p8h17jtvcuo.tex

\[ H(A) = -\int_\mathbb{{S}^n}  \hat{f}_h(x)\log  \hat{f}_h(x) \,dx  \]



where $dx$ is the \href{https://en.wikipedia.org/wiki/Spherical_measure}{spherical measure} on $\mathbb{{S}^n}$. We need an embedding into the unit sphere because there is no probability measure on the chemical space.

Note that this entropy depends on the choices of the bandwidth $h$ and of the embedding.