Kernel width in Gaussian kernel is sometimes called kernel bandwidth or kernel radius, variance or metric window . Wider kernel bandwidth will span to larger domain. You can imagine kernel width as the width of a window center at the data point and give weighing value to any points located in the window. These weights will be used as local average for all points within that window.
The kernel bandwidth works as smoothing parameter.
If you change the kernel bandwidth into smaller value, for example
, then you need to use
to find the new weights. The initial value matters for the search using MS Solver. The result of smaller bandwidth is rather rough as shown in the figure below
Changing the kernel bandwidth to slightly higher value of , and will make the value smoother but at the cost of stretching the estimated value of y into negative as illustrated in the figures below.
Please take note that these charts above are generated from the same data and the same smoothing function but at different kernel width .