  • Geologic activity

  • Planetary orbits

  • Weather

  • Fluid flow

  • databases


Fractal dimensions l.jpg
Fractal Dimensions

  • Number of possible dimensions?

  • Fractal dimension computation

    • Dq = 1/(q-1)*(logSipiq)/(log r)

      • Hausdorff dimension

      • Information dimension

      • Correlation dimension


Examples l.jpg
Examples

  • Event Anomalies in time series

  • Self similarity in association rules

  • Analyzing patterns in datacubes

  • Incremental clustering


Event anomalies l.jpg
Event Anomalies

  • Time series

    • Stock price changes

    • TCP connection occurrence

  • Example

    • Half open TCP connections

    • Network Spoofing


Methodology l.jpg
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


Self similarity in association rules l.jpg
Self Similarity in Association Rules

  • Parameters associated with a rule

    • Support

    • Confidence

  • Distribution of these transactions???

    • Seasonal

    • Promotional

    • Regular


Fractals in association rules l.jpg
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 k+1th itemset


Analyzing patterns in datacubes l.jpg
Analyzing Patterns in datacubes

  • Patterns

    • Null cells (no aggregate)

  • Compute fractal dimension of null cells

  • Drastic changes imply anomalous trends


Incremental clustering l.jpg
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


Conclusions l.jpg
Conclusions

  • Fractals are powerful parameters used to uncover anomalous patterns in the databases

  • Paper discusses techniques that can be used, but none are implemented.


References l.jpg
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/similar/similar.html

  • http://tqd.advanced.org/3288/julia.html

  • http://www.tsi.enst.fr/~marquez/FRACTALS/fdim/node7.html

  • http://www.physics.unlv.edu/~thanki/thesis/node14.html


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