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Top2. Mean-Shift Method
Given the 
samples 
, 
=1, 
, 
, in the d-dimensional space Rd, then the Mean-shift vector at the 
is defined that:
(1)
is a district of high-dimensional spheroid with radius 
, and satisfies the following relation of 
in order of gather:
(2)
is the number of points in the 
samples 
, which falls into the 
district. (
- 
) is the deviation vector of the sample 
. The Mean Shift vector 
which is defined in Equation (1) is the average value of the deviation vectors of the 
samples which fall into the 
district opposite the 
point. If the sample 
is got from the sample of the probability density function 
, non-zero probability density gradient points to the direction at which the probability density increases most. On average, the samples in the 
district mostly fall at along the direction of probability density gradient, therefore the corresponding Mean-shift vector 
points to the direction of the probability density gradient (Comaniciu & Meer, 2002). From Equation (1), as long as it is the sample which falls into 
district, the contribution to 
calculation is all similar no matter its distance from 
, however, the sample which is near the 
is more effective to the statistics characteristic that estimates 
surroundings, therefore the concept of kernel function is introduced. As important values of all samples 
are different, therefore a weighted coefficient is used for each sample. So the expand basic form of Mean-shift is:
where: