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P(x) = k/(NV)  
 
P(x) = k/(NV)  
  
where, k is the number of samples in V.
+
where, k is the number of samples in V, N is the total number of samples, and V is the volume surrounding x.
    , N is the total number of samples.
+
    , V is the volume surrounding x.
+
  
 
This estimate is computed by two approaches
 
This estimate is computed by two approaches
  
 
1) Parzen window approach
 
1) Parzen window approach
; Fixing the volume V and determining the number k of data points inside V
+
  - Fixing the volume V and determining the number k of data points inside V
  
 
2) KNN(K-Nearest Neighbor)
 
2) KNN(K-Nearest Neighbor)
  ;Fixing the value of k and determining the minimum volume V that encompasses k points in the dataset
+
  - Fixing the value of k and determining the minimum volume V that encompasses k points in the dataset
  
  

Revision as of 22:21, 7 April 2008

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

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