(27) The non vector case is not mentioned in detail. However, we have the equation ; (28) is the number of points in k th cluster and is the total number of points 3.2 Clustering and K-means If the temperature is very high, the exponent of the equation (26) goes to zero, and all centers have equal probability. In that case, all centers have the position, (29) If the temperature decreases, the points tend to close to a center by stages, and in the zero temperature limit, K-means solution can be found by assigning each point with the nearest center. Figure 1 declares the idea behind the annealing which is that we could not find false minima at high (infinite) temperature where the object function is smooth, and the free energy is minimized. If we decrease the temperature slowly, we close to the minima at lower temperature. Hence, the annealing is robust as long as temperature lowered slow enough. [1] In the figure, temperatures T2 and T3 show that the false minima at finite temperature. Tihs process is being approximated in deterministic annealing. The approximation includes modifying integrals by evaulating functions through their mean values. 3.3 Multiscale ( Hierarchical ) and Continous Clustering
(27) The non vector case is not mentioned in detail. However, we have the equation ; (28) is the number of points in k th cluster and is the total number of points 3.2 Clustering and K-means If the temperature is very high, the exponent of the equation (26) goes to zero, and all centers have equal probability. In that case, all centers have the position, (29) If the temperature decreases, the points tend to close to a center by stages, and in the zero temperature limit, K-means solution can be found by assigning each point with the nearest center. Figure 1 declares the idea behind the annealing which is that we could not find false minima at high (infinite) temperature where the object function is smooth, and the free energy is minimized. If we decrease the temperature slowly, we close to the minima at lower temperature. Hence, the annealing is robust as long as temperature lowered slow enough. [1] In the figure, temperatures T2 and T3 show that the false minima at finite temperature. Tihs process is being approximated in deterministic annealing. The approximation includes modifying integrals by evaulating functions through their mean values. 3.3 Multiscale ( Hierarchical ) and Continous Clustering
Y790-final%20paper.docx