1. Clustering using Wavelets and Meta-Ptrees Anne Denton, Fang Zhang

2. What do we want to do? Clustering huge amount of spatial data accumulated from satellite images, GIS system,etc. Compare methods between Wavelets Trans. and Meta-Ptree, try to mix them up. Try to find a efficient method to do clustering on accuracy.

3. What is a good clustering method? Ability to identify clusters of arbitrary shapes nested within one another have holes, etc Good time efficiency High quality on accuracy

4. Why do we use wavelet? Insensitive to the ordering of input data Do not make any assumption about the number of clusters present Ability to classify or cluster objects at a different level of accuracy Handling noise and outliers

5. Special characteristics (1) It is a high dimensional basis for some high dimensional data. For 2-dimension, if the wavelet set is given by for indices of a linear expansion would be for some set of coefficients

6. Special characteristics (2) Most of the energy of the data is well represented by a few expansion coefficients, ( The set of expansion coefficients are called the discrete wavelet transform ) Wavelet transforms operations increase linearly with the length of the data. The clustering of the coefficients from the data can be done efficiently.

7. The data I got

8. Steps Data from Ag maps Clustering the data by DWT coefficients Mix with Meta-Ptree Calculate the sum of each cluster Visualization

9. Are Wavelets and P-trees related? Both operate on multiple scales Same quadrant-based structure Same problems with quadrant boundaries (i.e., if wavelets work so do P-trees!) Technical similarity Moving averages of Haar Wavelets can be efficiently computed from P-trees

10. So are P-trees and Wavelets the same thing? Wavelets are transformations in an orthogonal space P-tree are not and should not be that: “Signal” approach cannot cover all data mining issues P-trees naturally represent concept hierarchies P-trees keep count information directly

11. Can we use P-trees for Clustering just as Wavelets? P-trees defined in structure space Clustering is done in attribute space (Wavelet clustering has same problem!) P-trees in attribute space? Counts other than 0 and 1 at leaf level Store results of anding of basic P-trees

12. What will Meta P-trees look like? Design decisions Break up into count bit planes?  Counts as attributes (special normalization) Keep one big Meta P-tree? Plan Compare approaches in practice

13. Potential for Meta P-trees Attribute space central to data mining Attribute space is huge, but sparse (maximum one point per data item)  Compression essential Mixed quadrants similar to detail coefficients for wavelets Naturally suggests a variant of density- based clustering