General Coefficient of Similarity

I've recently read an interested paper published in 1971 [1] that presents a really well organized discussion on what it means to measure the similarity between two objects (or individuals), and how to deal with missing information and dichotomous features.

Let $s_{ij}^{(k)}$ be the similarity between two objects $i$ and $j$ according to their $k$-th feature. Also let $\delta_{ij}^{(k)} \in \{0,1\}$ indicate whether feature $k$ of $i$ and $j$ can be compared ($\delta_{ij}^{(k)}=1$) or not ($\delta_{ij}^{(k)}=0$). For example, when $i$ and/or $j$ are missing feature $k$, then $\delta_{ij}^{(k)} = 0$. Accordingly, the overall similarity $S_{ij}$ between $i$ and $j$ can be written as
$$S_{ij} = \frac{ \sum_k w(x_i^{(k)},x_j^{(k)}) s_{ij}^{(k)} }{ \sum_k w(x_i^{(k)},x_j^{(k)}) \delta_{ij}^{(k)} }$$
where $x_i^{(k)}$ and $x_j^{(k)}$ are the values for the $k$-th feature of $i$ and $j$, respectively, and the $w(x_i^{(k)},x_j^{(k)})$ are the weights assigned to the different features. Interestingly, the weights are expressed as a function of the feature values, rather than being constant. This allows for elegantly dealing with hierarchical features, among other things (see [1], Section 4.1).

[1] J. C. Gower. "A General Coefficient of Similarity and Some of Its Properties." Biometrics, Vol. 27, No. 4. (Dec., 1971), pp. 857-871. (http://venus.unive.it/romanaz/modstat_ba/gowdis.pdf)