2. Chaotic Mining: Knowledge Discovery Using the Fractal Dimension Daniel Barbara George Mason University Information and Software Engineering Department dbarbara@gmu.edu By Dhruva Gopal

3. Fractals  What are fractals  Property of a fractal  Self Similarity

5. Uses of fractals  Geologic activity  Planetary orbits  Weather  Fluid flow  databases

6. Fractal Dimensions  Number of possible dimensions?  Fractal dimension computation  D q = 1/(q-1)*(log  i p i q )/(log r)  Hausdorff dimension  Information dimension  Correlation dimension

7. Examples  Event Anomalies in time series  Self similarity in association rules  Analyzing patterns in datacubes  Incremental clustering

8. Event Anomalies  Time series  Stock price changes  TCP connection occurrence  Example  Half open TCP connections  Network Spoofing

9. Methodology  Half open connections are self similar  Collect data points every  seconds  Moving window of k *  (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

10. Self Similarity in Association Rules  Parameters associated with a rule  Support  Confidence  Distribution of these transactions???  Seasonal  Promotional  Regular

11. 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

12. Analyzing Patterns in datacubes  Patterns  Null cells (no aggregate)  Compute fractal dimension of null cells  Drastic changes imply anomalous trends

13. 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

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

15. 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://tori.postech.ac.kr/softwares/  http://www.math.umass.edu/~mconnors/fractal/similar/similar.html http://www.math.umass.edu/~mconnors/fractal/similar/similar.html  http://tqd.advanced.org/3288/julia.html http://tqd.advanced.org/3288/julia.html  http://www.tsi.enst.fr/~marquez/FRACTALS/fdim/node7.html http://www.tsi.enst.fr/~marquez/FRACTALS/fdim/node7.html  http://www.physics.unlv.edu/~thanki/thesis/node14.html http://www.physics.unlv.edu/~thanki/thesis/node14.html