Change to Kernel Smoother

Introduction

I recently changed a whole load of the functions in the ssci JavaScript library. One of these changes was the way that the kernel smoothing function worked.

The previous function was fairly slow and didn’t scale particularly well. In fact, the main loop of the function would suggest that it scales as O(n^2).

I therefore decided to make a change to the function. Instead of looping over every point and then calculating the weight at every other point, I’ve changed it so that:

• It loops through every point similarly to the previous function
• Then for point n it calculates the weight at the central point (i.e. point n)
• It then loops through every point lower (in the array) than n and calculates the weight. If the weight of this point is lower than a certain threshold to the central point, then the loop ends.
• It then loops through every point higher (in the array) than n and calculates the weight. If the weight of this point is lower than a certain threshold to the central point, then the loop ends.

The default setting of the threshold is 0.001 (i.e. 0.1%). The way the function operates though does mean two assumptions have been made.

• The data has already been ordered in the x-coordinate within the array.
• The kernel function being used must always decrease from the central point beyond this threshold.

The rest of this entry can be read on my new blog...