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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:
(3) where: