I have a hyperspectral image where the pixels are 21 channels. So each pixel $\in \mathbb{R}^{21}$. I want to perform clustering on the pixels with similarity defined by two different measures, one how close the pixels are, and the other how similar the pixel values are.
Thus if $X_1$ and $X_2$ are the locations of pixels $p_1$ and $p_2$ I have: $$S_X = \|X_1-X_2\|^2_2$$ and $$S_p = \|p_1-p_2\|^2_2$$.
I have seen these measures combined into a single measure like this: $$ S= e^{-\frac{S_p}{\sigma^2_p}} \times \,\, e^{-\frac{S_X}{\sigma^2_X}} $$
My question: Is there a right way and a wrong way to combine measures like this, or if it improves my clustering can I combine the measures in any way that suits me?
My question is vaguely related to Combining multiple similarity measures.