Computation and Sparsity

To form an estimation of the kernel density using Parzen Windows, 8 (or 7) must be evaluated for all $n$ random samples. The sum in 8 (or 7) is another $n$ evaluations of the window function, which in itself is a function of $d$ the number of dimensions. In subsequent sections on support vector density estimation, an equally robust estimate involving considerably less computation will be considered.

Figure 6: Kernel Bandwidth Selection [Ihl03]: Three bandwitdh selection methods are compared: the entropy and bandwidth of each are: ROT (0.1037, 0.0761), LCV (0.0439, 0.0215), HALL(0.0491, 0.0268). Notice the positive correlation between the entropy and the bandwidth; intuitively as the bandwidth increases the kernel density estimate gets smoother and closer to a uniform distribution which has the maximal entropy.