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The non-parametric density estimation is
 
  
P(x) = k/(NV)
 
 
where, k is the number of samples in V, N is the total number of samples, and V is the volume surrounding x.
 
 
This estimate is computed by two approaches
 
 
1) Parzen window approach
 
  - Fixing the volume V and determining the number k of data points inside V
 
 
2) KNN(K-Nearest Neighbor)
 
- Fixing the value of k and determining the minimum volume V that encompasses k points in the dataset
 
 
 
* The advantages of non-parametric techniques
 
- No assumption about the distribution required ahead of time
 
- With enough samples we can converge to an target density
 
 
* The disadvantages of non-parametric techniques
 
- If we have a good classification, the number of required samples may be very large
 
- Computationally expensive
 

Revision as of 22:24, 7 April 2008

Alumni Liaison

Ph.D. on Applied Mathematics in Aug 2007. Involved on applications of image super-resolution to electron microscopy

Francisco Blanco-Silva