Clustering using Wavelets and Meta-Ptrees

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