Module 7:Data Representation
  Lecture 35: Wavelets
 

                                            

 

 

Dimensionality reduction using Haar wavelets
  • Retain sum and lower level detail coefficients
  • For example, retain 1 sum (at level 0) and 3 detail (1 at level 0 and 2 at level 1) coefficients
  • Contractive
  • Alternatively, for a database of objects, retain those coefficients whose variances are highest
  • Another option is to zero out coefficients whose absolute values are below a threshold
  • What happens when dimensionality is not a power of 2?
 
  • Pad zeros at end: latter half becomes less important
 
  • Pad equal amount of zeros in each half: should be done recursively