Abstract: Kernel density estimation provides solid foundation for density based clustering algorithm construction While binned approximation is shown to be an efficient mechanism for fast kernel density computation, it is also proven to be a promising approach to construct robust clustering algorithms This paper deals with formation and accuracy of the binned kernel density estimators, presents mean squared error bounds for the closeness of such estimators to the unbinned kernel density estimators To improve the accuracy of the binning method, a nave grid level approximated density estimator is constructed, followed by a detailed proof of its mean squared error bounds The improved approach constructs binned density estimator by substituting the center of a grid with the gravity center of the data points, which results in better estimation accuracy without loss of computation efficiency As a main concern, the close relation between the density based clustering algorithms and the kernel estimation methods is revealed