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where, k is the number of samples in V. | where, k is the number of samples in V. | ||
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N is the total number of samples. | N is the total number of samples. | ||
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V is the volume surrounding x. | V is the volume surrounding x. | ||
Revision as of 21:20, 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.
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
