Noise-benefit FRSDE for speedup of density estimation on large data

Fast Reduced set density estimator (FRSDE) is an important technique to realize the fast kernel density estimation based on the fast minimal enclosing ball (MEB) approximation technique. However, its performance on the running time is severely affected by the approximation parameter ε used in this algorithm, where a smaller value will lead to more accurate approximation but heavy learning burden. In this study, we reveal that the random Gaussian white noise manually added to the data will speed up the learning and accordingly propose a speedup version of FRSDE, i.e., the noise-benefit FRSDE (NB-FRSDE). NB-FRSDE can realize such a speedup because a larger value of ε can be used on the noisy version of the original data to obtain the equivalent approximation performance, which only can be obtained by FRSDE on the original data with a smaller value of ε. The distinctive characteristics of NB-FRSDE exist in the following aspects: (1) its implementation is very simple because NB-FRSDE is the same as FRSDE except that there are Gaussian noises manually added to the original data in NB-FRSDE. (2) While most of the existing machine learning methods always try to remove the noise in order to overcome the influence of noise, NB-FRSDE benefits from the manually added noise in the sense of the average running time. The experimental studies on density estimation and its application to image segmentation demonstrate the above advantages.